Generalised Hydrodynamics of Particle Creation and Decay

TL;DR

This paper investigates how unstable particles influence the dynamics of integrable 1+1D quantum field theories, using generalized hydrodynamics to analyze their creation and decay signatures in various initial states.

Contribution

It introduces a detailed analysis of unstable particle effects within the generalized hydrodynamics framework, extending understanding of their signatures in out-of-equilibrium settings.

Findings

Signatures of unstable particle creation and decay are observed in particle densities.

The dependence of these signatures on initial state parameters is quantitatively analyzed.

Different initial temperature profiles affect the observable signatures of unstable particles.

Abstract

Unstable particles rarely feature in conjunction with integrability in 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present in the spectrum whilst the scattering matrix is diagonal and solves the usual bootstrap equations. In the standard scattering picture, unstable particles result from complex poles of the $S$-matrix located in the unphysical sheet of rapidity space. Since they are not part of the asymptotic spectrum, their presence is only felt through the effect they have on physical quantities associated either to the theory as a whole (i.e.~scaling functions, correlation functions) or to the stable particles themselves (i.e.~energy/particle density). In two recent publications, the effect of unstable particles in different out-of-equilibrium settings has been studied. It has been shown that their presence is associated with specific signatures in many quantities of physical interest. A good way to select those quantities is to adopt the generalised hydrodynamic approach and to consider the effective velocities and particle densities of the stable particles in the theory. For an initial state given by a spacial gaussian profile of temperatures peaked at the origin, time evolution gives rise to particle and spectral particle densities that exhibit hallmarks of the creation and decay of unstable particles. While these signatures have been observed numerically elsewhere, this paper explores their quantitative and qualitative dependence on the parameters of the problem. We also consider other initial states characterised by "inverted gaussian" and "double gaussian" temperature profiles.