Sinai Diffusion at Quasi-1D Topological Phase Transitions

TL;DR

This paper investigates a novel quantum transport phenomenon called Sinai diffusion in disordered topological quantum wires, revealing a universal anomalous retardation in excitation propagation at phase transitions.

Contribution

It introduces a new universality class of quantum transport characterized by Sinai diffusion in topological superconductors at criticality.

Findings

Identification of Sinai diffusion as a transport mechanism

Microscopic theory explaining anomalous retardation

Implications for heat propagation in topological superconductors

Abstract

We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indexes. Focusing on the example of thermal transport in class D (`Majorana') quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations -- a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.