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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 study a Majorana zero-energy state bound to a hedgehog-like point defect in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac type effective Hamiltonian. We first give an explicit wave function of a Majorana…

Superconductivity · Physics 2011-10-11 Ken-Ichiro Imura , Takahiro Fukui , Takanori Fujiwara

We prove that at large disorder, Anderson localization in $\Z^d$ is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is…

Spectral Theory · Mathematics 2007-05-23 Avy Soffer , Wei-Min Wang

We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…

Mathematical Physics · Physics 2018-01-03 Günter Stolz

A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has…

Strongly Correlated Electrons · Physics 2022-10-20 Peru d'Ornellas , Ryan Barnett , Derek K. K. Lee

Disorder is ubiquitous in solid-state systems, and its crucial influence on transport properties was revealed by the discovery of Anderson localization. Generally speaking, all bulk states will be exponentially localized in the strong…

Disordered Systems and Neural Networks · Physics 2023-11-01 Tong Wang , Zhiming Pan , Keith Slevin , Tomi Ohtsuki

This paper is devoted to the study of the random displacement model on $\R^d$. We prove that, in the weak displacement regime, Anderson and dynamical localization holds near the bottom of the spectrum under a generic assumption on the…

Mathematical Physics · Physics 2015-05-13 Fatma Ghribi , Frédéric Klopp

We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic…

Disordered Systems and Neural Networks · Physics 2009-11-07 J. Heinrichs

In the present note we show dynamical localization for an Anderson model with missing sites in a discrete setting at the bottom of the spectrum in arbitrary dimension $d$. In this model, the random potential is defined on a relatively dense…

Mathematical Physics · Physics 2013-04-30 Constanza Rojas-Molina

In this paper, we study quasi-periodic CMV matrices with Verblunsky coefficients given by the skew-shift. We prove the positivity of Lyapunov exponents and Anderson localization for most frequencies, which establish the analogous results of…

Spectral Theory · Mathematics 2022-09-16 Yanxue Lin , Daxiong Piao , Shuzheng Guo

We elucidate the different mechanisms of wave localisation in disordered finite systems of subwavelength resonators, where the disorder is in the spatial arrangement of the resonators. To do so, we employ the capacitance matrix formalism…

Disordered Systems and Neural Networks · Physics 2025-07-10 Habib Ammari , Silvio Barandun , Alexander Uhlmann

By means of variable moment kernel polynomial method, we analyze the localization properties of $\beta$-graphyne sheet subjected to the Anderson disorder. To detect the localization transition we focus on the scaling behavior of the…

Materials Science · Physics 2021-01-20 G. X. Wang

We establish Anderson localization for 1-d discrete Schr\"odinger operators with positive weights. The distinctive feature of this work lies in the degeneracy of the weights, with both the potentials and weights assumed to be analytic and…

Mathematical Physics · Physics 2026-02-20 Yingdu Dong , Haoxuan Liu , Zuhong You , Xiaoping Yuan

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

Combining scattering matrix theory with non-linear $\sigma$-model and Keldysh technique we develop a unified theoretical approach enabling one to non-perturbatively study the effect of electron-electron interactions on weak localization and…

Mesoscale and Nanoscale Physics · Physics 2015-05-20 Dmitri S. Golubev , Andrew G. Semenov , Andrei D. Zaikin

We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…

We establish large sets of Anderson localized states for the quasi-periodic nonlinear Schr\"odinger equation on $\mathbb Z^d$, thus extending Anderson localization from the linear (cf. Bourgain [Geom. Funct. Anal., 17(3):682--706, 2007]) to…

Mathematical Physics · Physics 2026-04-20 Yunfeng Shi , W. -M. Wang

Effects of randomness have supplied fundamental problems in condensed matter physics and localization due to interference of quantum mechanical electrons are well studied as the Anderson localization. Although we have well established…

Disordered Systems and Neural Networks · Physics 2015-06-24 M. Kishi , Y. Hatsugai

Anderson localization of electron states on graphene lattice with diagonal and off-diagonal (OD) disorder in the absence of magnetic field is investigated by using the standard finite-size scaling analysis. In the presence of diagonal…

Disordered Systems and Neural Networks · Physics 2008-01-03 Shi-Jie Xiong , Ye Xiong

We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model, the Anderson-Edwards model. Using the density-matrix renormalization group…

Strongly Correlated Electrons · Physics 2015-06-11 S. Nishimoto , S. Ejima , H. Fehske