Related papers: Critical behaviour in the QCD Anderson transition
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…
In QCD with two flavors of massless quarks, the chiral phase transition is plausibly in the same universality class as the classical four component Heisenberg antiferromagnet. Therefore, renormalization group techniques developed in the…
Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
From transfer-matrix calculation of localization lengths and their finite-size scaling analyses, we evaluate critical exponents of the Anderson metal-insulator transition in three dimensional (3D) orthogonal class with particle-hole…
We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams…
We report improved numerical estimates of the critical exponent of the Anderson transition in Anderson's model of localization in $d=4$ and $d=5$ dimensions. We also report a new Borel-Pad\'e analysis of existing $\epsilon$ expansion…
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…
A picture of thermal QCD phase change based on the analogy with metal-to-insulator transition of Anderson type was proposed in the past. In this picture, a low-$T$ thermal state is akin to a metal with deeply infrared (IR) Dirac modes…
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 interplay of topology and disorder in quantum dynamics has recently attracted significant attention across diverse platforms, including solid-state devices, ultracold atoms, and photonic systems. Here, we report on a topological…
We report a numerical analysis of the Anderson transition in a quantum-chaotic system, the quasiperiodic kicked rotor with three incommensurate frequencies. It is shown that this dynamical system exhibits the same critical phenomena as the…
The center phase transition of QCD and of fundamentally charged scalar QCD at non-vanishing temperature is investigated within a Dyson-Schwinger approach. The temperature dependence of the scalar/quark propagator is studied with generalized…
I discuss the properties of electron states in amorphous Si based on large scale calculations with realistic several thousand atom models. A relatively simple model for the localized to extended (Anderson) transition is reviewed. Then, the…
The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating…
We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized…
Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase.…
Based on a local mean-field theory approach at Anderson localization, we find a distribution function of critical temperature from that of disorder. An essential point of this local mean-field theory approach is that the information of the…
We discuss a possible mechanism leading to localisation of the low-lying Dirac eigenmodes in high-temperature lattice QCD, based on the spatial fluctuations of the local Polyakov lines in the partially ordered configurations above $T_c$.…
We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters allowing for the engineered realization of distinct topological phases. The option to directly monitor…