Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems

TL;DR

This paper develops a quantum dynamical field theory to analyze non-equilibrium phase transitions in driven open systems, highlighting the influence of non-linear noise and quantum fluctuations beyond semiclassical models.

Contribution

It introduces a novel quantum dynamical field theory framework and compares it with semi-classical approaches, applying it to driven-dissipative condensates and Bose gases.

Findings

Quantum criticality differs from classical driven systems.

Non-linear noise significantly affects phase transition behavior.

The quantum phase transition does not correspond to classical counterparts.

Abstract

We develop a quantum dynamical field theory for studying phase transitions in driven open systems coupled to Markovian noise, where non-linear noise effects and fluctuations beyond semiclassical approximations influence the critical behaviour. We systematically compare the diagrammatics, the properties of the renormalization group flow and the structure of the fixed points, of the novel quantum dynamical field theory and of its semi-classical counterpart, which is employed to characterise dynamical criticality in three dimensional driven-dissipative condensates. As an application, we perform the Keldysh Functional Renormalization of a one dimensional driven open Bose gas, where a tailored diffusion Markov noise realises an analog of quantum criticality for driven-dissipative condensation. We find that the associated non-equilibrium quantum phase transition does not map into the critical behaviour of its three dimensional classical driven counterpart.