Related papers: Topology dependent quantities at the Anderson tran…
We report a novel scale-independent, Aharonov-Bohm flux controlled crossover from critical orthogonal to critical unitary statistics at the disorder induced metal insulator transition. Our numerical investigations show that at the critical…
The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension $\xt$. We consider the case when the boundary…
We analyze the scaling behavior of the higher Lyapunov exponents at the Anderson transition. We estimate the critical exponent and verify its universality and that of the critical conductance distribution for box, Gaussian and Lorentzian…
The Anderson metal-insulator transition is a continuous phase transition driven by disorder. It remains a challenging problem to theoretically determine universal critical properties at the transition. The Anderson transition in a model…
It is shown that the universal behavior of the spacing distribution of nearest energy levels at the metal--insulator Anderson transition is indeed dependent on the boundary conditions. The spectral rigidity $\Sigma^2(E)$ also depends on the…
A simple Kronig-Penney model for one-dimensional (1D) mesoscopic systems with $\delta $ peak potentials is used to study numerically the influence of a spatial disorder on the conductance fluctuations and distribution at different regimes.…
Recently we found an Anderson-type localization-delocalization transition in the QCD Dirac spectrum at high temperature. Using spectral statistics we obtained a critical exponent compatible with that of the corresponding Anderson model.…
Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the…
The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation…
Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling…
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 the critical dynamics of matter waves at the 3D Anderson mobility edge in cold-atom disorder quench experiments. General scaling arguments are supported by precision numerics for the spectral function, diffusion coefficient, and…
We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number $m+1 = 3$, with a box distribution of…
We report a numerical analysis of corrections to finite size scaling at the Anderson transition due to irrelevant scaling variables and non-linearities of the scaling variables. By taking proper account of these corrections, the…
The scaling behavior of the thermoelectric transport properties in disordered systems is studied in the energy region near the metal-insulator transition. Using an energy-dependent conductivity $\sigma$ obtained experimentally, we extend…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
Superconductor-topological insulator-superconductor Josephson junctions have been fabricated in order to study the width dependence of the critical current, normal state resistance and flux periodicity of the critical current modulation in…
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a…
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization…