Phonon dynamics in correlated quantum systems driven away from equilibrium

TL;DR

This paper develops a formalism to derive the exact dynamics of an extended bosonic system from the reduced density matrix of a correlated fermionic sub-system, enabling insights into phonon behavior in nonequilibrium quantum systems.

Contribution

It introduces a method to obtain the full bosonic dynamics from the fermionic sub-system's reduced density matrix in correlated quantum systems.

Findings

Phonon dynamics are influenced by frequency, coupling strength, and bias voltage.

The formalism reveals how phonon behavior varies across bistability regimes.

Application to an extended Holstein model demonstrates the approach's effectiveness.

Abstract

A general form of a many-body Hamiltonian is considered, which includes an interacting fermionic sub-system coupled to non-interacting extended fermionic and bosonic systems. We show that the exact dynamics of the extended bosonic system can be derived from the reduced density matrix of the sub-system alone, despite the fact that the latter contains information about the sub-system only. The advantage of the formalism is immediately clear: While the reduced density matrix of the sub-system is readily available, the formalism offers access to observables contained in the full density matrix, which is often difficult to obtain. As an example, we consider an extended Holstein model and study the nonequilibrium dynamics of the, so called, "reaction mode" for different model parameters. The effects of the phonon frequency, the strength of the electron-phonon couplings, and the source-drain bias voltage on the phonon dynamics across the bistability are discussed.