Low-energy effective theory of non-thermal fixed points in a multicomponent Bose gas

TL;DR

This paper develops a low-energy effective theory for non-thermal fixed points in multicomponent Bose gases, revealing universal scaling behaviors and characterizing fixed points through analytical and numerical methods.

Contribution

It introduces a novel effective theory describing Goldstone modes in multicomponent Bose gases, facilitating analysis of non-thermal fixed points with a focus on experimental relevance.

Findings

The theory describes universal scaling functions and exponents.

Numerical results for N=3 confirm analytical predictions.

Gaussian fixed point dominated by relative phases identified.

Abstract

Non-thermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of non-thermal fixed points in a bosonic quantum many-body system by integrating out long-wave-length density fluctuations. The system consists of $N$ distinguishable spatially uniform Bose gases with $\mathrm{U}(N)$-symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relative-phase excitations. It is similar in character to the non-linear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal non-local coupling function depending, in the large-$N$ limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the non-thermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields $N$. Numerical results for $N=3$ allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.