Related papers: Non-perturbative localization for quasi-periodic J…

For an arbitrary Hermitian period-$T$ Jacobi operator, we assume a perturbation by a Wigner-von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, $S$, of the spectral…

Scale-free localization emerging in non-Hermitian physics has recently garnered significant attention. In this work, we explore the interplay between scale-free localization and Anderson localization by investigating a unidirectional…

We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence…

For the almost Mathieu operator $(H_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+2\lambda \cos2\pi(\theta+n\alpha)u_n$, Avila and Jitomirskaya guess that for a.e. $\theta$, $H_{\lambda,\alpha,\theta}$ satisfies Anderson localization if $…

We prove Anderson localization for all Diophantine frequencies and all non-resonant phases for a model that arises from 2D quantum walk model subject to an external magnetic field. This is the first localization result for all Diophantine…

The celebrated Kitaev chain reveals a captivating phase diagram in the presence of various disorders, encompassing multifractal states and topological Anderson phases. In this work, we investigate the localization and topological properties…

We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e.…

We explore to what extent the relation between the absolute continuous spectrum and non-existence of subordinate generalized eigenvectors, known for scalar Jacobi operators, can be formulated also for block Jacobi operators with…

In this paper, we study cubic and quintic nonlinear Schr\"odinger systems on 3-dimensional tori, with initial data in an adapted Hilbert space $H^s_{\underline{\lambda}},$ and all of our results hold on rational and irrational rectangular,…

We prove long time Anderson localization for nonlinear random Schroedinger equation in $\ell^2$ by making a Birkoff normal form type transform to creat an energy barrier where there is essentially no mode propagation. One of the new…

For the multi-particle Anderson model with correlated random potential in the continuum, we show under fairly general assumptions on the inter-particle interaction and the random external potential, the Anderson localization which consists…

The Wigner-von Neumann method, which was previously used for perturbing continuous Schr\"{o}dinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi…

The stability of localization in the presence of interactions remains an open problem, with finite-size effects posing significant challenges to numerical studies. In this work, we investigate the perturbative stability of noninteracting…

We investigate the role of a quasiperiodically driven electric field in a one-dimensional disordered fermionic chain. In the clean non-interacting case, we show the emergence of dynamical localization - a phenomenon previously known to…

We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…

We study Schr\"odinger operators on quantum graphs where the number of edges between points is determined by orbits of a "shift of finite type". We prove Anderson localization for these systems.

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…

The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially periodic roll solutions which are known to be stable against…

For tridiagonal block Jacobi operators, the standard transfer operator techniques only work if the off-diagonal entries are invertible. Under suitable assumptions on the range and kernel of these off-diagonal operators which assure a…

We prove that a disordered analog of the Su-Schrieffer-Heeger model exhibits dynamical localization (i.e. the fractional moments condition) at all energies except possibly zero energy, which is singled out by chiral symmetry. Localization…