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We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of…

Mathematical Physics · Physics 2017-02-15 Trésor Ekanga

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…

Quantum Gases · Physics 2020-10-16 Filippo Stellin , Giuliano Orso

We establish exponential localization for a multi-particle Anderson model in a Euclidean space of an arbitrary dimension, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we…

Mathematical Physics · Physics 2010-04-09 Anne Boutet de Monvel , Victor Chulaevsky , Peter Stollmann , Yuri Suhov

We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…

Mathematical Physics · Physics 2015-05-13 Michael Aizenman , Simone Warzel

This paper is a complement to our earlier work \cite{BCSS10b}. With the help of the multi-scale analysis, we derive, from estimates obtained in \cite{BCSS10b}, dynamical localization for a multi-particle Anderson model in a Euclidean space…

Mathematical Physics · Physics 2010-07-23 Victor Chulaevsky , Anne Boutet de Monvel , Yuri Suhov

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,…

Mathematical Physics · Physics 2014-02-28 Victor Chulaevsky

We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results…

Mathematical Physics · Physics 2020-04-07 Trésor Ekanga

We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice…

Mathematical Physics · Physics 2016-04-01 Raphael Ducatez

We consider a continuous one dimensional model of two charged interacting particles in a random potential. The electric repulsion is strictly one dimensional and it inhibits Anderson localization. In fact, the spectrum is continuous. The…

Disordered Systems and Neural Networks · Physics 2009-10-31 J. C. Flores

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…

Disordered Systems and Neural Networks · Physics 2015-05-30 Serpil Sucu , Saban Aktas , S. Erol Okan , Zehra Akdeniz , Patrizia Vignolo

We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical…

Mathematical Physics · Physics 2024-08-16 Nishant Rangamani , Xiaowen Zhu

We consider the multi-particle Anderson tight-binding model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low…

Mathematical Physics · Physics 2013-12-30 Trésor Ekanga

We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.

Mathematical Physics · Physics 2021-05-25 John Z. Imbrie

We show, using quasi-exact numerical simulations, that Anderson localization of one-dimensional particles in a disordered potential survives in the presence of attractive interaction between particles. The localization length of the…

We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel…

Disordered Systems and Neural Networks · Physics 2021-09-01 Reza Sepehrinia

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a d-dimensional lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.

Mathematical Physics · Physics 2009-11-13 Victor Chulaevsky , Yuri Suhov

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.

Mathematical Physics · Physics 2020-07-16 Trésor Ekanga

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,…

Mathematical Physics · Physics 2009-07-10 A. Boutet de Monvel , V. Chulaevsky , P. Stollmann , Y. Suhov

We consider the Anderson model with Bernoulli potential on the 3D lattice, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. We follow the framework by Bourgain-Kenig and…

Analysis of PDEs · Mathematics 2021-03-16 Linjun Li , Lingfu Zhang

A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling…

Strongly Correlated Electrons · Physics 2009-11-07 Matthew T. Glossop , David E. Logan