Related papers: Multi-particle localization at low energy for the …
We extend the renormalized quasiparticle description of the symmetric Anderson model in a magnetic field $H$, developed in earlier work, to the non-symmetric model. The renormalized parameters are deduced from the low energy NRG fixed point…
Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this…
We present a scaling theory of the many-body localisation transition in terms of emergent, characteristic energyscales. The analysis is based on the decomposition of the eigenstates in the basis of trivially localised states, resolved in…
We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find…
Understanding random lasing is a formidable theoretical challenge. Unlike conventional lasers, random lasers have no resonator to trap light, they are highly multimode with potentially strong modal interactions and they are based on…
A one-dimensional system of masses with nearest-neighbor interactions and periodic boundary conditions is used to study mode decay and ergodicity in nonlinear, disordered systems. The system is given an initial periodic displacement, and…
We study the Anderson localization of atomic gases exposed to three-dimensional optical speckles by analyzing the statistics of the energy-level spacings. This method allows us to consider realistic models of the speckle patterns, taking…
We explore the potential of a static electric field to induce Anderson localization of light in a large three-dimensional (3D) cloud of randomly distributed, immobile atoms with a degenerate ground state (total angular momentum $J_g = 0$)…
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
We give a short summary of the fixed-energy Multi-Scale Analysis (MSA) of the Anderson tight binding model in dimension $d\ge 1$ and show that this technique admits a straightforward extension to multi-particle systems. We hope that this…
We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. Although a conventional perspective suggests that…
We use a bootstrap argument to enhance the eigensystem multiscale analysis, introduced by Elgart and Klein for proving localization for the Anderson model at high disorder. The eigensystem multiscale analysis studies finite volume…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
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…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…
We numerically study the dynamics of cold atoms in a two-dimensional disordered potential. We consider an anisotropic speckle potential and focus on the classical regime, which is relevant to some recent experiments. First, we study the…
We introduce a new approach for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model at high disorder. In contrast to the usual strategy, we do not study finite…
We show that many-body localization, which exists in tight-binding models, is unstable in a continuum. Irrespective of the dimensionality of the system, many-body localization does not survive the unbounded growth of the single-particle…
The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…