相关论文: Mobility Edge for the Anderson Model on the Bethe …

We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…

The location of the mobility edge is a long standing problem in Anderson localization. In this paper, we show that the effective confining potential introduced in the localization landscape (LL) theory predicts the onset of delocalization…

The energy level spacing distribution of a tight-binding hamiltonian is monitored across the mobility edge for a fixed disorder strength. Any mixing of extended and localized levels is avoided in the configurational averages, thus…

We construct a quasiperiodic lattice model in curved spacetime to explore the crossover concerning both condensed matter and curved spacetime physics. We study the related Anderson localization and find that the model has a clear boundary…

Localization properties of non-interacting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy…

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge…

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…

We revisit the Anderson localization problem on Bethe lattices, putting in contact various aspects which have been previously only discussed separately. For the case of connectivity 3 we compute by the cavity method the density of states…

We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.

We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. Demarcating boundaries between localised and extended states in the space of system parameters and energy,…

In this paper we consider some Anderson type models, with decaying randomness and the free parts having long range tails. The randomness may decay at different rates in different directions, though in majority of directions we require some…

Recent experiments on non-interacting ultra-cold atoms in correlated disorder have yielded conflicting results regarding the so-called mobility edge, i.e. the energy threshold separating Anderson localized from diffusive states. At the same…

Mobility edges commonly arise in one-dimensional quasiperiodic systems once exact self-duality is broken, yet their origin is typically understood only at the level of individual Hamiltonians. Here we show that mobility edge positions are…

In this Letter we study numerically the Anderson model on partially disordered random regular graphs (RRG) considered as the toy model for a Hilbert space of interacting disordered many-body system. The protected subsector of zero-energy…

It is shown, using high-precision numerical simulations, that the mobility edge of the 3d Anderson model depends on the boundary hopping term t in the infinite size limit. The critical exponent is independent of it. The renormalized…

We investigate the appearance of mobility edges in a one-dimensional non-Hermitian tight-banding model with alternating hopping constants and slowly varying quasi-periodic on-site potentials. Due to the presence of slowly varying exponent,…

We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport…

In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the…

Hyperbolic lattices, formed by tessellating the hyperbolic plane with regular polygons, exhibit a diverse range of exotic physical phenomena beyond conventional Euclidean lattices. Here, we investigate the impact of disorder on hyperbolic…

We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands…