Transseries for causal diffusive systems

TL;DR

This paper develops a transseries framework for analyzing the late-time behavior of causal diffusive systems, exemplified by the telegrapher's equation, revealing transient effects and Stokes phenomena in nonequilibrium dynamics.

Contribution

It introduces a transseries approach to describe late-time nonequilibrium dynamics without symmetry assumptions, highlighting the organization of solutions into perturbative and nonperturbative parts.

Findings

Identification of novel transient contributions in causal diffusive systems

Discovery of Stokes phenomena affecting transseries structure

Application to the telegrapher's equation as a key example

Abstract

The large proper-time behaviour of expanding boost-invariant fluids has provided many crucial insights into quark-gluon plasma dynamics. Here we formulate and explore the late-time behaviour of nonequilibrium dynamics at the level of linearized perturbations of equilibrium, but without any special symmetry assumptions. We introduce a useful quantitative approximation scheme in which hydrodynamic modes appear as perturbative contributions while transients are nonperturbative. In this way, solutions are naturally organized into transseries as they are in the case of boost-invariant flows. We focus our attention on the ubiquitous telegrapher's equation, the simplest example of a causal theory with a hydrodynamic sector. In position space we uncover novel transient contributions as well as Stokes phenomena which change the structure of the transseries based on the spacetime region or the choice of initial data.