Related papers: Localization transitions and mobility edges in qua…
We construct families of symmetric, antisymmetric, and asymmetric solitary modes in one-dimensional bichromatic lattices with the second-harmonic-generating ($\chi ^{(2)}$) nonlinearity concentrated at a pair of sites placed at distance…
We propose a realization of the one-dimensional random dimer model and certain N-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the…
One way of making the transition between the quasi-long range order in a chain of S=1/2 spins coupled antiferromagnetically and the true long range order that occurs in a plane, is by assembling chains to make ladders of increasing width.…
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 develop a theory of two-dimensional Bloch-Landau-Zener (BLZ) oscillations of wavepackets in incommensurate moir\'e lattices under the influence of a weak linear gradient. Unlike periodic systems, aperiodic lattices lack translational…
The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies…
We study the effect of quasiperiodic perturbations on one-dimensional all-bands-flat lattice models. Such networks can be diagonalized by a finite sequence of local unitary transformations parameterized by angles $\theta_i$. Without loss of…
We study fermionic ladders with identical disorder along the leg direction. Following recent experiments we focus, in particular, on how an initial occupation imbalance evolves in time. By considering different initial states and different…
Coupling a 1D quasiperiodic interacting system to a Markovian bath, we study the avalanche instability of the many body localized phase numerically, finding that many body localization (MBL) is more stable in pseudorandom quasiperiodic…
We pinpoint the spectral decomposition for the Anderson tight-binding model with an unbounded random potential on the Bethe lattice of sufficiently large degree. We prove that there exist a finite number of mobility edges separating…
Moire lattices consist of two identical periodic structures overlaid with a relative rotation angle. Present even in everyday life, moire lattices have been also produced, e.g., with coupled graphene-hexagonal boron nitride monolayers,…
We investigate the properties of mobility edge in an Aubry-Andr\'e-Harper model with non-reciprocal long-range hopping. The results reveal that there can be a new type of mobility edge featuring both strength-dependent and scale-free…
We study the superfluid response and localization dynamics from static and mobile impurities. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a $\mathbb{U}(1)$ gauge…
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 investigate the dynamical evolution of a parity-time ($\mathcal{PT}$) symmetric extension of the Aubry-Andr\'{e} (AA) model, which exhibits the coincidence of a localization-delocalization transition point with a $\mathcal{PT}$ symmetry…
We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. Firstly, we strictly demonstrate that there exists an interesting dual mapping relation between $|a|<1$ and $|a|>1$ with regard to the potential…
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…
We show the localization transition and its effect on two dynamical processes for an extended Aubry-Andr\'e-Harper model with incommensurate on-site and hopping potentials. After specifying an extended Aubry-Andr\'e-Harper model, we check…
We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and non-fluctuating long-range hopping integrals . It was argued recently [A. Rodriguez at al.,…
We present non-linear dynamical features of two-photon double-cavity optical bistability exhibited by a three level ladder system in the mean field limit. The system exhibits a hump like feature in the lower branch of the bistable response,…