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The random hopping models exhibit many fascinating features, such as diverging localization length and density of states as energy approaches the bandcenter, due to its particle-hole symmetry. Nevertheless, such models are yet to be…

Quantum Gases · Physics 2012-02-22 Yue Zou , Ryan Barnett , Gil Refael

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

Many-body localization in an $XY$ model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping)…

Disordered Systems and Neural Networks · Physics 2015-11-17 Alexander L. Burin

In this paper we study spectral properties of Jacobi operators. In particular, we prove two main results: (1) that perturbing the diagonal coefficients of Jacobi operator, in an appropriate sense, results in exponential localization, and…

Spectral Theory · Mathematics 2016-09-20 Valmir Bucaj

A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A…

Disordered Systems and Neural Networks · Physics 2019-03-20 P. Nosov , I. M. Khaymovich , V. E. Kravtsov

We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by…

Disordered Systems and Neural Networks · Physics 2007-09-27 Md Fhokrul Islam , Hisao Nakanishi

In this paper, we study the interacting random particles with power-law long-rang hopping. Via the multi-scale analysis arguments for the Green's function, we establish the power-law localization for all energy with strong disorder.

Mathematical Physics · Physics 2025-03-26 Wenwen Jian , Yingte Sun

We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then,…

Statistical Mechanics · Physics 2007-05-23 G. C. Ferrario , V. G. Benza

We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not…

Spectral Theory · Mathematics 2012-10-11 François Germinet , Frédéric Klopp

Reentrant localization has recently been observed in systems with quasi-periodic nearest-neighbor hopping, where the interplay between dimerized hopping and staggered disorder is identified as the driving mechanism. However, the robustness…

Disordered Systems and Neural Networks · Physics 2024-12-19 Pei-Jie Chang , Qi-Bo Zeng , Jinghui Pi , Dong Ruan , Gui-Lu Long

We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a…

Disordered Systems and Neural Networks · Physics 2026-04-22 Bibek Saha , Sthitadhi Roy

We study states arising from fluctuations in the disorder potential in systems with long-range hopping. Here, contrary to systems with short-range hopping, the optimal fluctuations of disorder responsible for the formation of the states in…

Disordered Systems and Neural Networks · Physics 2024-02-21 V. Temkin , A. S. Ioselevich

We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The potentials are located on a randomly distorted lattice…

Mathematical Physics · Physics 2016-04-06 Henrik Ueberschaer

We prove power-law dynamical localization for polynomial long-range hopping lattice operators with uniform electric field under any bounded perturbation. Actually, we introduce new arguments in the study of dynamical localization for…

Functional Analysis · Mathematics 2026-03-18 M. Aloisio

Some properties of $d$-dimensional disordered models with long-range random hopping amplitudes are investigated numerically at criticality. We concentrate on the correlation dimension $d_2$ (for $d=2$) and the nearest level spacing…

Disordered Systems and Neural Networks · Physics 2007-05-23 E. Cuevas

We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping…

Quantum Physics · Physics 2009-11-10 L. F. Santos , M. I. Dykman , M. Shapiro , F. M. Izrailev

We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…

Mathematical Physics · Physics 2016-11-18 Alexander Elgart , Mira Shamis , Sasha Sodin

We prove that the random Schrodinger operators on $\mathbb{R}^3$ with independent, identically distributed random variables and single-site potentials given by $\delta$-functions on $\mathbb{Z}^3$, exhibit both dynamical localization and…

Mathematical Physics · Physics 2025-09-03 Peter D. Hislop , Werner Kirsch , M. Krishna

In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the…

Mathematical Physics · Physics 2009-02-26 François Germinet , Abel Klein , Benoît Mandy

We investigate a one-dimensional tight-binding model in which onsite potentials $\{\varepsilon_i\}$ exhibit power-law spatial correlations (with exponent $\alpha$) and the hopping amplitudes decay as $t_{ij}\sim |i-j|^{-\beta}$. This…

Strongly Correlated Electrons · Physics 2025-11-25 Mohammad Pouranvari