Zero-frequency Limit Research Articles

Logarithmic soft theorems and soft spectra

Using universal predictions provided by classical soft theorems, we revisit the energy emission spectrum for gravitational scatterings of compact objects in the low-frequency expansion. We calculate this observable beyond the zero-frequency limit, retaining an exact dependence on the kinematics of the massive objects. This allows us to study independently the ultrarelativistic or massless limit, where we find agreement with the literature, and the small-deflection or post-Minkowskian (PM) limit, where we provide explicit results up to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(G5). These confirm that the high-velocity limit of a given PM order is smoothly connected to the corresponding massless result whenever the latter is analytic in the Newton constant G. We also provide explicit expressions for the waveforms to order ω−1, log ω, ω(log ω)2 in the soft limit, ω → 0, expanded up to sub-subleading PM order, as well as a conjecture for the logarithmic soft terms of the type ωn−1(log ω)n with n ≥ 3.

Dynamical tidal Love numbers of Kerr-like compact objects

We develop a framework to compute the tidal response of a Kerr-like compact object in terms of its reflectivity, compactness, and spin, both in the static and the frequency-dependent case. Here we focus on the low-frequency regime, which can be solved fully analytically. We highlight some remarkable novel features, in particular, the following: (i) Even in the zero-frequency limit, the tidal Love numbers (TLNs) depend on the linear-in-frequency dependence of the object’s reflectivity in a nontrivial way. (ii) Intriguingly, although the static limit of the (phenomenologically more interesting) frequency-dependent TLNs is continuous, it differs from the strictly static TLNs for compact objects other than black holes. This shows that earlier findings regarding the static TLNs of ultracompact objects correspond to a measure-zero region in the parameter space, though the logarithmic behavior of the TLNs in the black hole limit is retained. (iii) In the nonrotating case, the TLNs in the zero-frequency limit (just like for a black hole), except when the reflectivity is R=1+O(Mω), in which case they vanish with a model-dependent scaling, which is generically logarithmic, in the black-hole limit. The TLNs initially grow with frequency, for any nonzero reflectivity, and then display oscillations and resonances tied up with the quasinormal modes of the object. (iv) For rotating compact objects, the TLNs decrease when the reflectivity decreases or the rotation parameter increases. Our results lay the theoretical groundwork to develop model-independent tests of the nature of compact objects using tidal effects in gravitational-wave signals. Published by the American Physical Society 2024

Electronic and optical characteristics of CaLiX3 (X = Cl, Br, I) perovskite compounds using the Tran–Blaha modified Becke–Johnson potential

We present the results of a comprehensive investigation using the full-potential linearized augmented plane wave approach to analyze the structural characteristics, electronic structures, and optical spectra of the perovskite compounds CaLiX3 (X = Cl, Br, or I). Various functionals were employed to simulate the exchange–correlation interactions. The calculated equilibrium structural parameters, obtained using the generalized gradient approximation, are consistent with the existing findings in the literature. The computed electronic structures reveal that the Tran–Blaha modified Becke–Johnson potential significantly enhances the bandgap. For all CaLiX3 compounds studied, we predicted an indirect bandgap. Additionally, we observed a gradual decrease in the bandgap as the atomic size of the X element increases. The electronic states constituting the various energy bands were evaluated by computing the partial and total densities of states. In addition, we computed a variety of optical spectra, including the complex dielectric function, absorption coefficient, refractive index, extinction coefficient, reflectivity, and electron energy loss function. The results demonstrate that a decrease in the bandgap leads to an increase in the zero-frequency limit of the dielectric function ε(0). The origins of the peaks and structures in the optical spectra were identified.

Anisotropic quasi-static permittivity of rare-earth scandate single crystals measured by terahertz spectroscopy

We report the real-valued static and complex-valued quasi-static anisotropic permittivity parameters of rare-earth scandate orthorhombic single crystal GdScO3 (GSO), TbScO3 (TSO), and DyScO3 (DSO). Employing continuous-wave terahertz spectroscopy (0.2–1 THz), the complex permittivity was extracted using an anisotropic ambient-film-ambient model. Data obtained from multiple samples of the same oxides and different surface cuts were analyzed simultaneously. The zero-frequency limit of the modeled data indicates that at room temperature the real part of the dielectric tensor components for GSO are ɛa = 22.7, ɛb = 19.3, and ɛc = 28.1; for DSO, ɛa = 20.3, ɛb = 17.4, and ɛc = 31.1; and for TSO, ɛa = 21.6, ɛb = 18.1, and ɛc = 30.3, with a, b, and c crystallographic axes constituting the principal directions for the permittivity tensor. These results are in excellent agreement with expectations from theoretical computations and with scarcely available data from previous experimental studies. Furthermore, our results evidence a noticeable attenuation, which increases with frequency, and are very significant especially at the higher frequency end of the measurement and along the c-direction in all samples. We suggest the attenuation is most likely caused by the onset of absorption due to long-wavelength active optical phonon modes. These results are important for electronic and potential sub-terahertz applications (e.g., quarter-wave plate) benefiting from the large index contrast along different directions in these materials.

Revealing quasi-excitations in the low-density homogeneous electron gas with model exchange–correlation kernels

Time-dependent density functional theory within the linear response regime provides a solid mathematical framework to capture excitations. The accuracy of the theory, however, largely depends on the approximations for the exchange–correlation (xc) kernels. Away from the long-wavelength (or q = 0 short wave-vector) and zero-frequency (ω = 0) limit, the correlation contribution to the kernel becomes more relevant and dominant over exchange. The dielectric function, in principle, can encompass xc effects relevant to describe low-density physics. Furthermore, besides collective plasmon excitations, the dielectric function can reveal collective electron–hole excitations, often dubbed “ghost excitons.” Besides collective excitons, the physics of the low-density regime is rich, as exemplified by a static charge-density wave that was recently found for rs > 69, and was shown to be associated with softening of the plasmon mode. These excitations are seen to be present in much higher density 2D homogeneous electron gases of rs ≳ 4. In this work, we perform a thorough analysis with xc model kernels for excitations of various nature. The uniform electron gas, as a useful model of real metallic systems, is used as a platform for our analysis. We highlight the relevance of exact constraints as we display and explain screening and excitations in the low-density region.

General theory of the viscosity of liquids and solids from nonaffine particle motions.

A microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. This formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel. Finally, it provides a microscopic solution to Maxwell's interpolation problem of viscoelasticity by naturally recovering Newton's law of viscous flow and Hooke's law of elastic solids in two opposite limits.

Quantum control of substitutional effects on the S-involved optoelectronic properties of BeSxSe1-X ternary alloys

The research on the quantum control of substitutional effects in BeSxSe1-x ternary alloys opens up exciting opportunities in semiconductor device engineering, photovoltaic, optoelectronic integration, and quantum information processing. By understanding and manipulating the optoelectronic properties of these alloys, researchers can pave the way for advanced technologies with enhanced performance, efficiency, and functionality in various fields. We are investigating how S alloying affects the structural, electronic and optical properties of tin chalcogenide materials. We are assessing the energy band structure and optical properties of BeSxSe1-x (x = 0%, 25%, and 50%) materials using density functional theory (DFT) within a full potential linearized augmented plane wave method (FP-LAPW) framework. The theoretically expected band energy gaps of BeSxSe1-x compounds indicate that S alloying improves their electrical and optical performances, based on the assumptions used in our calculations. The majority of the bonds in the BeSxSe1-x materials (x = 0%, 25%, and 50%) are covalent. All ternary alloys and binary compounds with (x = 0%, 25%, and 50%) exhibit direct (R-Γ) band gap semiconductor behavior, with a band gap energy (Eg). Each alloy system shows a nonlinear increase in the band gap (Eg) with increasing x. As BeSxSe1-x compound belongs to strongly correlated systems, therefore modified Becke–Johnson potential is used to calculate formation enthalpy (ΔHf), and optical properties of the compounds. The intense peaks in the imaginary part of the dielectric function εi(ω) in each spectrum are contributed by chalcogen Se, Be, and S optical excitations. Similar to the trend of band gap variation (Eg) with x, the zero-frequency limit of each imaginary dielectric function as well as the extinction coefficient, refractive index, and real dielectric function, exhibit a corresponding trend of change.

Frequency-dependent Faraday and Kerr rotation in anisotropic nonsymmorphic Dirac semimetals

We calculate the frequency-dependent longitudinal and Hall conductivities and the Faraday and Kerr rotation angles for a single sheet of anisotropic Dirac semimetal protected by nonsymmorphic symmetry in the presence of a Zeeman term coupling to the out-of-plane component of the spin. While the Zeeman term causes a rotation of the plane of polarization of the light, the anisotropy causes the appearance of an elliptically polarized component in an initially linearly polarized beam. The two effects can be combined in a single complex Faraday rotation angle. At the zero-frequency limit, we find a finite value of the Faraday rotation angle, which is given by $2{\ensuremath{\alpha}}_{F}$, where ${\ensuremath{\alpha}}_{F}$ is the effective fine structure constant associated with the velocity of the linearly dispersing Dirac fermions. We also find a logarithmic enhancement of the Faraday (and Kerr) rotation angles as the frequency of the light approaches the absorption edge associated with the Zeeman-induced gap. While the enhancement is reduced by impurity scattering, it remains significant for an attainable level of material purity. These results indicate that two-dimensional Dirac materials protected by nonsymmorphic symmetry are responsive to Zeeman couplings and can be used as platforms for magneto-optic applications, such as the realization of polarization-rotating devices.

Bulk viscosity of resonantly interacting fermions in the quantum virial expansion

We consider two-component fermions with a zero-range interaction both in two and three dimensions and calculate the bulk viscosity for an arbitrary scattering length in the high-temperature regime. We evaluate the Kubo formula for the bulk viscosity using an expansion with respect to the fugacity, which acts as a small parameter at high temperatures. In the zero-frequency limit of the Kubo formula, pinch singularities emerge that reduce the order of the fugacity by one. These singularities can turn higher-order vertex corrections at nonzero frequencies into the leading order at zero frequency, so that all such contributions have to be resummed. We present an exact microscopic computation for the bulk viscosity in the high-temperature regime by taking into account these pinch singularities. For negative scattering lengths, we derive the complete bulk viscosity at second order in fugacity and show that a self-consistent equation to resum the vertex corrections is identical to a linearized kinetic equation. For positive scattering lengths, a new type of pinch singularity arises for bound pairs. We show that the pinch singularity for bound pairs leads to a first-order contribution to the bulk viscosity, which is one order lower than that for negative scattering lengths, and that the vertex corrections also provide first-order contributions. We propose a new kinetic equation for bound pairs that derives from a self-consistent equation to resum the vertex corrections.

Drude weights in one-dimensional systems with a single defect

Ballistic transport of a quantum system can be characterized by Drude weight, which quantifies the response of the system to a uniform electric field in the infinitely long timescale. The Drude weight is often discussed in terms of the Kohn formula, which gives the Drude weight by the derivative of the energy eigenvalue of a finite-size system with the periodic boundary condition in terms of the Aharonov-Bohm flux. Recently, the Kohn formula is generalized to nonlinear responses. However, the nonlinear Drude weight determined by the Kohn formula often diverges in the thermodynamic limit. In order to elucidate the issue, in this work we examine a simple example of a one-dimensional tight-binding model in the presence of a single defect at zero temperature. We find that its linear and non-linear Drude weights given by the Kohn formula (i) depend on the Aharonov-Bohm flux and (ii) diverge proportionally to a power of the system size. We argue that the problem can be attributed to different order of limits. The Drude weight according to the Kohn formula (``Kohn--Drude weight'') indicates the response of a finite-size system to an adiabatic insertion of the Aharonov-Bohm flux. While it is a well-defined physical quantity for a finite-size system, its thermodynamic limit does not always describe the ballistic transport of the bulk. The latter should be rather characterized by a ``bulk Drude weight'' defined by taking the thermodynamic limit first before the zero-frequency limit. While the potential issue of the order of limits has been sometimes discussed within the linear response, the discrepancy between the two limits is amplified in nonlinear Drude weights. We demonstrate the importance of the low-energy excitations of $O(1/L)$, which are excluded from the Kohn--Drude weight, in regularizing the bulk Drude weight.

Thermal conductivity of a weakly interacting Bose gas in quasi-one-dimension.

Transport coefficients are typically divergent for quantum integrable systems in one dimension, such as a Bose gas with a two-body contact interaction. However, when a one-dimensional system is realized by confining bosons into a tight matter waveguide, an effective three-body interaction inevitably arises as leading perturbation to break the integrability. This fact motivates us to study the thermal conductivity of a Bose gas in one dimension with both two-body and three-body interactions. In particular, we evaluate the Kubo formula exactly to the lowest order in perturbation by summing up all contributions that are naively higher orders in perturbation but become comparable in the zero-frequency limit due to the pinch singularity. Consequently, a self-consistent equationfor a vertex function is derived, showing that the thermal conductivity in quasi-one-dimension is dominated by the three-body interaction rather than the two-body interaction. Furthermore, the resulting thermal conductivity in the weak-coupling limit proves to be identical to that computed based on the quantum Boltzmann equation and its temperature dependence is numerically determined.

Tunable bulk photovoltaic effect in strained γ -GeSe

Recently, Lee et al. [Nano Lett. 21, 4305 (2021)] synthesized the monochalcogenide GeSe in a polar phase, referred to as the $\ensuremath{\gamma}$-phase. Motivated by this work, we study the shift current of $\ensuremath{\gamma}$-GeSe and its tunability via an in-plane uniaxial strain. Using first-principles calculations, we uncover the electronic structure of strained $\ensuremath{\gamma}$-GeSe systems. We then calculate the frequency-dependent shift current conductivities at various strains. The tunability increases the shift current to $\ensuremath{\sim}40$ $\ensuremath{\mu}{\mathrm{A/V}}^{2}$ for visible light. Moreover, the direction of the shift current can be inverted by a light strain. Markedly, noticeable behavior is found in the zero-frequency limit, which can be indicative of band inversion and electronic phase transition driven by the strain. Our results suggest that the shift current can be tangible proof of bulk electronic states of $\ensuremath{\gamma}$-GeSe.

Variable thermal transport in black, blue, and violet phosphorene from extensive atomistic simulations with a neuroevolution potential

Phosphorus has diverse chemical bonds, and even in its two-dimensional form, there are three stable allotropes: black phosphorene (Black-P), blue phosphorene (Blue-P), and violet phosphorene (Violet-P). Due to the complexity of these structures, no efficient and accurate classical interatomic potential has been developed for them. In this paper, we develop an efficient machine-learned neuroevolution potential model for these allotropes and apply it to study thermal transport in them via extensive molecular dynamics (MD) simulations. Based on the homogeneous nonequilibrium MD method, the thermal conductivities are predicted to be 12.5±0.2 (Black-P in armchair direction), 78.4±0.4 (Black-P in zigzag direction), 128±3 (Blue-P), and 2.36±0.05 (Violet-P) Wm−1K−1. The underlying reasons for the significantly different thermal conductivity values in these allotropes are unraveled through spectral decomposition, phonon eigenmodes, and phonon participation ratio. Under external tensile strain, the thermal conductivity in black-P and violet-P are finite, while that in blue-P appears unbounded due to the linearization of the flexural phonon dispersion that increases the phonon mean free paths in the zero-frequency limit.

Dynamical Born effective charges

We extend the definition of the Born effective charge to the dynamical regime. This is equal to the Fourier transform of the total electronic current divided by the Fourier transform of the velocity of a particular nucleus. The usual static Born effective charges are recovered in the zero-frequency limit. We calculate these charges for a selection of materials using time-dependent density functional theory in an all-electron code where the nuclei move along a chosen trajectory. A rich response function emerges with prominent resonance peaks. The finite value for the Born effective charge of metals is also reproduced. The dynamical Born effective charges are thus a natural choice of observable for probing the fundamental nonadiabatic coupling of electrons and nuclei.

Fluctuating hydrodynamics of dilute electrolyte solutions: systematic perturbation calculation of effective transport coefficients governing large-scale dynamics

We study the transport properties of dilute electrolyte solutions on the basis of the fluctuating hydrodynamic equation, which is a set of nonlinear Langevin equations for the ion densities and flow velocity. The nonlinearity of the Langevin equations generally leads to effective kinetic coefficients for the deterministic dynamics of the average ion densities and flow velocity; the effective coefficients generally differ from the counterparts in the Langevin equations and are frequency-dependent. Using the path-integral formalism involving auxiliary fields, we perform systematic perturbation calculations of the effective kinetic coefficients for ion diffusion, shear viscosity, and electrical conductivity, which govern the dynamics on the large length scales. As novel contributions, we study the frequency dependence of the viscosity and conductivity in the one-loop approximation. Regarding the conductivity at finite frequencies, we derive the so-called electrophoretic part in addition to the relaxation part, where the latter has originally been obtained by Debye and Falkenhagen; it is predicted that the combination of these two parts gives rise to the frequency ω max proportional to the salt density, at which the real part of the conductivity exhibits a maximum. The zero-frequency limits of the conductivity and shear viscosity coincide with the classical limiting laws for dilute solutions, derived in different means by Debye, Falkenhagen, and Onsager. As for the effective kinetic coefficients for slow ion diffusions in large length scales, our straightforward calculation yields the cross kinetic coefficient between cations and anions. Further, we discuss the possibility of extending the present study to more concentrated solutions.

Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis

We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.

Freezing and thawing magnetic droplet solitons.

Magnetic droplets are non-topological magnetodynamical solitons displaying a wide range of complex dynamic phenomena with potential for microwave signal generation. Bubbles, on the other hand, are internally static cylindrical magnetic domains, stabilized by external fields and magnetostatic interactions. In its original theory, the droplet was described as an imminently collapsing bubble stabilized by spin transfer torque and, in its zero-frequency limit, as equivalent to a bubble. Without nanoscale lateral confinement, pinning, or an external applied field, such a nanobubble is unstable, and should collapse. Here, we show that we can freeze dynamic droplets into static nanobubbles by decreasing the magnetic field. While the bubble has virtually the same resistance as the droplet, all signs of low-frequency microwave noise disappear. The transition is fully reversible and the bubble can be thawed back into a droplet if the magnetic field is increased under current. Whereas the droplet collapses without a sustaining current, the bubble is highly stable and remains intact for days without external drive. Electrical measurements are complemented by direct observation using scanning transmission x-ray microscopy, which corroborates the analysis and confirms that the bubble is stabilized by pinning.

Mass of Abrikosov vortex in high-temperature superconductor YBa_2Cu_3O_{7-delta }

For more than four decades, mass of Abrikosov vortices defied experimental observations. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBa_2Cu_3O_{7-delta } film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex core and yield the diagonal fluxon mass of 2.2 times 10^8 electron masses per centimeter at 45 K and zero-frequency limit, and even larger off-diagonal mass of 4.9 times 10^8 m_e/cm.

Application of radial basis functions neutral networks in spectral functions

The reconstruction of spectral function from correlation function in Euclidean space is a challenging task. In this paper, we employ the Machine Learning techniques in terms of the radial basis functions networks to reconstruct the spectral function from a finite number of correlation data. To test our method, we first generate one type of correlation data using a mock spectral function by mixing several Breit-Wigner propagators. We found that compared with other traditional methods, TSVD, Tikhonov, and MEM, our approach gives a continuous and unified reconstruction for both positive definite and negative spectral function, which is especially useful for studying the QCD phase transition. Moreover, our approach has considerably better performance in the low frequency region. This has advantages for the extraction of transport coefficients which are related to the zero frequency limit of the spectral function. With the mock data generated through a model spectral function of stress energy tensor, we find our method gives a precise and stable extraction of the transport coefficients.

Infrared divergences and the eikonal exponentiation

The aim of this article is to explore the interplay between the eikonal resummation in impact-parameter space and the exponentiation of infrared divergences in momentum space for gravity amplitudes describing collisions of massive objects. The eikonal governs the classical dynamics relevant to the two-body problem, and its infrared properties are directly linked to the zero-frequency limit of the gravitational wave emission spectrum and to radiation-reaction effects. Combining eikonal and infrared exponentiations it is possible to derive these properties at a given loop order starting from lower-loop data. This is illustrated explicitly in $\mathcal{N}=8$ supergravity and in general relativity by deriving the divergent part of the two-loop eikonal from tree-level and one-loop elastic amplitudes.