Related papers: Two critical localization lengths in the Anderson …
We explore the critical properties of the localization transition in the non-Hermitian Aubry-Andre-Stark (AAS) model with quasiperiodic and Stark potentials, where the non-Hermiticity comes from the nonreciprocal hopping. The localization…
We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced…
In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-) or many-body localized phase. This approximation, which consists in summing over the amplitudes of only the shortest…
In this work, we investigate the Anderson localization problems of the generalized Aubry-Andr\'{e} model (Ganeshan-Pixley-Das Sarma's model) with an unbounded quasi-periodic potential where the parameter $|\alpha|\geq1$. The Lyapunov…
We report a new attractive critical point occurring in the Anderson localization scaling flow of symplectic models on fractals. The scaling theory of Anderson localization predicts that in disordered symplectic two-dimensional systems weak…
Roughly half of numerical investigations of the Anderson transition are based on consideration of an associated quasi-1D system and postulation of one-parameter scaling for the minimal Lyapunov exponent. If this algorithm is taken…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
Subsequent to the ideas presented in our previous papers [J.Phys.: Condens. Matter {\bf 14} (2002) 13777 and Eur. Phys. J. B {\bf 42} (2004) 529], we discuss here in detail a new analytical approach to calculating the phase-diagram for the…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…
We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths $1/2$ and $1$…
We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of…
The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its…
We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are…
We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution…
We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expansion around the fixed point and the bifurcation parameter,…
The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified…