Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions

TL;DR

This paper investigates whether multiple steady-states can exist in nonequilibrium quantum systems with electron-phonon interactions, using advanced numerical methods to demonstrate the uniqueness of steady-states and the conditions for bistability.

Contribution

It combines a reduced density matrix approach with multiconfiguration time-dependent Hartree methods to analyze steady-state existence and bistability in quantum transport models.

Findings

A unique steady-state exists regardless of initial electronic conditions.

Bistability can occur depending on initial phonon states.

Phonon frequency and coupling strength influence relaxation and bistability.

Abstract

The existence of more than one steady-state in a many-body quantum system driven out-of-equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this Letter, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the relaxation to steady-state and on the emergence of bistability is discussed.