Related papers: Scattering for general-type Dirac systems on the s…
Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone is introduced to study resonances in any energy region for the Stark Hamiltonians with non-globally analytic potentials. The non-trapping resolvent…
We study a general limiting framework for the convergence of sequences of additive functionals of diffusions to L\'evy subordinators, and provide explicit sufficient conditions that both ensure convergence and characterize the law of the…
We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features…
In this work, we investigate the emergence of Weyl points in an inversion symmetry-breaking 1T-NiTe$_2$ system. Through first-principles calculations based on the density functional theory combined with tight-binding methods, we find three…
We study Weyl-type perturbation theorems in the context of linear closed relations. We establish general results on perturbations for dissipative relations. In the particular case of selfadjoint relations, we study finite-rank perturbations…
In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different…
A low-energy model is built to study systems such as Dirac/Weyl semimetals, according to statistical quantum electrodynamics formalism. We report that the introduction of a pseudoscalar, associated to longitudinal photons propagating along…
The exact solution of the Dirac equation for fermions coupled to an external periodic chiral condensate (chiral spiral) is used to obtain the exact formula for the Wigner function (up to the quantum loop corrections). We find that the…
In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
We apply the method of self-adjoint extensions of Hermitian operators to the low-energy, continuum Hamiltonians of Weyl semimetals in bounded geometries and derive the spectrum of the surface states on the boundary. This allows for the full…
We study canonical systems that are reflectionless on an open set. In this situation, the two half line $m$ functions are holomorphic continuations of each other and may thus be combined into a single holomorphic function. This idea was…
We review some recent rigorous results on the semiclassical behavior ($\epsilon\downarrow0$) of the scattering data of a non-self-adjoint Dirac operator with potential $A\exp\{iS/\epsilon\}$ where both $A$ and $S$ are differentiable…
We solve the noncommutative Noether's problem for the reflection groups by showing that the skew field of the invariants of the Weyl algebra under the action of any reection group is a Weyl field, that is isomorphic to a skew field of some…
We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the…
Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by…
We study particular classes of states on the Weyl algebra $\mathcal{W}$ associated with a symplectic vector space $S$ and on the von Neumann algebras generated in representations of $\mathcal{W}$. Applications in quantum physics require an…
We show that hybrid Dirac and Weyl semimetals can be realized in a three-dimensional Luttinger semimetal with quadratic band touching (QBT). We illustrate this using periodic kicking scheme. In particular, we focus on a momentum-dependent…
The Weyl-Sims classification for a second-order ordinary differential equation with general complex coefficients is investigated. Connections are then established between the associated m-function and the spectral properties of…
Let g be a complex semisimple Lie algebra, and f : g --> g/G the adjoint quotient map. Springer theory of Weyl group representations can be seen as the study of the singularities of f. We give a generalization of Springer theory to visible,…