Related papers: Lifshits tails for randomly twisted quantum wavegu…
We study diffraction catastrophes of wave functions in diffeomorphism invariant quantum theories, for which $\hat H\Psi=0$. These wave functions can be represented in terms of integrations over cycles in a complexified lapse variable $N$.…
We study the ergodic properties of Delone-Anderson operators, using the framework of randomly coloured Delone sets and Delone dynamical systems. In particular, we show the existence of the integrated density of states and, under some…
We consider Schr\"odinger operators on $L^2(R^d)$ with a random potential concentrated near the surface $R^{d_1}\times\{0\}\subset R^d $. We prove that the integrated density of states of such operators exhibits Lifshits tails near the…
In the present note, we determine the ground state energy and study the existence of Lifshitz tails near this energy for some non monotonous alloy type models. Here, non monotonous means that the single site potential coming into the alloy…
We investigate the behavior near zero of the integrated density of states $\ell$ for random Schr\"{o}dinger operators $\Phi(-\Delta) + V^{\omega}$ in $L^2(\mathbb R^d)$, $d \geq 1$, where $\Phi$ is a complete Bernstein function such that…
We establish the Lifschitz-type singularity around the bottom of the spectrum for the integrated density of states for a class of subordinate Brownian motions in presence of the nonnegative Poissonian random potentials, possibly of infinite…
The properties of semiconductors, insulators, and photonic crystals are defined by their electronic or photonic bands, and the gaps between them. When the material is disordered, Lifshitz tails appear: these are localized states that…
We study the asymptotic behaviour of stationary densities of one-dimensional random diffeomorphisms, at the boundaries of their support, which correspond to deterministic fixed points of extremal diffeomorphisms. In particular, we show how…
This paper is devoted to the asymptotics of the density of surfacic states near the spectral edges for a discrete surfacic Anderson model. Two types of spectral edges have to be considered : fluctuating edges and stable edges. Each type has…
We consider Schr\"{o}dinger operators on $L^{2}({\mathbb R}^{d})\otimes L^{2}({\mathbb R}^{\ell})$ of the form $ H_{\omega}~=~H_{\perp}\otimes I_{\parallel} + I_{\perp} \otimes {H_\parallel} + V_{\omega}$, where $H_{\perp}$ and…
In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis, called Lifshitz tails. In the case of asymmetric matrices,…
We consider the $d$-dimensional fractional Anderson model $(-\Delta)^\alpha+ V_\omega$ on $\ell^2(\mathbb Z^d)$ where $0<\alpha\leq 1$. Here $-\Delta$ is the negative discrete Laplacian and $V_\omega$ is the random Anderson potential…
This paper investigates the mathematical properties of independent-electron models for twisted bilayer graphene by examining the density-of-states of corresponding single-particle Hamiltonians using tools from semiclassical analysis. This…
In this work we investigate the nonperturbative decay dynamics of a quantum emitter coupled to a composite right/left handed transmission line (CRLH-TL). Our theory captures the contributions from the different spectral features of the…
We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under…
As put forth by Kerov in the early 1990s and elucidated in subsequent works, numerous properties of Wigner random matrices are shared by certain linear maps playing an important r\^ole in the representation theory of the symmetric group. We…
We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling…
We study the set of points returning infinitely often to a sequence of targets dependent on the starting points. With an assumption of decay of correlations for L1 against bounded variations, we prove a generalized quantitative recurrence…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
We make an overview of spectral-geometric effects of twisting and bending in quantum waveguides modelled by the Dirichlet Laplacian in an unbounded three-dimensional tube of uniform cross-section. We focus on the existence of Hardy-type…