相关论文: Localization and mobility edge for sparsely random…

The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in…

Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2 model with finite…

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…

We analyze the disorder driven localization of the two dimensional Bose-Hubbard model by evaluating the full low energy quasiparticle spectrum via a recently developed fluctuation operator expansion method. For any strength of the local…

We consider a particular class of lattice Schr\"odinger operators with deterministic potentials depending upon an infinite number of parameters in an auxiliary measurable space. We prove exponential dynamical localization for generic…

In his influential work Choquet systematically studied capacities on Boolean algebras in a topological space, and gave a probabilistic interpretation for completely monotone (and completely alternating) capacities. Beyond complete…

In this paper we introduce and study a family of self-adjoint realizations of the Laplacian in $L^2(\mathbb{R}^2)$ with a new type of transmission conditions along a closed bi-Lipschitz curve $\Sigma$. These conditions incorporate jumps in…

We consider a two dimensional magnetic Schroedinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate…

A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…

We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a…

Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. This feature offers…

Objects driven through periodically modulated potential-energy landscapes in two dimensions can become locked in to symmetry-selected directions that are independent of the driving force's orientation. We investigate this problem in the…

We explore properties of a Gross-Pitaevskii chain subject to an incommensurate periodic potential, i.e., a nonlinear Aubry-Andre model. We show that the condensate crucially impacts the properties of the elementary excitations. In contrast…

We study a one-dimensional quasiperiodic system described by the Aubry-Andr\'e model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the…

We address that a single-band tight-binding Hamiltonian defined on a self-similar corral substrate can give rise to a set of non-diffusive localized modes that follow the same hierarchical distribution. As the lattice, the spatial extent of…

We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum, the resolvent on a large square is likely to decay…

In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon…

We show the existence of stable bound orbits for the massive and massless particles moving in the simplest microstate geometry spacetime in the bosonic sector of the five-dimensional minimal supergravity. In our analysis, reducing the…

We introduce and experimentally demonstrate a class of surface bound states with algebraic decay in a one-dimensional tight-binding lattice. Such states have an energy embedded in the spectrum of scattered states and are structurally stable…

We study the soliton mobility in nonlocal nonlinear media with an imprinted fading optical lattice. The results show that the transverse mobility of solitons varies with the lattice decay rate and the nonlocality degree, which provides an…