Non-equilibrium time evolution and rephasing in the quantum sine-Gordon model

TL;DR

This paper compares two theoretical methods to study the non-equilibrium dynamics of the sine-Gordon model, providing predictions for phase evolution in coupled bosonic condensates, but finds limitations in explaining experimental phase-locking.

Contribution

It demonstrates the agreement of truncated Wigner and conformal space approaches for early oscillations in the sine-Gordon model, offering a solid theoretical framework for its dynamics.

Findings

Methods agree for initial oscillations

Homogeneous sine-Gordon dynamics cannot fully explain phase-locking

Hints at the importance of inhomogeneity or additional degrees of freedom

Abstract

We discuss the non-equilibrium time evolution of the phase field in the sine-Gordon model using two very different approaches: the truncated Wigner approximation and the truncated conformal space approach. We demonstrate that the two approaches agree for a period covering the first few oscillations, thereby giving a solid theoretical prediction in the framework of sine-Gordon model, which is thought to describe the dynamics of two bosonic condensates in quasi-one-dimensional traps coupled via a Josephson tunneling term. We conclude, however, that the recently observed phase-locking behavior cannot be explained in terms of homogeneous sine-Gordon dynamics, which hints at the role of other degrees of freedom or inhomogeneity in the experimental system.