Related papers: Finite-time scaling at the Anderson transition for…
We investigate Anderson localization in a three dimensional (3d) kicked rotor. By a finite size scaling analysis we have identified a mobility edge for a certain value of the kicking strength $k = k_c$. For $k > k_c$ dynamical localization…
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 transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to…
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling…
To date the most precise estimations of the critical exponent for the Anderson transition have been made using the transfer matrix method. This method involves the simulation of extremely long quasi one-dimensional systems. The method is…
The Anderson localization transition is one of the most well studied examples of a zero temperature quantum phase transition. On the other hand, many open questions remain about the phenomenology of disordered systems driven far out of…
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 compute the number level variance $\Sigma_{2}$ and the level compressibility $\chi$ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the…
We study the three-dimensional Anderson model of localization with anisotropic hopping, i.e., weakly coupled chains and weakly coupled planes. In our extensive numerical study we identify and characterize the metal-insulator transition by…
In this paper we present a thorough study of transport, spectral and wave-function properties at the Anderson localization critical point in spatial dimensions $d = 3$, $4$, $5$, $6$. Our aim is to analyze the dimensional dependence and to…
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 possibility of driving an Anderson metal-insulator transition in the presence of scale-free disorder by changing the correlation exponent is numerically investigated. We calculate the localization length for quasi-one-dimensional…
We use the random Green's matrix model to study the scaling properties of the localization transition for scalar waves in a three-dimensional (3D) ensemble of resonant point scatterers. We show that the probability density $p(g)$ of…
Due to their analytical tractability, random matrix ensembles serve as robust platforms for exploring exotic phenomena in systems that are computationally demanding. Building on a companion letter [arXiv:2312.17481], this paper investigates…
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…
The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order…
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction…
The critical exponents of continuous phase transitions of a Hermitian system depend on and only on its dimensionality and symmetries. This is the celebrated notion of the universality of continuous phase transitions. Here we report the…