相关论文: Trace formula for dielectric cavities III: TE mode…
We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two…
Formulas for transverse conductance and dielectric permeability in quantum non-degenerate and Maxwellian collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles…
Under general assumptions, the numbers of semiclassical resonances is known to be bounded from above by a negative power of $h$ which is given by the fractal dimension of the trapped set. In this paper we provide examples of operators with…
Following the discovery of topological insulators (TIs), topological Dirac/Weyl semimetal has attracted much recent interest. A prevailing mechanism for the formation of Weyl points is by breaking time-reversal symmetry (TRS) or spatial…
The quantum-mechanical expression for the polarization of a crystalline solid does not bear any resemblance to the (trivial) expression for the dipole of a bounded crystallite; and in fact it has been proved via a conceptually different…
An overview is provided over the physics of dielectric microcavities with non-paraxial mode structure; examples are microdroplets and edge-emitting semiconductor microlasers. Particular attention is given to cavities in which two spatial…
The first switchable electric polarization in metals was recently discovered in bilayer and trilayer WTe2. Strangely, despite the tininess of the ordered polarization, the ferroelectricity survives up to 350 K, rendering the mechanism of…
The continuous spectrum to the spectral side of the Arthur-Selberg trace formula is described in terms of intertwining operators, whose normalising factors involve quotients of $L$-functions. In this paper, we derive two expressions in the…
Transverse acoustic (TA) phonon waves are analogous to electromagnetic waves and can carry a certain angular momentum. In this paper, we study the electron-TA phonon couplings in three-dimensional pentatellurides and explore the conditions…
We solve the Weyl electron scattered by a spherical step potential barrier. Tuning the incident energy and the potential radius, one can enter both quasiclassical and quantum regimes. Transport features related to far-field currents and…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
The local trace function introduced in \cite{Dut} is used to derive equations that relate multiwavelets and multiscaling functions in the context of a generalized multiresolution analysis, without appealing to filters. A construction of…
In this paper, the regularized trace formulas for a diffusion operator which include conformable fractional derivatives of order {\alpha} (0<{\alpha \leq 1}) is obtained.
We study theoretically the ultrafast electron dynamics of three-dimensional Weyl semimetals in the field of a laser pulse. For a circularly-polarized pulse, such dynamics is governed by topological resonance, which manifests itself as a…
We present a quantum model to calculate the dipole-dipole coupling between electronic excitations in the conduction band of semiconductor quantum wells. We demonstrate that the coupling depends on a characteristic length, related to the…
We investigate trace formulas in $\varepsilon$-deformed W-algebras, highlighting a novel connection to the modular double of $\mathfrak{q}$-deformed W-algebras. In particular, we show that torus correlators in the additive (Yangian) setting…
The trace formulas commonly used in discussing spectral properties of quantum or wave systems are derived simply and directly from the Bogomolny transfer operator. Special cases are the Gutzwiller formula, the Berry-Tabor formula, and the…
We present an analysis of electromagnetic oscillations in a spherical conducting cavity filled concentrically with either dielectric or vacuum layers. The fields are given analytically, and the resonant frequency is determined numerically.…
We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat…
We construct a trace map on the chiral homology of chiral Weyl algebra for any smooth Riemann surface. Our trace map can be viewed as a chiral version of the deformed HKR quasi-isomorphism. This also provides a mathematical rigorous…