Non-equilibrium time evolution of bosons from the functional renormalization group

TL;DR

This paper introduces a functional renormalization group method to study the non-equilibrium time evolution of interacting bosons, providing a new way to derive accurate long-time dynamics without secular growth.

Contribution

It develops a novel RG approach using an out-scattering rate as a flow parameter to solve the quantum Boltzmann equation for bosons out of equilibrium.

Findings

Derives exact RG flow equations for non-equilibrium self-energies.

Provides an approximate solution to the quantum Boltzmann equation free of secular terms.

Validates the approach with an exactly solvable toy model.

Abstract

We develop a functional renormalization group approach to obtain the time evolution of the momentum distribution function of interacting bosons out of equilibrium. Using an external out-scattering rate as flow parameter, we derive formally exact renormalization group flow equations for the non-equilibrium self-energies in the Keldysh basis. A simple perturbative truncation of these flow equations leads to an approximate solution of the quantum Boltzmann equation which does not suffer from secular terms and gives accurate results even for long times. We demonstrate this explicitly within a simple exactly solvable toy model describing a quartic oscillator with off-diagonal pairing terms.