Related papers: Quantum ergodicity for the Anderson model on regul…
Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases…
We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the…
In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities,…
The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…
We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams…
We theoretically investigate the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots using an…
In analogy with usual Anderson localization taking place in time-independent disordered quantum systems where the disorder acts in configuration space, systems exposed to temporally disordered potentials can display Anderson localization in…
We study the propagation of coherent waves in a nonlinearly-induced random potential, and find regimes of self-organized criticality and other regimes where the nonlinear equivalent of Anderson localization prevails. The regime of…
The single particle eigenstates of the Aubry-Andr\'e-Harper model are known to show a delocalization-localization transition at a finite strength of the quasi-periodic disorder. In this work, we point out that an intimate relationship…
Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for…
We establish exponential localization for a two-particle Anderson model in a Euclidean space ${\mathbb R}^{d}$, $d\ge 1$, in presence of a non-trivial short-range interaction and a random external potential of the alloy type. Specifically,…
We generalize the two-channel (Edwards) fermion-boson model describing quantum transport in a background medium to the more realistic case of dispersive bosons. Using the variational exact diagonalization technique, we numerically solve the…
We prove that arithmetic quantum unique ergodicity holds on compact arithmetic quotients of $GL(2,\mathbb{Q}_p)$ for automorphic forms belonging to the principal series. We interpret this conclusion in terms of the equidistribution of…
We consider an Anderson lattice model with a spin 1/2 degenerated conduction electron band and localized ionic CEF-levels, classified according to the irreducible representation of the point group of the lattice. We present the…
We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic,…
We introduce and study a toy model for anomalous transport and Griffiths effects in one dimensional quantum disordered isolated systems near the Many-Body Localization (MBL) transitions. The model is constituted by a collection of 1d…
The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…
In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…