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In this paper, we presented a simple and robust algorithm for QPE using compressed sensing. For the single eigenvalue estimation (i.e., QPE), we rigorously established its Heisenberg-limit scaling in Theorem 2 and numerically demonstrated its performance compared to other state-of-the-art QPE algorithms in Sec. 4. Our ... | Compressed sensing, in essence, is similar to non-adaptive MM-QCELS. Both methods aim to fit the sampled data using a signal ansatz. However, they differ in sampling strategies and optimization objectives. In MM-QCELS, times are sampled from a continuous probability distribution, and the cost function minimizes the tot... | For a Heisenberg-limited QPE algorithm with maximal runtime Tmaxsubscript𝑇T_{\max}italic_T start_POSTSUBSCRIPT roman_max end_POSTSUBSCRIPT, if the size of the time samples needed is 𝒪(polylogTmax)𝒪polysubscript𝑇\mathcal{O}(\mathrm{poly}\log T_{\max})caligraphic_O ( roman_poly roman_log italic_T start_POSTSUBSCRI... | In discrete sampling protocols, would it be possible to shorten the maximal runtime by biased sampling of times? What is the limitation in the discrete scenario? Can we achieve a similar improvement to the Gaussian filter method in [18]? | In our numerical experiments, the test of another sampling (Algorithm 3) is actually unnecessary. Is it possible to show this analytically as well? | C |
The same strategy is used to compute density_matrixT(v)subscriptdensity_matrix𝑇𝑣\texttt{density\_matrix}_{T}\left(v\right)density_matrix start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT ( italic_v ). | We compare the asymptotic computational costs of the density matrix algorithm and the baseline algorithm that utilizes canonicalization, as discussed in Section 3.2.1. In Theorem 6.1, we establish that the density matrix algorithm can be more efficient in approximating a general tensor network as an embedding tree. The... | We will show in Section 6.4 that the cost of the density matrix algorithm is upper-bounded by the canonicalization-based algorithm. | In Algorithm 4, the computation of each density matrix occurs only once. Considering that the embedding tree T𝑇Titalic_T is limited to being a rooted binary tree, there are at most three density matrices to be calculated for each vertex v𝑣vitalic_v in the embedding tree. Below we bound the asymptotic computational co... | Specifically, we show in Section 6.4 that the asymptotic computational cost of the algorithm is upper-bounded by the cost of the canonicalization-based algorithm, and we show in Section 8 that for many input tensor networks, the proposed algorithm substantially reduces the overall execution time. | C |
Fig. 7 examines the effects of the parameter cOsubscript𝑐Oc_{\rm O}italic_c start_POSTSUBSCRIPT roman_O end_POSTSUBSCRIPT on the time-domain profiles. Here, for small values of time t𝑡titalic_t, both scalar and electromagnetic perturbations exhibit very similar profiles, with minimal differences in their oscillation ... | The analysis of the perturbation potential provides valuable insights into the nature of the QNMs for both scalar and electromagnetic perturbations. The variations in the potential with respect to parameters such as the multipole moment l𝑙litalic_l, the model parameter α𝛼\alphaitalic_α, the coupling parameter cOsubsc... | The charge parameter Q𝑄Qitalic_Q has a significant and nonlinear impact on the QNM spectrum of black holes. As shown in Figs. 13 and 14, both the oscillation frequency (real part of QNMs) and the damping rate (imaginary part of QNMs) increase as Q𝑄Qitalic_Q increases. This behavior holds true for both scalar and elec... | Finally, in Fig. 8, the time-domain profiles are plotted with varying values of the charge parameter Q𝑄Qitalic_Q. The results indicate that the black hole charge has a noticeable effect on the oscillation frequency for both scalar and electromagnetic perturbations. As Q𝑄Qitalic_Q increases, the oscillation frequencie... | Physically, the increase in oscillation frequency with higher Q𝑄Qitalic_Q can be understood in the context of the black hole’s enhanced electric field. As the black hole’s charge increases, the strength of its electromagnetic field grows, which leads to more tightly bound perturbations. This results in higher frequenc... | C |
In addition, a number of potential improvement may be anticipated. The usage of permutations on the residual indices in step (vi) in Subsection II.3 is a posterior collection. It may be feasible to be performed as a prior with the step (iiid) of using linear combinations of excitation operators. That would lead to a si... | In the present work, we reported the further formulations for the linear combinations of the projection manifolds, the hash-table canonicalization algorithm, and the numerical results for the previous general-order open-shell CC method based on the PSA scheme wang2024general . The energy differences between the present... | We further notice the differences between PSA and spin-orbital CC are mainly at the CCSD levels. For example, in the OH molecule, the difference between the PSA-T[1|2]delimited-[]conditional12[1|2][ 1 | 2 ]R[1|2]delimited-[]conditional12[1|2][ 1 | 2 ]-CCSD and the spin-orbital CCSD is about 6 ×\times× 10-5 a.u., that i... | Adapting spatial orbitals in open-shell CC methods bartlett1995coupled ; christiansen2006coupled ; Bartlett:07 ; crawford2007introduction ; Bartlett:09 ; bartlett2012coupled ; Lyakh:12 ; bartlett2024perspective ; Helgaker:00book ; Harris:99 ; Olsen:00 ; Hirata:00 ; hirata2003tensor ; Kallay:00 ; kallay2001higher ; auer... | The number of resulting equations can be large at higher order PSA-CC and spin adaptations. This could slow down the computations. Though for a given basis set, the finite dimensional vector space for the computations from the spatial orbitals is smaller than from the spin orbitals. One may then expect a further optimi... | D |
Although the above AFM band-folding analysis based on the tight-binding model helps us to characterize the momentum-dependent pseudogap, it requires the abrupt collapse of the ΔksubscriptΔ𝑘\Delta_{k}roman_Δ start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT parameter around (π𝜋\piitalic_π, 0), indicating the breakdown of... | suggests that the Mott physics is at the origin of the pseudogap of electron-doped cuprates through the enhanced electron correlations without long-range AFM correlations, as in the case of the hole-doped cuprates Maier et al. (2002); Civelli et al. (2005); Kyung et al. (2006); Ferrero et al. (2009); Sakai et al. (2010... | As for the global momentum dependence of the pseudogap, the ARPES results reported by Matsui et al. Matsui et al. (2005) and Ikeda et al. Ikeda et al. (2009) have indicated the reduction of pseudogap magnitude upon approaching (π𝜋\piitalic_π, 0). This momentum dependence cannot be understood within the simple AFM band... | So far, the pseudogap of the electron-doped cuprates has been observed through the measurements of optical conductivity Onose et al. (2001); Wang et al. (2006), scanning tunneling spectroscopy Zimmers et al. (2007), and ARPES Armitage et al. (2001); Matsui et al. (2005); Park et al. (2007); Matsui et al. (2007); Richar... | One scenario to explain the overall band structure without assuming the long-range AFM order is the nodeless pseudogap proposed by Sakai et al. Sakai et al. (2010, 2013), based on a CDMFT calculation Kotliar et al. (2001) on the Hubbard model. They | D |
However, as highlighted in discussions of entanglement entropy, the AdS/CFT correspondence inherently features nonlocality[9]. | Then, the training can be interpreted as a correction due to quantum effects corresponding to nonlocality. | This nonlocality, which arises from quantum mechanical effects, is also expected to permute or spread information beyond the classical distortions of time and space mentioned earlier. | Note that our discussion of nonlocality concerns how quantum effects can spread or mix information in ways that exceed classical correlations. | However, note that nonlocality stemming from quantum effects manifests as the mixing and spreading of information, and it can be partially emulated even within classical CA models. | B |
The main purpose of this paper is to prove (1.2.2) for M=N−1𝑀𝑁1M=N-1italic_M = italic_N - 1 (Theorem 4.5.2). | with monodromy q𝑞qitalic_q. Recall that q𝑞qitalic_q is assumed to be a transcendental complex number. | use the Weil genericity of q𝑞qitalic_q assumption. Anyway, ℰℰ{\mathcal{E}}caligraphic_E is rigid and contains all the | In this paper we deal with the case M=N−1𝑀𝑁1M=N-1italic_M = italic_N - 1 for generic q𝑞qitalic_q. The advantage of the M=N−1𝑀𝑁1M=N-1italic_M = italic_N - 1 assumption is that in this case the group UM,Nsubscript𝑈𝑀𝑁U_{M,N}italic_U start_POSTSUBSCRIPT italic_M , italic_N end_POSTSUBSCRIPT is | In other words, assuming that q𝑞qitalic_q is transcendental111Probably the assumption that q𝑞qitalic_q is not | D |
The time the GAN post-processing takes is negligible in comparison, taking 0.35 seconds per model year on a V100 GPU and 37.17 seconds on a single CPU. The quantile mapping is similarly efficient taking 0.59 seconds per model year on a CPU. | This can be explained by the fact that the precipitation of the future scenario lies well outside the training distribution. | Down-scaling applications that increase the resolution of the ESM could be a direction for future research. | A potential direction for future research could be to develop a stochastic model that directly learns the uncertainties. | taking ERA5 reanalysis data as ground truth. Note that any other, and especially purely observational, precipitation dataset with sufficient temporal resolution could readily be used instead. | B |
|\langle\pi|\varphi\rangle|^{2},italic_λ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( | italic_φ ⟩ ) = start_UNDERACCENT | italic_π ⟩ end_UNDERACCENT start_ARG max end_ARG | ⟨ italic_π | italic_φ ⟩ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT , | }{\mathcal{N}^{2}}<\lambda^{2}| ⟨ italic_π | over~ start_ARG italic_φ end_ARG ⟩ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = divide start_ARG 1 end_ARG start_ARG caligraphic_N start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG | ⟨ italic_π | italic_φ ⟩ + italic_θ ⟨ italic_π | italic_η ⟩ | start_POSTSUPERSCRIPT 2 en... | |\langle\pi|\varphi\rangle|^{2},italic_λ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( | italic_φ ⟩ ) = start_UNDERACCENT | italic_π ⟩ end_UNDERACCENT start_ARG max end_ARG | ⟨ italic_π | italic_φ ⟩ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT , | While computing λ2superscript𝜆2\lambda^{2}italic_λ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT for a generic pure state is, in principle, difficult | G(|φ⟩)=1−λ2(|φ⟩)𝐺ket𝜑1superscript𝜆2ket𝜑G(|\varphi\rangle)=1-\lambda^{2}(|\varphi\rangle)italic_G ( | italic_φ ⟩ ) = 1 - italic_λ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( | italic_φ ⟩ ) | C |
A different argument to prove chiral symmetry breaking using ’t Hooft anomaly matching was pursued independently by Schwimmer in Ref. Schwimmer (1982). He considered an SU(Nf|Nf)𝑆𝑈conditionalsubscript𝑁𝑓subscript𝑁𝑓SU(N_{f}|N_{f})italic_S italic_U ( italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT | italic... | It would be desirable to extend the work of Schwimmer to the case of a massless spectrum with exotics, and prove that a generic PMC solution can be always written in terms of irreps of SU(Nf|Nf)𝑆𝑈conditionalsubscript𝑁𝑓subscript𝑁𝑓SU(N_{f}|N_{f})italic_S italic_U ( italic_N start_POSTSUBSCRIPT italic_f end_POSTSU... | In order to elevate this simple and elegant argument to the level of a proof of chiral symmetry breaking, one should demonstrate that it works for a generic spectrum with exotics and that it gives the most general solution of PMC, i.e. that every PMC solution is a collection of superalgebra irreps. This evidence is sti... | The alternative approach proposed by Schwimmer in Ref. Schwimmer (1982) makes use of the SU(Nf|Nf)𝑆𝑈conditionalsubscript𝑁𝑓subscript𝑁𝑓SU(N_{f}|N_{f})italic_S italic_U ( italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT | italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT ) superalgebra and does not re... | We have shown that the form of PMC[Nf,1]subscript𝑁𝑓1[N_{f},1][ italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT , 1 ] is Nfsubscript𝑁𝑓N_{f}italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT-dependent in general, which implies that PMC[Nf+1,1]PMCsubscript𝑁𝑓11\text{PMC}[N_{f}+1,1]PMC [ italic_N start_P... | B |
(c) Fusion and Fission of half-skyrmions, accompanying annihilation and creation of -1/2 disclinations. This process occurs in a diffusionless manner and becomes the dominant contribution to the structural relaxation as shown in Fig. 5. | A notable feature arising from half-skyrmion dynamics is the fusion and fission of half-skyrmions, as marked in Fig. 3(a) and (b), where two half-skyrmions merge into a large single half-skyrmion (fusion) and vice versa (fission). This process is schematically described in Fig. 3(c), accompanied by the annihilation and... | (c) Fusion and Fission of half-skyrmions, accompanying annihilation and creation of -1/2 disclinations. This process occurs in a diffusionless manner and becomes the dominant contribution to the structural relaxation as shown in Fig. 5. | (d) Schematic representation of half-skyrmions (left) and skyrmions (right). Molecular orientation becomes perpendicular (parallel) to the center in half-skyrmions (skyrmions). The vorticity q𝑞qitalic_q and skyrmion number Nsksubscript𝑁skN_{\rm sk}italic_N start_POSTSUBSCRIPT roman_sk end_POSTSUBSCRIPT read (q,Nsk)=(... | (d) Schematic illustration of annihilation process of disclinations with vorticity q=−1/2𝑞12q=-1/2italic_q = - 1 / 2. | D |
There are two viable possibilities: the heavy neutrinos Nisubscript𝑁𝑖N_{i}italic_N start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT can be either lighter or heavier than the new scalars. | The expected number of heavy neutrinos produced at the interaction point and decaying with a displacement of at least x1subscript𝑥1x_{1}italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and at most x2subscript𝑥2x_{2}italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, can be obtained by combining the production and decay... | In this case oscillations can occur between the members of the quasi-Dirac pair, preventing the cancellations that would otherwise suppress the LNV signal. Assuming this oscillation is effective, which holds for an ideal detector as long as ΔM≫ΓNmuch-greater-thanΔ𝑀subscriptΓ𝑁\Delta M\gg\Gamma_{N}roman_Δ italic_M ≫ r... | We first discuss the novel production mechanisms for the heavy neutrinos and scalars, and then discuss their decay modes and resulting collider signatures. | Therefore, the ratio between the LNC and LNV decay modes when the heavy quasi-Dirac neutrinos are produced as real particles is given by [16, 20] | C |
However, we show that the conventional approach is not enough to define the interactions between two open, coupled non-equilibrium thermodynamic systems. Therefore, we introduce new interaction schemes and theorems to define the correct interaction equations. Below, for simplicity, we label dark matter and dark energy ... | The continuity equation for a non-equilibrium system 1111 which interacts with the system 2222 should be presented in the form as | Change of the source X𝑋Xitalic_X can be defined as X=Γ1x2𝑋subscriptΓ1subscript𝑥2X=\Gamma_{1}x_{2}italic_X = roman_Γ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT where x2subscript𝑥2x_{2}italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT is the energy flux from system 1 to t... | As seen from Fig.3, the energy x1subscript𝑥1x_{1}italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT flows from system 1 to system 2 and acts on system 2. Similarly, x2subscript𝑥2x_{2}italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT flows from the system 2 to the system 1 and acts on the system 1. While x1subscript𝑥1x_... | The interactions between two coupled non-equilibrium systems can be obtained from the energy conservation law of statistical thermodynamics and is given in a simple form as | A |
A similar accuracy metrics was suggested in the study of IBD and LTID [47] for the harmonic potential case. We use it for the free particle case as well as the same harmonic one (in the following section). Criteria like (59) have been applied only for the range such that |Cp∗(τ∗)|>0.01superscriptsubscript𝐶𝑝superscr... | The harmonic potential case is a basic model for microscopical interactions and correspondingly, to validate the quality of auto-correlations [47]. In addition, several real systems can be approximated at first order by such interactions in the case of small departures from equilibrium positions. The corresponding Lan... | As the simulated systems exhibit the hallmark of scale separation, computational strategies rely on the reduction of fast degrees of freedom in favor of retaining the slow, important ones. A similar consideration apply to representing systems in contact with a heat reservoir that does not need to be represented in full... | A similar accuracy metrics was suggested in the study of IBD and LTID [47] for the harmonic potential case. We use it for the free particle case as well as the same harmonic one (in the following section). Criteria like (59) have been applied only for the range such that |Cp∗(τ∗)|>0.01superscriptsubscript𝐶𝑝superscr... | Here and hereinafter, the subscript sim differentiates numerical values unless expressed explicitly. The expression is a version of the diffusion equation [45] in the case of a particle at rest at time τ∗=0superscript𝜏0\tau^{*}=0italic_τ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT = 0 that is assigned a given initial ... | A |
The advantages of studying the hadronic final state are as follows. The large hadronic branching ratio and significant mass difference between VLQ and the scalar significantly boost the top quark. As a result, reconstructing the top quark as a boosted fatjet additionally provides the inherent properties of the jet. Fur... | Table 4: After applying various kinematic event selection cuts, signal and background events (in fb) indicate the efficiency for each set of cuts to reduce the backgrounds. The kinematic cuts (C1-C4) are described in the text. After applying the C4 cut, the remaining events are passed for the multivariate analysis. | (C4) pruned mass of the two leading jets MJ0,MJ1>120subscript𝑀subscript𝐽0subscript𝑀subscript𝐽1120M_{J_{0}},M_{J_{1}}>120italic_M start_POSTSUBSCRIPT italic_J start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT end_POSTSUBSCRIPT , italic_M start_POSTSUBSCRIPT italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT > ... | All the signal and background processes are passed through all these event selection criteria up to C4 before passing events to MVA. We create two separate signal and background classes. The combined background is the weighted combination of all the different background processes. Each signal and background class is ra... | The normalized distribution of the BDT response for test and train samples of both signal (BP1) and background classes is plotted on the left side of Figure 10. We find signal and background are well separated. With the cut applied to the BDT output, the signal and background efficiency, as well as the statistical sign... | A |
Temperature-dependent magnetic susceptibility was measured using a 7 Tesla Cryogenic Ltd SQUID (superconducting quantum interference device) magnetometer with a Helium-3 probe from 0.3 K to 2 K and with a Helium-4 probe from 2 K to 300 K. For the Helium-3 measurements, a small crystalline YbZn2GaO5 sample of 1.04 mg wa... | The inelastic neutron scattering (INS) experiments were performed on the Fine-Resolution Fermi Chopper Spectrometer (SEQUOIA) [49] and the Cold Neutron Chopper Spectrometer (CNCS) [50] at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory. For the SEQUOIA experiment, 6.5 g of pure powder samples of YbZn... | Neutron Powder Diffraction (NPD) measurement of YbZn2GaO5 was collected using the General Materials Diffractometer (GEM) at the ISIS Neutron and Muon Source (Rutherford Appleton Laboratory, United Kingdom) [48]. The sample was loaded into an 8 mm diameter vanadium sample holder, and the NPD pattern was collected at roo... | Temperature-dependent magnetic susceptibility was measured using a 7 Tesla Cryogenic Ltd SQUID (superconducting quantum interference device) magnetometer with a Helium-3 probe from 0.3 K to 2 K and with a Helium-4 probe from 2 K to 300 K. For the Helium-3 measurements, a small crystalline YbZn2GaO5 sample of 1.04 mg wa... | The poly-crystalline sample of YbZn2GaO5 was synthesized using a solid-state reaction route. The high-purity precursors of Yb2O3 (99.9%percent\%%), Ga2O3 (99.9%percent\%%), and ZnO (99.9%percent\%%) with 5%percent\%% excess ZnO were used and mixed thoroughly and then pressed into a pellet. The pellets were sintered at ... | B |
The expressions of Df0subscript𝐷subscript𝑓0D_{f_{0}}italic_D start_POSTSUBSCRIPT italic_f start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT end_POSTSUBSCRIPT, Da0subscript𝐷subscript𝑎0D_{a_{0}}italic_D start_POSTSUBSCRIPT italic_a start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT end_POSTSUBSCRIPT, and Dσ0subscript𝐷subscript𝜎0D_{\sig... | Accordingly, BESIII has recently measured the semileptonic Ds+superscriptsubscript𝐷𝑠D_{s}^{+}italic_D start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT decays BESIII:2023wgr ; BESIII:2021drk . | have been extracted in Refs. Flatte:1976xu ; Flatte:1976xv ; Baru:2004xg ; Abele:1998qd ; Bugg:2008ig ; LHCb:2014ooi ; LHCb:2014vbo | Abele:1998qd ; BESIII:2020hfw , and LHCb:2019sus ; Oller:2004xm ; Cheng:2022vbw ; BES:2004mws ; Zou:1993az , respectively: | The S0→M1M2→subscript𝑆0subscript𝑀1subscript𝑀2S_{0}\to M_{1}M_{2}italic_S start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT → italic_M start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_M start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT strong decay is defined as Cheng:2022vbw | C |
ΠlSsubscriptsuperscriptΠ𝑆𝑙\displaystyle\Pi^{S}_{l}roman_Π start_POSTSUPERSCRIPT italic_S end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT | −r212S¯ijrS¯jkrS¯kir,superscript𝑟212superscriptsubscript¯𝑆𝑖𝑗𝑟superscriptsubscript¯𝑆𝑗𝑘𝑟superscriptsubscript¯𝑆𝑘𝑖𝑟\displaystyle-\frac{r^{2}}{12}\overline{S}_{ij}^{r}\overline{S}_{jk}^{r}% | 12∂τijr∂(r2)=12∇2τijr+A¯ikrA¯jkr,τijr=0=0,formulae-sequence12superscriptsubscript𝜏𝑖𝑗𝑟superscript𝑟212superscript∇2superscriptsubscript𝜏𝑖𝑗𝑟superscriptsubscript¯𝐴𝑖𝑘𝑟superscriptsubscript¯𝐴𝑗𝑘𝑟superscriptsubscript𝜏𝑖𝑗𝑟0012\frac{\partial\tau_{ij}^{r}}{\partial(r^{2})}=\frac{1}{2}\nabla^{2}\tau_{ij}... | r248ω¯irω¯jrS¯ijr,superscript𝑟248superscriptsubscript¯𝜔𝑖𝑟superscriptsubscript¯𝜔𝑗𝑟superscriptsubscript¯𝑆𝑖𝑗𝑟\displaystyle\frac{r^{2}}{48}\overline{\omega}_{i}^{r}\overline{\omega}_{j}^{r% | −112∫0r2(S¯ikθS¯jkθ¯ϕ−S¯ikθ¯ϕS¯jkθ¯ϕ)S¯ijrdθ2,112superscriptsubscript0superscript𝑟2superscript¯superscriptsubscript¯𝑆𝑖𝑘𝜃superscriptsubscript¯𝑆𝑗𝑘𝜃italic-ϕsuperscript¯superscriptsubscript¯𝑆𝑖𝑘𝜃italic-ϕsuperscript¯superscriptsubscript¯𝑆𝑗𝑘𝜃italic-ϕsuperscriptsubscript¯𝑆𝑖𝑗𝑟differential-dsupersc... | A |
The concept of extra dimensions and brane worlds has been a topic of interest for many years. Initially, the extra dimensions are supposed to be compactified on the scale of the Planck length Antoniadis (1990); Arkani-Hamed, Dimopoulos, and Dvali (1998); Antoniadis et al. (1998). While in the Randall-Sundrum brane mode... | The key to gauge invariance of the effective action is the interrelation between masses of the KK modes with the vector-scalar and scalar-scalar coupling constants. Building on our prior research Fu et al. (2016a, b, 2020); Fu, Zhong, and Liu (2019); Fu, Zhao, and Sun (2022); Fu (2022), we found that the effective acti... | It is well known that the Stueckelberg mechanism Ruegg and Ruiz-Altaba (2004) or Higgs mechanism Higgs (1964) is necessary to preserve the gauge invariance of massive gauge field. These two mechanisms respectively introduce a Stueckelberg field or a Goldstone boson to maintain the symmetry of the gauge field. We observ... | To address this, we begin by reviewing the method for studying the gauge invariance of the effective action of a bulk free U(1)gauge field. From this, we show that the relationships between the coupling coefficients will determine the gauge invariance. Next, we consider a brane model with the following general line-ele... | This study begun with an examination of the methodology for deriving the effective action of a massless bulk U(1)𝑈1U(1)italic_U ( 1 ) gauge field through a general KK decomposition within branes of codimension 2. The effective action implies the existence of two distinct types of scalar KK modes that couple with the ... | B |
Our model has rich phenomenology. Direct detection experiments (χN→χN→𝜒𝑁𝜒𝑁\chi N\to\chi Nitalic_χ italic_N → italic_χ italic_N mediated by A′superscript𝐴′A^{\prime}italic_A start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT) like PandaX-II Yang et al. (2021) constrain the kinetic mixing between A′superscript𝐴′A^{\prim... | where σVsubscript𝜎𝑉\sigma_{V}italic_σ start_POSTSUBSCRIPT italic_V end_POSTSUBSCRIPT is the viscosity cross section Tulin et al. (2013b); Cline et al. (2014); Yang and Yu (2022) and v0subscript𝑣0v_{0}italic_v start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the velocity dispersion. Analytic formulae of DM scattering cross... | Recently, the NANOGrav, CPTA, EPTA and PPTA collaborations have presented new observations of stochastic gravitational waves (GWs) using pulsar timing arrays (PTAs) Agazie et al. (2023); Xu et al. (2023); Antoniadis et al. (2023); Reardon et al. (2023). In particular, the NANOGrav Agazie et al. (2023) and CPTA Xu et al... | Overall, for dwarf galaxies or galaxies with a DM average velocity ⟨v⟩delimited-⟨⟩𝑣\langle v\rangle⟨ italic_v ⟩ around 10−2001020010-20010 - 200 km/s, the cross section σ/mDM𝜎subscript𝑚DM\sigma/m_{\text{DM}}italic_σ / italic_m start_POSTSUBSCRIPT DM end_POSTSUBSCRIPT needs to be within the range 𝒪(1)−𝒪(10)𝒪1𝒪1... | Furthermore, the very distinct gravothermal evolution of SIDM halo, which start with core formation-expansion and followed by core collapse Balberg et al. (2002); Koda and Shapiro (2011); Essig et al. (2019); Huo et al. (2020); Nishikawa et al. (2020); Sameie et al. (2020); Kahlhoefer et al. (2019); Turner et al. (2021... | D |
Table 1: Saturated THz amplitude and central frequency of the THz pulse emitted from heterostructures CoFeB (2nm)/NM. | To gain deeper insights into the fabricated THz emitters, we analyzed the correlation between the amplitude of the emitted THz field at 1 THz and the varying thicknesses of the CoFeB layer in stacks with specified NM layers, see Fig. 3 (a) and (b). The THz emitters composed of pure Pt layers demonstrate the highest THz... | Figure 3: (a) The amplitude of the THz signal at a frequency of 1 THz as a function of CoFeB-layer thicknesses for stacks containing different NM layers and varying thicknesses. The amplitude is measured in attovolt-seconds. (b) A magnified scale of the THz signal for stacks comprising NM layers Ru, Au, and AgBi. (c) T... | Dependence of THz Signal Amplitude, Central Frequency, and Bandwidth on Heterostructure Thickness and NM Materials: Fig. 2 illustrates the emitted THz signal as a function of delay time and laser spot position for distinct samples. Accordingly, irrespective of the type of metal layers, no THz emission is detected at th... | To optimize spintronic THz emitters performance, we conducted a comparative study on SiO22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT/CoFeB/NM heterostructures, where the CoFeB layer thickness varied from 0 to 5nm, and different heavy metals (Pt, W, Au) and alloys (Pt%92{}_{\%92}start_FLOATSUBSCRIPT % 92 end_FLOATS... | A |
In the analysis that follows, we only consider the parameters that fall within the red areas, where we have two local maxima that describe from left to right. | In this situation, we may have 1 or 2 local maxima of the effective potential for different parameters. | In the analysis that follows, we only consider the parameters that fall within the red areas, where we have two local maxima that describe from left to right. | When we select the appropriate value of λ𝜆\lambdaitalic_λ to construct the U(r)𝑈𝑟U(r)italic_U ( italic_r ) as shown in Fig. 2(a), there are two local maxima of the effective potential. | Choosing different values of the parameters, we may have from 00 to 3333 local maxima of the effective potential, as shown in the left image of Fig. 5. | A |
We note that the KDE’s bandwidth acts like a control parameter with potential room for user-controlled fine-tuning in the computation of its value, somewhat analogous to the σ𝜎\sigmaitalic_σ of the narrow Gaussian method. However, unlike the narrow Gaussian method where σ𝜎\sigmaitalic_σ can in principle be chosen to ... | To carry out parameter estimation for each event that passes our selection criteria, we use public data [19, 20] from GWTC-1 through GWTC-3. We use lalinference_mcmc [18, 21, 22, 23], which implements Markov chain Monte Carlo (MCMC) with the Metropolis-Hastings algorithm and lalinference_nest, which implements nested s... | Because of these considerations, we conclude that the weighted SVD-assisted random draw method produces constraints that are unreliable and are likely to be underestimates of the true uncertainties in the measurement of SME coefficients. We verify this claim by testing this method against its Bayesian counterparts in a... | We note that the KDE’s bandwidth acts like a control parameter with potential room for user-controlled fine-tuning in the computation of its value, somewhat analogous to the σ𝜎\sigmaitalic_σ of the narrow Gaussian method. However, unlike the narrow Gaussian method where σ𝜎\sigmaitalic_σ can in principle be chosen to ... | We present the results of the KDE method upon its use in the analysis of the events marked * listed in tables I through III (except for GW170817 for which we do not use the fixed posteriors due to the inability of the KDE to estimate very narrow densities) in Fig. 4 as our final result. | D |
(b) False-color scanning electron microscopy of a 2×2222\times 22 × 2 germanium quantum dot device, nominally identical to the one used here. | Next, we manipulate the spins by two simultaneous microwave pulses on plunger gates P2𝑃2P2italic_P 2 and P4𝑃4P4italic_P 4, with a duration tpsubscript𝑡pt_{\mathrm{p}}italic_t start_POSTSUBSCRIPT roman_p end_POSTSUBSCRIPT and microwave frequencies fP2subscript𝑓𝑃2f_{P2}italic_f start_POSTSUBSCRIPT italic_P 2 end_... | We focus on the spin qubits Q1𝑄1Q1italic_Q 1 and Q2𝑄2Q2italic_Q 2, while Q3𝑄3Q3italic_Q 3 and Q4𝑄4Q4italic_Q 4 remain in their ground state. | We analyze three resonance lines [dashed lines in Fig. 2(b)] resulting from bichromatic rotation of Q1𝑄1Q1italic_Q 1 and Q2𝑄2Q2italic_Q 2. | We operate Q1𝑄1Q1italic_Q 1 and Q2𝑄2Q2italic_Q 2 with microwave bursts applied to P2𝑃2P2italic_P 2 and P4𝑃4P4italic_P 4. | D |
Finally, we can compare our numerics with the numerics on spreading of wave packets in the following way. Since we see a hint of a deviation from the τ∝λ−4proportional-to𝜏superscript𝜆4\tau\propto\lambda^{-4}italic_τ ∝ italic_λ start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT law, one could ask how hard it would be to pr... | We define the decorrelation time τ𝜏\tauitalic_τ as the time at which η𝜂\etaitalic_η reaches a fixed value η0subscript𝜂0\eta_{0}italic_η start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT (for clarity, we also use the notation τη0subscript𝜏subscript𝜂0\tau_{\eta_{0}}italic_τ start_POSTSUBSCRIPT italic_η start_POSTSUBSCRIPT 0 e... | We provide for the first time a direct comparison between numerical observations and mathematical bounds for the KG chain. As an alternative to the speed of spreading or the diffusion constant, we focus on the decorrelation time in thermal equilibrium as it is more accessible to a proper mathematical treatment and to n... | We have run the dynamics up to a time t=1010𝑡superscript1010t=10^{10}italic_t = 10 start_POSTSUPERSCRIPT 10 end_POSTSUPERSCRIPT for the smallest values of λ𝜆\lambdaitalic_λ. | Let us fix an arbitrary threshold value 0<q<10𝑞10<q<10 < italic_q < 1 for the decorrelation parameter η𝜂\etaitalic_η, as in Figure 3. | D |
Instead, we do investigate how much the dynamics at positive temperature and at weak interaction is slowed down by its proximity to a localized system. We will explain later how this connects to an interesting ongoing debate, but first, we introduce the model and set the stage. | We focus here on the dynamics at λ=0𝜆0\lambda=0italic_λ = 0: The chain is harmonic and the system is decomposed into a set of |ΛL|subscriptΛ𝐿|\Lambda_{L}|| roman_Λ start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT | independent modes. | The disordered Klein-Gordon chain with a quartic interaction is a prototypical example of an interacting classical many-body system, | The fate of Anderson localization in the presence of genuine many-body interactions, or anharmonicity, is a matter of considerable interest and debate, | It is also important to consider sufficiently generic interactions, see e.g. [12] for an example of a many-body system that, despite probably being chaotic, exhibits subdiffusive transport. | B |
We consider strained Si/SiGe devices. Because of the mismatch of lattice constant between the materials, a force develops at their interfaces, resulting in a displacement field 𝒖(𝒓)𝒖𝒓\boldsymbol{u}(\boldsymbol{r})bold_italic_u ( bold_italic_r ) for the atoms. Consequently, in equilibrium the lattice constants of t... | In linear elasticity theory \citeSKosevich1986sm the change of lengths in a deformed body is given by the strain tensor | To calculate the effect of strain due to lattice mismatch, we simulate the strain tensor elements εijsubscript𝜀𝑖𝑗\varepsilon_{ij}italic_ε start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT in our devices by solving the differential equation in Eq. (S5) numerically. In particular, we use the FEM implemented in ... | Our system comprising two materials with different lattice constants ai(𝒓)subscript𝑎𝑖𝒓a_{i}(\boldsymbol{r})italic_a start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( bold_italic_r ) and two different elastic stiffness tensors Cijkl(𝒓)subscript𝐶𝑖𝑗𝑘𝑙𝒓C_{ijkl}(\boldsymbol{r})italic_C start_POSTSUBSCRIPT ita... | In the Supplemental Material we provide more details on the simulation of the strain tensor in our devices via the finite element method and continuum elasticity theory. We show results on the strain tensor components that cause the localization of the electron wave function in certain areas of the device cross section... | A |
While this paper has demonstrated implementations for parallel collimator SPECT and LM-TOF PET, there exist many other modalities not presently included in the software, including (but not limited to) diverging/converging/pinhole SPECT, various forms of computed tomography, (CT), magnetic resonance (MR) imaging, and co... | This work describes the python library PyTomography and highlights specific use cases in SPECT and PET imaging. The software architecture facilitates the development of different imaging modalities and likelihoods that can all interface with the same reconstruction algorithms. The goal of this research was to create a ... | Overall, the aim of this study is to introduce the community to the PyTomography software project, demonstrate its current capabilities and flexibility, and to encourage community involvement in the continuation of its development. Example applications are explored in SPECT and PET reconstruction, though the library al... | To this end, we developed the python library PyTomography with the priorities to: (i) implement standard and traditional imaging modalities and reconstruction algorithms, (ii) disseminate recent research developments, such as the deep image prior [8], and (iii) encourage community involvement via extensive documentatio... | In this work, the software architecture of PyTomography was demonstrated and use cases were explored on both SPECT and PET data. The efficient reconstruction times, shown in Table 3, can enable researchers to perform extensive studies on digital/physical phantom and patient data that may include multiple patients, nois... | A |
In the main text, we show that magnetoelastic couplings in the triangular lattice with D3 symmetry lead to non-zero integer band Chern numbers. | To understand the effects of the lattice symmetry, we study the topological classification of the equivalent phononic system | In the main text, we show that magnetoelastic couplings in the triangular lattice with D3 symmetry lead to non-zero integer band Chern numbers. | For the triangular lattice with D3 symmetry, the symmetry-adapted form [46] of J𝐽Jitalic_J-tensor is | Below in Fig. S1 we plot the dispersion with the color showing the chirality for K2=0subscript𝐾20K_{2}=0italic_K start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 0, and we find the bands are modified by the magnetoelastic effects but are not fully gapped and the chirality is zero for any 𝐤𝐤\mathbf{k}bold_k. | A |
The predicted effects of PSOI are highly sensitive to the Rashba constant, α𝛼\alphaitalic_α, which naturally drives the search for materials that i) exhibit giant Rashba effect, and ii) allow for ample tunability of the Rashba splitting by the external electric field. Promising candidates include thin layers of Bi2Se... | The predicted effects of PSOI are highly sensitive to the Rashba constant, α𝛼\alphaitalic_α, which naturally drives the search for materials that i) exhibit giant Rashba effect, and ii) allow for ample tunability of the Rashba splitting by the external electric field. Promising candidates include thin layers of Bi2Se... | In this section we work out consequences of the phenomenological Rashba spin-orbit coupling, Eq. (1), for electron-electron interaction Hamiltonian. To this end consider a 3D Rashba system without structure inversion asymmetry. A 2D case is a simple particular case of this consideration, which is briefly mentioned in t... | The notion of pair spin-orbit interactions (PSOI) [31] represents a conceptual shift from these traditional SOI mechanisms. Unlike the single-particle RSOI, which arises from external electric fields, PSOI originates directly from the Coulomb fields of conduction band electrons. Therefore, PSOI does not rely on structu... | Yet, a significant gap persists in reliably estimating the Rashba coupling constant, particularly concerning the response of layered materials to in-plane electric fields. The Rashba coupling in promising 3D systems remains largely unknown. Many existing estimates rely on ARPES measurements, which mainly probe the Rash... | D |
1Ωh−2M−M2(1−1−ε2)>0.1subscriptΩℎ2𝑀superscript𝑀211superscript𝜀20\dfrac{1}{\Omega_{h}}-2M-M^{2}(1-\sqrt{1-\varepsilon^{2}})>0.divide start_ARG 1 end_ARG start_ARG roman_Ω start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT end_ARG - 2 italic_M - italic_M start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( 1 - square-root start... | According to the relation (52), when ε→0→𝜀0\varepsilon\rightarrow 0italic_ε → 0, the black hole is the near extreme case, and when ε=0𝜀0\varepsilon=0italic_ε = 0, the black hole is the extreme case. Using the relation (52), the condition (51) for destroying the event horizon of the black hole is simplified as | For the case of near-extreme black holes, that is, when the dimensionless parameter ε→0→𝜀0\varepsilon\to 0italic_ε → 0, for the cold dark matter halo-black hole, its result can be obtained by calculating the conditional expression (53) as | while for the ultralight dark matter halo-black hole, its result can be obtained by calculating the conditional expression (53) as | Combining formulas (85), (86) and (87), since the time interval dt𝑑𝑡dtitalic_d italic_t, the parameter ε𝜀\varepsilonitalic_ε, and the dark matter parameters k1subscript𝑘1k_{1}italic_k start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT or k2subscript𝑘2k_{2}italic_k start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT are all first-order ... | B |
In Fig. 8, the score for the random acting agents is approximately 00, since the cooperative sequential coin game is a zero-sum game. The evolutionary-trained VQC approache, however, perform significantly better leading to an average score around 7777. The total coins collected depicted in Fig. 9(a) suggests that in co... | As depicted in Fig. 8, a better result is achieved by the VQC approach compared to random. On this basis, we compare the performance of this VQC approach to that of a neural network with a comparable number of parameters. | In our experiments, we showed that our VQC approach performs significantly better compared to a neural network with a similar amount of trainable parameters. Compared to the larger neural network, we can see that the VQC approach achieves similar results, showing the effectiveness of using VQCs in a MAQRL environment. ... | In the previous section, we observed that a neural network with the same number of parameters as the VQC of our approach cannot match the VQC’s performance. We will now compare the results with a neural network that has significantly more parameters. Again, mutation only is used for the evolution of subsequent generati... | Here we exploit the higher expressive power of VQCs compared to conventional neural networks [Chen et al., 2022]. Similar to [Chen et al., 2022], we define the expressive power as the capacity to represent particular functions with a constrained number of parameters. Note that the VQC has 148148148148 parameters (3 * 6... | A |
There are several steps to solving the optimization problem as shown in Fig. 3. In this section, we will discuss the process of solving the optimization problem on IBM’s superconducting (gate based) quantum computers, and bench-marking them with quantum simulators and classical tools like CPLEX and Simulated Annealing. | In this paper, we are proposing a turn based model in a 3D lattice for the protein folding problem. The peptide chain is coarse grained into a C-alpha backbone model where each bead represents the C-alpha atom of individual amino acids in the peptide sequence. Further, the interaction model could either be in the class... | This exercise has to be carried out for all pairs of (i,j)𝑖𝑗(i,j)( italic_i , italic_j ). This will penalize all non-adjacent beads from having equal sets of coordinates. This kind of a constraint (non-overlap in any one dimension) ensures minimum contradiction with the main objective function, which tries to bring t... | To run it in a Quantum hardware or simulator using quantum algorithms, we need to generate the Hamiltonian operator from the formulation. The detailed steps are discussed in the following sections. As discussed above, there is randomness in the formulation when the overlap and diagonal crossing constraints are taken in... | In this paper we have discussed a novel turn based protein folding formulation that can be run on Quantum computing hardwares using variational algorithms. The highlight of the formulation is in the increased degrees of freedom that a turn has while going from one protein molecule to the next. We ran our formulation us... | C |
For diagnostics, we employ Frequency-Resolved Optical Gating (FROG) and an Optical Spectrum Analyzer | (OSA) to measure the temporal and spectral profiles, respectively. Additionally, a Time-Stretch Dispersive | Stretched temporal profiles recorded by the oscilloscope for modes of {1}1\mathrm{\{1\}}{ 1 }, {2}2\mathrm{\{2\}}{ 2 }, and {3}3\mathrm{\{3\}}{ 3 }, respectively. | respectively. The stretched temporal profiles demonstrate robustness over 250250250250 round trips and a dip is clearly observed at the center of the | FGVD and nonlinearity. (a) and (d): The normalized temporal intensity and gradient (−∂I/∂t𝐼𝑡-\partial I/\partial t- ∂ italic_I / ∂ italic_t). (b) and (e): The corresponding temporal phase and | A |
The previous paper Yahiaoui2018 proposed the EIT from bright-bright modes coupling, which is similar to Fig. 2 (b). However, our CIT is demonstrated in Fig. 2 (c). Note that Fig. 2 (b) and (c) have different polarization. Therefore, in our paper, two dark modes can not be excited by external field without bright mode ... | The CIT dip comes from the interference of dark modes due to asymmetric dark modes. The interference of dark modes can provide the Fano shape in the transmission spectrum, as shown in Fig. 2 (b). Fig. 2 (b) demonstrates the transmission spectrum of dark modes with x-polarized THz wave without bright mode and this confi... | Figure 6: The electric field (left) and current density field (right) at CIT frequency, with corresponding to our example as shown in the red line in Fig. 2 (c) at around 0.72 THz. | Therefore, the energy of bright mode can not flow to dark modes due to the suppression of dark modes. Consequently, bright mode can excite by external THz wave again, which causes the CIT effect, as shown in the blue, green and red lines of Fig. 2 (c). As we can see from the results, all the maximum frequencies of Fano... | For better understanding, We plot the electric field and current density field at CIT frequency, as shown in fig. 6 with corresponding to around 0.72 THz for the red line in Fig. 2 (c). As we can obtain from the results, the dark modes present two opposite modes which provide destructive interference between the dark m... | D |
Although our examples were restricted to the examination of two bodies, there is nothing in the analysis presented here that does not immediately extend to a greater number of bodies. We are eager to see these techniques used to describe many-body elastic interactions, though it may be that the simpler far-field intera... | This paper is organized as follows. We begin in §2 with a review of the mathematical model, including a discussion of boundary conditions and surface tractions, and we recall from Ref. [12] the effective boundary technique that allows for the solution of a weak (finite) anchoring problem based on the solution of a stro... | Helpful conversations with Nicholas Abbott, Thomas Powers, and Raghav Venkatraman are gratefully acknowledged. SES acknowledges the UW–Madison Office of the Vice Chancellor for Research and Graduate Education and funding from the Wisconsin Alumni Research Foundation. | We begin with a description of the general problem, and recall the relevant structure developed for the case of a single immersed body [12]. Consider a two-dimensional nematic liquid crystal outside N𝑁Nitalic_N simply-connected bodies, as illustrated in Fig. 1 for N=2𝑁2N=2italic_N = 2. The liquid crystal domain and t... | Among the most alluring (and analytically challenging) features of liquid crystals are the prevalence of topological singularities, which satisfy global conservation laws [46, 3]. The locations of the defects on the surface or in the fluid depend on the relationship between the bulk elastic energy and the surface ancho... | B |
The momentum-averaged positions 𝔼(𝐳(t))𝔼𝐳𝑡\mathbb{E}({\bf z}(t))blackboard_E ( bold_z ( italic_t ) ) and velocities ddt𝔼(𝐳(t))𝑑𝑑𝑡𝔼𝐳𝑡\frac{d}{dt}\mathbb{E}({\bf z}(t))divide start_ARG italic_d end_ARG start_ARG italic_d italic_t end_ARG blackboard_E ( bold_z ( italic_t ) ) are discrete analogs of mome... | In particular, considerations of the analogies between biology and physics via the virial theorem led us to generalize the work of [18] and to derive the ecological simple harmonic oscillator, which to our knowledge is the first example of such an oscillator that emerges solely from maternal effects and does not requir... | The momentum-averaged positions 𝔼(𝐳(t))𝔼𝐳𝑡\mathbb{E}({\bf z}(t))blackboard_E ( bold_z ( italic_t ) ) and velocities ddt𝔼(𝐳(t))𝑑𝑑𝑡𝔼𝐳𝑡\frac{d}{dt}\mathbb{E}({\bf z}(t))divide start_ARG italic_d end_ARG start_ARG italic_d italic_t end_ARG blackboard_E ( bold_z ( italic_t ) ) are discrete analogs of mome... | Ultimately, analogies between the Price equation and the virial theorem point towards potentially productive directions for exploration in both biology and physics. The statistical framing of the virial theorem in (5) highlights phenomena that may have been overlooked in the physics realm. For example, the first term o... | In genetics, the natural time increment to consider is discrete (generation), whereas in physics continuous-time is more natural. Thus, the discrete Price equation pertains to change in a trait after a single generation, whereas the virial theorem is formulated with continuous-time, and is additionally time averaged. H... | A |
Nevertheless, providing reference implementations avoids duplication efforts in writing file writers and parsers, aiming at obtaining a robust library that can be easily reused, maintained, and where bugs can be quickly resolved. To efficiently address this goal, it is useful to select a popular language such as Python... | The concept of MLWF can be actually extended to multiparticle Bloch states and has been recently applied to excitons, which are two-particle correlated e-h excitations and where maximal localization can be defined with respect to an average e-h coordinate in real space [171]. | The efficient interpolation in reciprocal space of k𝑘kitalic_k-dependent quantities is arguably the most common application of WFs, enabling the calculation of simple (e.g., the band structure) or complex (e.g., electron-phonon coupling) electronic-structure properties. A large part of this review is devoted to the fu... | Nevertheless, we stress that the concept of a common parsing library is not limited to the Python language, but can also be applied to other emerging | Nevertheless, providing reference implementations avoids duplication efforts in writing file writers and parsers, aiming at obtaining a robust library that can be easily reused, maintained, and where bugs can be quickly resolved. To efficiently address this goal, it is useful to select a popular language such as Python... | C |
={u∈H˙1(ℝd):u is radially symmetric}.absentconditional-set𝑢superscript˙𝐻1superscriptℝ𝑑𝑢 is radially symmetric\displaystyle=\{u\in\dot{H}^{1}(\mathbb{R}^{d}):u\text{ is radially symmetric}\}.= { italic_u ∈ over˙ start_ARG italic_H end_ARG start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT ( blackboard_R start_POSTSUPERSC... | Note that the restriction q<2∗𝑞superscript2q<2^{*}italic_q < 2 start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT in (2) is necessary, namely the quadratic form h[u]ℎdelimited-[]𝑢h[u]italic_h [ italic_u ] is really weaker than ‖∇u‖L22superscriptsubscriptnorm∇𝑢superscript𝐿22\|\nabla u\|_{L^{2}}^{2}∥ ∇ italic_u ∥ start_POS... | In the radial case, we can work directly with the quadratic form h[u]ℎdelimited-[]𝑢h[u]italic_h [ italic_u ] in (1). We have | Let us show that (4) fails if d≥4𝑑4d\geq 4italic_d ≥ 4 or if θ≠1/3𝜃13\theta\neq 1/3italic_θ ≠ 1 / 3. First, the necessity of θ≤1/d𝜃1𝑑\theta\leq 1/ditalic_θ ≤ 1 / italic_d can be seen from the radial case as explained in Theorem 3 (i). To be precise, we consider the example in (18) with ε>0𝜀0\varepsilon>0italic_ε >... | In this short article we are interested in interpolation inequalities involving the quadratic form h[u]ℎdelimited-[]𝑢h[u]italic_h [ italic_u ] and Lpsuperscript𝐿𝑝L^{p}italic_L start_POSTSUPERSCRIPT italic_p end_POSTSUPERSCRIPT-norms of u𝑢uitalic_u. A classical result in this direction is the Gagliardo–Nirenberg ty... | B |
{s}(r^{\prime},\vartheta^{\prime})\,e^{i\ell(\vartheta-\vartheta^{\prime})}\,.start_ROW start_CELL ( italic_R start_POSTSUBSCRIPT roman_P , ± end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( roman_F ) end_POSTSUPERSCRIPT ( italic_λ ) bold_italic_ψ ) start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( italic_r , italic_ϑ ) = ∫ st... | To begin with, from (2.21), (2.22) and (2.23) (see also [OLBC10, §10.27 and §10.29(ii)]), we deduce that | To say more, using (2.8), (2.9) and (3.8), together with the Bessel connection formula [OLBC10, Eq. 10.27.8], for any 𝐪∈ℂ4𝐪superscriptℂ4\mathbf{q}\in\mathbb{C}^{4}bold_q ∈ blackboard_C start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT, we infer | In the second line we have used the connection formulas reported in [OLBC10, Eqs. 10.27.6 and 10.27.8]. | Notice that the kernel in (2.22) is slightly different, compared to [AT98], as we write it using the modified Bessel functions of second kind Iν,Kνsubscript𝐼𝜈subscript𝐾𝜈I_{\nu},K_{\nu}italic_I start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT , italic_K start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT in place of the Be... | C |
This could potentially signal the PDW origin of superconductivity in these strongly correlated quantum materials as well. | The finite interaction range R0subscript𝑅0R_{0}italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT in this case has the same electrostatic origin as the Thomas-Fermi screening. | In the repulsive case, V(r)>0𝑉𝑟0V(r)>0italic_V ( italic_r ) > 0, Eq. (1) models a screened Coulomb interaction, where R0subscript𝑅0R_{0}italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT plays role of the Thomas-Fermi screening length scaling as λFγ−1/(D−1)≫λFmuch-greater-thansubscript𝜆𝐹superscript𝛾1𝐷1subscript�... | Importantly, the electron-electron interaction, U(τ,𝒓)𝑈𝜏𝒓U(\tau,\bm{r})italic_U ( italic_τ , bold_italic_r ), within our model is instantaneous and assumed to have a finite range R0subscript𝑅0R_{0}italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT that significantly exceeds the average inter-electron distance given... | It might be possible to change the interaction range R0subscript𝑅0R_{0}italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT in these materials in a controlled way by gates, which affect the screening, and thereby test our predictions. | D |
Here, v(z,ω)𝑣𝑧𝜔v(z,\omega)italic_v ( italic_z , italic_ω ) is the speed of light in the medium, and 𝒢(z,K,ω)𝒢𝑧𝐾𝜔\mathcal{G}(z,K,\omega)caligraphic_G ( italic_z , italic_K , italic_ω ) the direction-dependent optical density of states specified in Appendix A. | In the calculations of optical cavities in Sec. III.1, the photon numbers are calculated by making direct use of the FED description deployed in Ref. 12. This description is well suited for calculating the net emission of a single layer assumed to have a given temperature and quasi-Fermi level separation. In Sec. III.2... | To recap, the objective of this Subsection is to study whether the total emission of extremely thin layers can be boosted with cavity effects and by how much. To do that, Eq. (1) is solved for structures illustrated in Fig. 1, with the structure in Fig. 1(a) representing a thin-film intracavity device including both an... | The dependence of the optical power on the cavity length is first illustrated in Fig. 2 for the intracavity structure of Fig. 1(a) with a single example. Here, the thicknesses of the GaAs emitter and absorber layers are 20 and 60 nm, respectively. As in Ref. 12, the emitted and absorbed optical powers depend on the cav... | The net RG rates [Rradsubscript𝑅𝑟𝑎𝑑R_{rad}italic_R start_POSTSUBSCRIPT italic_r italic_a italic_d end_POSTSUBSCRIPT in Eq. (1)] discussed in the previous paragraph for applied biases 0.8 V and 1.0 V are illustrated in more detail in Fig. 7. In Fig. 7, Rrad(z)subscript𝑅𝑟𝑎𝑑𝑧R_{rad}(z)italic_R start_POSTSUBS... | A |
Moreover, the eigenspectra of open cavities show both continuous and discrete branches [18, 19] and a non-singular transformation is required so that their topology is preserved [20, 21]. | Finally, from a numerical standpoint, the computation of resonances in open systems is complicated by the reflection of the leaky waves at the necessarily finite-grid boundaries. To tackle this issue, we use Perfectly Matched Layers (PML), whose analysis and performance for spectral problems have been extensively docum... | The scheme validated through this work suggests a viable way to design the shape of twin open cavities, i.e. those cavities intended to resonate with the same spectrum of a reference cavity, but having a different geometry. We have chosen examples to display the versatility of the approach, i.e. a resonant Helmholtz ca... | Perhaps the most striking and well-studied effect enabled by TA is cloaking, allowing perfect concealment of an arbitrary object using a singular transformation. However, another strategy proposed in the work by Li et al. [14], the so-called carpet cloak, requires non-singular transformations, making this route more s... | The stretch of the geometry induces an anisotropic density whose principal components are aligned with the radial and the tangential directions of the cavity, similarly to the invisibility cloak for axisymmetric obstacles see, e.g., [38]. This situation lends itself to the use of a layered arrangement of two homogeneou... | A |
0italic_q = 2 italic_k start_POSTSUBSCRIPT italic_p italic_r italic_o italic_b italic_e end_POSTSUBSCRIPT ≈ 0). At the very low frequency (<<<100 GHz) a Brillouin mode is expected to be detected in the SL (similarly to the one observed in STO) but is not since its characteristic period of oscillation (typically the one... | It is first worth mentioning that magnon mode at 0.7 THz has already been reported in BiFeO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT nanostructures [26] arising from a magnon mode folding caused by the magnetic cycloid. Such a mode can be excluded in our case since we have a confined and strained multiferroic n... | In this work, by analysing electron and X-ray diffraction patterns, we reveal the existence of rich multiple structural orders in a BiFeO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT/LaFeO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT (BFO/LFO) superlattice. We show that besides the known in-plane orthorhombic d... | The origin of this mode at 0.7 THz might have another origin. Different hypothesis can be discussed. First of all, one could envision also a shear acoustic mode folding. Considering the shear velocity of around 3000 m.s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT [30, 33, 38, 39], one can expect a zone cen... | Neutron diffraction data were collected on the long wavelength time-of-flight diffractometer WISH [41] located at the second target station of the ISIS Pulsed Neutron and Muon Source, United Kingdom. By nature, neutron diffraction allows the average structure of the whole superlattice (and the substrate) to be measured... | A |
In this section, we formulated the transport coefficients, specifically shear and bulk viscosities, for medium QGP following the theoretical framework developed in Ref. [46]. It is important to emphasize that this formulation is conducted in the limit of zero chemical potential. Furthermore, the analysis assumes the sy... | With the obtained values of the fit parameters in the Table 1, the thermodynamic variables are plotted as a function of the scaled temperature (solid line) in the Fig. (3) for the gluonic plasma as well as for the medium QGP along with the corresponding lattice findings. A decent match with the lattice data can be obse... | For the medium slightly out of equilibrium, the distribution function f(x,p)𝑓𝑥𝑝f(x,p)italic_f ( italic_x , italic_p ) could be written as | Now, while formulating the bulk viscosity for gluons, the coefficients 𝒜1subscript𝒜1\mathcal{A}_{1}caligraphic_A start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT(corresponding to ϵ1subscriptitalic-ϵ1\epsilon_{1}italic_ϵ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT) and 𝒜2subscript𝒜2\mathcal{A}_{2}caligraphic_A start_POSTSUBSCRIP... | It could also be realized that the deviation from the local equilibrium is related to the function ϕ(x,p)italic-ϕ𝑥𝑝\phi(x,p)italic_ϕ ( italic_x , italic_p ) as | B |
}-2\,t\,a-c_{x}=0.italic_b + italic_v start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT = 0 , 2 italic_a + italic_b start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT = 0 , 2 italic_b italic_v start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT + italic_a start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT - italic_t italic_b - italic_... | In terms of the matrix Y1subscript𝑌1Y_{1}italic_Y start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT appearing in (3.16), we have | In the first line we use (4.14), in the second one we use (3.13), and in the last one we use Proposition 3.9. | We use the first three to determine a,b,c𝑎𝑏𝑐a,b,citalic_a , italic_b , italic_c in terms of v𝑣vitalic_v and its derivatives, as claimed in (4.5). | In terms of (4.14) and cαsubscript𝑐𝛼c_{\alpha}italic_c start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT defined in (3.33), we have | C |
For our quasicrystal, there are five reflection planes (ℛℛ{\cal{R}}caligraphic_R) dividing the system into two mirror-symmetric halves. They bisect the edges of the central decagon at right angles; see Fig. 1(a). The flux associated with the plaquettes intersecting ℛℛ{\cal{R}}caligraphic_R are fixed by property (i). Fo... | The boundary states, on the other hand, are strongly localized along the edges leading to a nearly size-independent IPR. To quantitatively study the relation between the boundary states and the local imbalance, we introduce ΔN=∑regions|NA1−NA2|Δ𝑁subscriptregionssubscript𝑁subscript𝐴1subscript𝑁subscript𝐴2\Delta N=\... | Due to the imbalance (e.g. without any loss of generality, more A1subscript𝐴1A_{1}italic_A start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT sites compared to A2subscript𝐴2A_{2}italic_A start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT), the number of rows and columns in G𝐺Gitalic_G are different, leading to some eigenstates with zero ... | Figure 3: Distribution of the fermionic wave function for (a) the lowest-E𝐸Eitalic_E bulk state, and (b) two representative boundary states associated with the marked arrows in Fig. 1(d), respectively. The blob size denotes the probability of finding the state at that site, and the color (red/blue) represents the subl... | The Hamiltonian defined on any finite system reveals an interesting excitation spectrum; see, for instance, Fig. 1(d) for the density of states (DOS) at the isotropic point. While a naive interpretation might lead us to conclude the existence of a gapless phase (with E=0𝐸0E=0italic_E = 0) over a broad range of paramet... | D |
The number N𝑁Nitalic_N of single diodes for Diode A is about 300, and that for Diode B is 7, respectively. | On the other hand, under the negative-illumination, the linear curve moves up due to the photocurrent generation. | The current sources represent photocurrent generation, and the parallel resistances are shunt resistances of the p-n junctions. | Similarly, the zero-bias resistance RDsubscript𝑅𝐷R_{D}italic_R start_POSTSUBSCRIPT italic_D end_POSTSUBSCRIPT is the sum of the resistances in the series p-n junctions, such as RD=N×rDsubscript𝑅𝐷𝑁subscript𝑟𝐷R_{D}=N\times r_{D}italic_R start_POSTSUBSCRIPT italic_D end_POSTSUBSCRIPT = italic_N × italic_r start_POS... | The photocurrent is given by short-circuit current ISCsubscript𝐼𝑆𝐶I_{SC}italic_I start_POSTSUBSCRIPT italic_S italic_C end_POSTSUBSCRIPT. | B |
Most recently, the 15-year pulsar timing data collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) presented convincing evidence for a low-frequency Gravitational Wave Background (GWB) [11], potentially originating from PBHs [12]. Future space-based GW interferometers like LISA, BBO,... | In the vast landscape of cosmology, inflation emerges as a crucial concept that sheds light on fundamental characteristics of the observable universe at large scales. Inflation explains critical aspects of the universe’s structure, such as its immense size, uniformity, isotropy, and overall geometry. It gives rise to p... | PBHs have been proposed as potential constituents of dark matter, accounting for anywhere from a fraction to the entirety of its abundance. One of the primary mechanisms for PBH formation in the early universe involves the amplification of the primordial curvature perturbation spectrum. | When the perturbation associated with the PBH enters the horizon, the PBH’s mass is dictated by the horizon’s mass. The relationship between the scale of the perturbation and the mass of the PBH during formation is expressed as follows, | The fractional abundance of the primordial black holes as a function of their mass is shown in Fig. 6. We have used the benchmark point parameters of table 3. For only the first two BPs, the PBHs can explain dark matter in totality. The shaded regions correspond to the various observational constraints [95, 96, 17]. | B |
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