Thermalization of nonequilibrium electrons in quantum wires

TL;DR

This paper investigates energy relaxation in one-dimensional quantum wires, revealing that three-particle collisions can be exactly mapped to a solvable Schrödinger equation, providing insights into thermalization timescales.

Contribution

It demonstrates an exact transformation of the collision integral into a Schrödinger equation with a Poschl-Teller potential for spinless electrons in quantum wires.

Findings

Identification of bound states as zero modes of the collision integral

Existence of a continuum of propagating modes separated by a gap

Determination of thermalization timescale from the inverse gap

Abstract

We study the problem of energy relaxation in a one-dimensional electron system. The leading thermalization mechanism is due to three-particle collisions. We show that for the case of spinless electrons in a single channel quantum wire the corresponding collision integral can be transformed into an exactly solvable problem. The latter is known as the Schrodinger equation for a quantum particle moving in a Poschl-Teller potential. The spectrum for the resulting eigenvalue problem allows for bound-state solutions, which can be identified with the zero modes of the collision integral, and a continuum of propagating modes, which are separated by a gap from the bound states. The inverse gap gives the time scale at which counterpropagating electrons thermalize.