Effective theory for the soft fluctuation modes in the spontaneously broken phase of the N-component scalar field theory

TL;DR

This paper derives an effective theory for low-frequency fluctuation modes in the broken phase of the O(N) scalar field theory, accounting for high-frequency effects and analyzing long-time behavior of Goldstone modes.

Contribution

It introduces a new length scale governing long-time asymptotics and proposes local equations for numerical simulation of the nonlinear dynamics.

Findings

Long-time asymptotics of Goldstone modes determined

A new length scale influences decay behavior

Local equations enable efficient numerical solutions

Abstract

The effective dynamics of the low-frequency modes is derived for the O(N) symmetric scalar field theory in the broken symmetry phase. The effect of the high-frequency fluctuations is taken into account at one-loop level exactly. A new length scale is shown to govern the long-time asymptotics of the linear response function of the Goldstone modes. The large time asymptotic decay of an arbitrary fluctuation is determined in the linear regime. We propose a set of local equations for the numerical solution of the effective non-linear dynamics. The applicability of the usual gradient expansion is carefully assessed.