Related papers: Semiclassical shape resonances for magnetic Stark …
This work is about uniform, plane, singly connected, strictly regular Hall-plates with an arbitrary number of peripheral contacts exposed to a uniform magnetic field of arbitrary strength. The strictly regular symmetry is the highest…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
This paper is concerned with the asymptotics of resonances in the semiclassical limit $h\to 0^+$ for $2\times 2$ matrix Schr\"odinger operators in one dimension. We study the case where the two underlying classical Hamiltonian trajectories…
We review recent theoretical and experimental developments in magnetic Weyl semimetals, focusing on the electromagnetic responses emerging from the interplay of their electronic band topology and magnetism. We begin by introducing the…
We study the cyclotron resonance in the electron-hole joint Fermi surface of a type-II Weyl semimetal. In magnetic field, the electron and hole pockets touching at the Weyl node are hybridized to form quantized Landau levels corresponding…
We begin with the time-dependent electric and magnetic dipole solution of Maxwell's equations in Minkowski space. This Maxwell field is then used to determine the behavior of the gravitational field (the Weyl tensor) as a second-order…
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the…
We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$. The total energy includes the field energy $\beta \int B^2$ and we minimize over all particle states and magnetic…
We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit…
The Haldane pseudopotential construction has been an extremely powerful concept in quantum Hall physics --- it not only gives a minimal description of the space of Hamiltonians but also suggests special model Hamiltonians (those where…
In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable…
Recently, we introduced a mathematical framework for the quantization of a particle in a variable magnetic field. It consists in a modified form of the Weyl pseudodifferential calculus and a C*-algebraic setting, these two points of view…
In this article, we consider fixed spin 1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give some asymptotic expansions for the ground state and the ground state energy of the…
We present the first purely semiclassical calculation of the resonance spectrum in the Diamagnetic Kepler problem (DKP), a hydrogen atom in a constant magnetic field with $L_z =0$. The classical system is unbound and completely chaotic for…
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…
We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…
Shortly after the discovery of Weyl semimetals properties related to the topology of their bulk band structure have been observed, e.g. signatures of the chiral anomaly and Fermi arc surface states. These essentially single particle…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
The behavior of three-dimensional (3D) semimetals under strong magnetic fields is a topic of recurring interest in condensed matter physics. Recently, the advent of Weyl and Dirac semimetals has brought about an interesting platform for…
An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl…