Related papers: Multi-particle localization at low energy for the …
We study the finite-time dynamics of an initially localized wave-packet in the Anderson model on the random regular graph (RRG). Considering the full probability distribution $\Pi(x,t)$ of a particle to be at some distance $x$ from the…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
We formulate empirically the rapidity density distribution of produced particles in multiple particle production. The assumed mechanism is that the produced particles are emitted isotropically from several emitting centers, located on the…
In this paper we consider an Anderson model with a large number of sites with zero interaction. For such models we study the spectral statistics in the region of complete localization. We show that Poisson statistics holds for such…
Anderson localization is a universal phenomenon affecting non-interacting quantum particles in disorder. In three spatial dimensions it becomes particularly interesting to study because of the presence of a quantum phase transition from…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
We prove the complete spectral and the strong dynamical Anderson localization in a two-particle random Schr\"odinger operators with the Poisson potential. The results apply with sufficiently weak interaction between the particle system.
Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum…
We consider a one-dimensional Anderson model where the potential decays in average like $n^{-\alpha}$, $\alpha>0$. This simple model is known to display a rich phase diagram with different kinds of spectrum arising as the decay rate…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be…
A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum particle in multi-dimensional Euclidean space under the influence of suitable random potentials has almost surely a pure-point component. The…
Disordered systems provide paradigmatic instances of ergodicity breaking and localization phenomena. Here we explore the dynamics of excitations in a system of Rydberg atoms held in optical tweezers. The finite temperature produces an…
We demonstrate that in pair plasma weakly nonlinear electromagnetic waves, $a_0 \leq 1$, experience Anderson self-localization. The beat between the driver and a back-scattered wave creates charge-neutral, large random density fluctuations…
We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where {\it all the particles are different} (APD). The equilibrium properties of this APD system were studied in our earlier work…
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by F\"urstenberg's theorem. That is, a…
Electronic properties of amorphous or non-crystalline disordered solids are often modelled by one-particle Schroedinger operators with random potentials which are ergodic with respect to the full group of Euclidean translations. We give a…
We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength U. The two-body problem is exactly mapped into an effective…
We consider a two-particle quantum systems in a d-dimensional Euclidean space with interaction and in presence of a random external potential (a continuous two-particle Anderson model). We establish Wegner-type estimates (inequalities) for…
We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case…