Related papers: Ballistic Behavior for Random Schr\"odinger Operat…
In this paper we study random perturbations of first order elliptic operators with periodic potentials. We are mostly interested in Hamiltonians modeling graphene antidot lattices with impurities. The unperturbed operator $H_0 := D_S + V_0$…
We consider Hermitian and symmetric random band matrices $H$ in $d \geq 1$ dimensions. The matrix elements $H_{xy}$, indexed by $x,y \in \Lambda \subset \Z^d$, are independent, uniformly distributed random variables if $\abs{x-y}$ is less…
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In these notes we give a review of the…
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles…
We diagonalise the Hamiltonian of the Temperley-Lieb loop model with open boundaries using a coordinate Bethe Ansatz calculation. We find that in the groundstate sector of the loop Hamiltonian, but not in other sectors, a certain constraint…
We consider Hermitian and symmetric random band matrices on the $d$-dimensional lattice $(\mathbb{Z}/L\mathbb{Z})^d$ with bandwidth $W$, focusing on local eigenvalue statistics at the spectral edge in the limit $W\to\infty$. Our analysis…
We study spectral properties of a system of two quantum particles on an integer lattice with a bounded short-range two-body interaction, in an external random potential field $V(x,\omega)$ with independent, identically distributed values.…
The Coordinate Bethe Ansatz (CBA) expresses, as a sum over permutations, the matrix element of an XXX Heisenberg spin chain Hamiltonian eigenstate with a state with fixed spins. These matrix elements comprise the wave functions of the…
We consider the Landau Hamiltonian perturbed by a long-range electric potential $V$. The spectrum of the perturbed operator consists of eigenvalue clusters which accumulate to the Landau levels. First, we obtain an estimate of the rate of…
We prove that the asymptotic distribution of resonances has a multilevel internal structure for the following classes of Hamiltonians H: Schr\"odinger operators with point interactions in $\mathbb{R}^3$, quantum graphs, and 1-D photonic…
The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…
The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…
We consider a macroscopic disordered system of free $d$-dimensional lattice fermions whose one-body Hamiltonian is a Schr\"{o}dinger operator $H$ with ergodic potential. We assume that the Fermi energy lies in the exponentially localized…
We study the semigroups of random Schr\"odinger operators of the form $\widehat{H}f=-\frac12f''+(V+\xi)f$, where $f:I\to\mathbb F^r$ ($\mathbb F=\mathbb R,\mathbb C,\mathbb H$) are vector-valued functions on a possibly infinite interval…
Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for…
The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lattice with $\delta$-type boundary conditions at the vertices,…
We study the localization properties of non-interacting waves propagating in a speckle-like potential superposed on a one-dimensional lattice. Using a decimation/renormalization procedure, we estimate the localization length for a…
As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the…
The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the…
We present analytically exact results to show that, certain quasi one-dimensional lattices where the building blocks are arranged in a random fashion, can have an absolutely continuous part in the energy spectrum when special correlations…