Related papers: Genuine localisation transition in a long-range ho…
We consider a quantized version of the Sinai-Derrida model for "random walk in random environment". The model is defined in terms of a Lindblad master equation. For a ring geometry (a chain with periodic boundary condition) it features a…
We investigate a one-dimensional tight-binding model in which onsite potentials $\{\varepsilon_i\}$ exhibit power-law spatial correlations (with exponent $\alpha$) and the hopping amplitudes decay as $t_{ij}\sim |i-j|^{-\beta}$. This…
We present strong numerical evidence for the existence of a localization-delocalization transition in the eigenstates of the 1-D Anderson model with long-range hierarchical hopping. Hierarchical models are important because of the…
We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite range hopping coupling (independent of the position). Due to long range homogeneous hopping, a gap between the ground state and the excited…
In disordered systems, the amplitudes of the localized states will decrease exponentially away from their centers and the localization lengths are characterizing such decreasing. In this article, we find a model in which each eigenstate is…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
We study biased random walkers on lattices with randomly dispersed static traps in one, two and three dimensions. As the external bias is increased from zero the system undergoes a phase transition, most clearly manifested in the asymptotic…
We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a…
The presence of a topologically non-trivial discrete invariants implies the existence of gapless modes in finite samples, but it does not necessarily imply their localization. The disappearance of the indirect energy gap in the bulk…
Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi…
The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered…
Real materials always contain, to some extent, randomness in the form of defects or irregularities. It is known since the seminal work of Anderson that randomness can drive a metallic phase to an insulating one, and the mechanism…
A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are…
Recent advance in quantum simulations of interacting photons using superconducting circuits offers opportunities for investigating the Bose-Hubbard model in various geometries with hopping coefficients and self-interactions tuned to both…
We will derive here the relaxation behavior of a simple quantum random matrix model. The aim is to derive the effective equations which rise when a random matrix interaction is taken in the weak coupling limit. The physical situation this…
We investigate the stability of current-carrying states with quasi-momentum $K$ in the Bose-condensed phase of the hard-core Bose-Hubbard model on a square lattice, where particles transfer between two sites separated by distance $r$ with…
In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…