Tails of Instability and Decay: a Hydrodynamic Perspective

TL;DR

This paper explores how unstable particles influence the non-equilibrium dynamics of quantum field theories, revealing new signatures like tail formation and long-lived unstable waves using hydrodynamic analysis in a 1+1D integrable model.

Contribution

It introduces a hydrodynamic framework to analyze the formation and decay of unstable particles in quantum field theory, highlighting their impact on out-of-equilibrium phenomena.

Findings

Unstable particles create observable tails and decay patterns in nonlinear waves.

A stable population of unstable particles can persist without decay for extended periods.

Signatures of unstable particles are likely universal across different systems.

Abstract

In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and life-time of the particle, observed in scattering events. In this paper, we uncover new, dynamical signatures of unstable excitations and show that they have a strong effect on the non-equilibrium properties of QFT. Focusing on a 1+1D integrable model, and using the theory of Generalized Hydrodynamics, we study the formation and decay of unstable particles by analysing the release of hot matter into a low-temperature environment. We observe the formation of tails and the decay of the emitted nonlinear waves, in sharp contrast to the situation without unstable excitations. We also uncover a new phenomenon by which a wave of a stable population of unstable particles may persist without decay for long times. We expect these signatures of the presence of unstable particles to have a large degree of universality. Our study shows that the out-of-equilibrium dynamics of many-body systems can be strongly affected not only by the spectrum, but also by excitations with finite life-times.