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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…

Mathematical Physics · Physics 2015-05-20 Alexander Elgart , Martin Tautenhahn , Ivan Veselic'

We show that the functional renormalization group is a numerically cheap method to obtain the low-energy behavior of the Anderson impurity model describing a localized interacting electron coupled to a bath of conduction electrons. Our…

Strongly Correlated Electrons · Physics 2013-05-23 Simon Streib , Aldo Isidori , Peter Kopietz

We study the three-dimensional two-band Anderson model of localization and compare our results to experimental results for amorphous metallic alloys (AMA). Using the transfer-matrix method, we identify and characterize the metal-insulator…

Disordered Systems and Neural Networks · Physics 2009-11-10 I V Plyushchay , R A Roemer , M Schreiber

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…

Mathematical Physics · Physics 2014-07-18 Victor Chulaevsky

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 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

We investigate the zero-temperature metal-insulator transition in a one-dimensional two-component Fermi gas in the presence of a quasi-periodic potential resulting from the superposition of two optical lattices of equal intensity but…

Quantum Gases · Physics 2017-01-25 Sebastiano Pilati , Vipin Kerala Varma

We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schr\"odinger operators on $\mathbb{Z}^d$ with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on…

Mathematical Physics · Physics 2025-03-04 Hongyi Cao , Yunfeng Shi , Zhifei Zhang

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…

Analysis of PDEs · Mathematics 2021-04-30 Wilhelm Schlag

Real materials always contain, to some extent, randomness in the form of defects or irregularities. It is known since the seminal work of Anderson that randomness can drive a metallic phase to an insulating one, and the mechanism…

We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $\theta$ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field…

Disordered Systems and Neural Networks · Physics 2023-06-28 Ihor Vakulchyk , Sergej Flach

We prove the Wegner bounds for the one-dimensional interacting multi-particle Anderson models in the continuum. The results apply to singular probability distribution functions such as the Bernoulli's measures. The proofs need the amplitude…

Mathematical Physics · Physics 2017-06-20 Trésor Ekanga

Uncorrelated disorder potential in one-dimensional lattice definitely induces Anderson localization, while quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. We investigate the…

Disordered Systems and Neural Networks · Physics 2021-09-27 R. Wang , K. L. Zhang , Z. Song

Delone operators are Schr\"odinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given "single-site potential" centred at the points of a Delone set. In this paper, we use…

Mathematical Physics · Physics 2025-01-06 Peter Müller , Constanza Rojas-Molina

We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous…

Disordered Systems and Neural Networks · Physics 2011-02-16 J. Biddle , D. J. Priour , B. Wang , S. Das Sarma

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…

Spectral Theory · Mathematics 2010-06-29 Helge Krueger

It is classical, following Furstenberg's theorem on positive Lyapunov exponent for products of random SL$(2, \mathbb R)$ matrices, that the one dimensional random Schr\"odinger operator has Anderson localization at arbitrary disorder. This…

Mathematical Physics · Physics 2022-01-04 Wencai Liu , W. -M. Wang

The Typical Medium Theory provides conceptually the simplest order parameter description of Anderson localization by self-consistently calculating the geometrically-averaged (typical) local density of states (LDOS). Here we show how spatial…

Disordered Systems and Neural Networks · Physics 2016-08-08 Samiyeh Mahmoudian , Vladimir Dobrosavljević

We establish non-perturbative Anderson localization for a wide class of 1D quasiperiodic operators with unbounded monotone potentials, extending the classical results on Maryland model and perturbative results for analytic potentials by…

Spectral Theory · Mathematics 2018-11-20 Ilya Kachkovskiy

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.…

Mathematical Physics · Physics 2007-05-23 Victor Chulaevsky , Yuri Suhov