Possible Quantum Critical Region tuned by the Disorder and Pauli-Blocking Effects

TL;DR

This paper explores how disorder and Pauli-blocking interactions influence localization in electron gases, using a quantum kinetic model to map out a phase diagram akin to known localization theories.

Contribution

It introduces a quantum discrete kinetic model incorporating disorder and Pauli-blocking effects to analyze localization phenomena in electron gases.

Findings

Phase diagram showing localization regions based on disorder strength and mean free path.

Qualitative resemblance to the Abrahams localization phase diagram.

Analysis of the effects of scattering orientation on localization.

Abstract

Based on the acoustic analog, we investigate both of the effects : disorder and (Pauli-blocking) interaction to the possible localization in electron gases by using the quantum discrete kinetic model. Effects of the disorder (or free-orientation : $\theta$ which is related to the relative direction of scattering of particles w.r.t. to the normal of the propagating plane-wave front) which is introduced into the \"{U}hling-Uhlenbeck equations together with those of the Pauli-blocking are presented. We obtain the possible phase diagram (related to the strength of disorders and the mean free path) which resembles qualitatively that proposed by Abrahams$^{1}$.