Non-equilibrium scalar field dynamics starting from Fock states: Absence of thermalization in one dimensional phonons coupled to fermions

TL;DR

This paper introduces a new Keldysh field theory approach to study non-equilibrium scalar field dynamics from Fock states, revealing that one-dimensional phonons coupled to fermionic baths do not thermalize due to conservation constraints and density of states effects.

Contribution

It develops a novel method for analyzing non-Gaussian initial conditions in non-equilibrium scalar fields and uncovers dimension-dependent thermalization behavior of phonons coupled to baths.

Findings

One-dimensional phonons do not thermalize with fermionic baths at any temperature.

Constraints from energy-momentum conservation restrict particle-hole excitations in 1D.

Higher dimensions exhibit thermalization due to weakened constraints.

Abstract

We propose a new method to study non-equilibrium dynamics of scalar fields starting from non-Gaussian initial conditions using Keldysh field theory. We use it to study dynamics of phonons coupled to non-interacting bosonic and fermionic baths, starting from initial Fock states. We find that in one dimension long wavelength phonons coupled to fermionic baths do not thermalize both at low and high bath-temperatures. At low temperature, constraints from energy-momentum conservation lead to a narrow bandwidth of particle-hole excitations and the phonons effectively do not see this bath. On the other hand, the strong band-edge divergence of the particle-hole density of states leads to an undamped polariton-like mode of the dressed phonons above the band edge of the particle-hole excitations. These undamped modes contribute to the lack of thermalization of long wavelength phonons at high temperatures. In higher dimensions, these constraints and the divergence of density of states are weakened and lead to thermalization at all wavelengths.