Late-Time Relaxation from Landau Singularities

TL;DR

This paper uses Landau singularity analysis within effective field theories to systematically identify nonlinear late-time relaxation modes, revealing how power-law decay arises from loop integral singularities.

Contribution

It introduces a systematic method to determine late-time relaxation behavior from Landau singularities without explicit loop calculations in effective theories.

Findings

Identifies nonlinear relaxation modes from frequency-space singularities.

Shows power-law decay arises when gapless modes are present.

Provides a broad, systematic framework for nonlinear late-time relaxation analysis.

Abstract

Nonlinear hydrodynamic interactions can change the relaxation of fluctuations from exponential to power-law decay at late times. Schwinger-Keldysh effective field theory provides a standard framework for describing such fluctuation effects, where the nonlinear late-time behavior is encoded in loop corrections. Extracting this behavior requires identifying the singularities of loop integrals, whose structure becomes increasingly intricate beyond simple models. We apply Landau singularity analysis to two-point functions in effective field theories and determine the singularities induced by nonlinear interactions without performing the loop integrations explicitly. From these frequency-space singularities, we extract nonlinear relaxation modes that control the late-time behavior. When gapless modes are present, these modes produce power-law decay at late times. Our results give a systematic singularity-based description of nonlinear late-time relaxation in a broad class of macroscopic effective theories.