Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization

TL;DR

This paper develops a theoretical framework to analyze charge fractionalization and local equilibration in one-dimensional systems like quantum Hall edges, using non-equilibrium bosonization and functional determinants, and compares results with experiments.

Contribution

It introduces a new method for evaluating functional determinants with overlapping pulses, advancing understanding of non-equilibrium charge dynamics.

Findings

Framework for evaluating determinants with overlapping pulses

Description of charge fractionalization dynamics

Comparison with recent experimental data

Abstract

In quantum Hall edge states and in other one-dimensional interacting systems, charge fractionalization can occur due to the fact that an injected charge pulse decomposes into eigenmodes propagating at different velocities. If the original charge pulse has some spatial width due to injection with a given source-drain voltage, a finite time is needed until the separation between the fractionalized pulses is larger than their width. In the formalism of non-equilibrium bosonization, the above physics is reflected in the separation of initially overlapping square pulses in the effective scattering phase. When expressing the single particle Green's function as a functional determinant of counting operators containing the scattering phase, the time evolution of charge fractionalization is mathematically described by functional determinants with overlapping pulses. We develop a framework for the evaluation of such determinants, describe the system's equilibration dynamics, and compare our theoretical results with recent experimental findings.