Effective field theory of time-translational symmetry breaking in nonequilibrium open system

TL;DR

This paper develops an effective field theory framework for understanding time-translational symmetry breaking in nonequilibrium open systems using the Schwinger-Keldysh formalism, accounting for noise and dissipation effects.

Contribution

It introduces a novel EFT approach that incorporates doubled symmetries and their explicit breaking due to noise and dissipation in open systems.

Findings

Constructed a general EFT for time-translational symmetry breaking in open systems.

Analyzed the symmetry structure and Nambu-Goldstone bosons in the presence of noise and dissipation.

Applied the framework to phenomena like synchronization, time crystals, and cosmic inflation.

Abstract

We develop the effective field theoretical (EFT) approach to time-translational symmetry breaking of nonequilibrium open systems based on the Schwinger-Keldysh formalism. In the Schwinger-Keldysh formalism, all the symmetries of the microscopic Lagrangian are doubled essentially because the dynamical fields are doubled to describe the time-evolution along the closed-time-path. The effective Lagrangian for open systems are then obtained by coarse-graining the microscopic Schwinger-Keldysh Lagrangian. As a consequence of coarse-graining procedure, there appear the noise and dissipation effects, which explicitly break the doubled time-translational symmetries into a diagonal one. We therefore need to incorporate this symmetry structure to construct the EFT for Nambu-Goldstone bosons in symmetry broken phases of open systems. Based on this observation together with the consistency of the Schwinger-Keldysh action, we construct and study the general EFT for time-translational symmetry breaking in particular, having in mind applications to synchronization, time crystal, and cosmic inflation.