Dissipation dynamics of a scalar field

TL;DR

This paper studies the dissipation rate of a scalar field near phase transitions using the functional renormalization group, providing insights relevant for dynamical simulations and confirming known critical exponents.

Contribution

It presents a detailed analysis of the dissipation rate and effective potential using the functional renormalization group on the Schwinger-Keldysh contour, including finite-size scaling for the critical exponent z.

Findings

Dissipation rate determined near phase transition and ordered phase.

Effective potential and dissipation rate computed for finite and infinite volumes.

Finite-size scaling yields a dynamic critical exponent z matching literature values.

Abstract

We investigate the dissipation rate of a scalar field in the vicinity of the phase transition and the ordered phase, specifically within the universality class of model A. This dissipation rate holds significant physical relevance, particularly in the context of interpreting effective potentials as inputs for dynamical transport simulations, such as hydrodynamics. To comprehensively understand the use of effective potentials and other calculation inputs, such as the functional renormalization group, we conduct a detailed analysis of field dependencies. We solve the functional renormalization group equations on the Schwinger-Keldysh contour to determine the effective potential and dissipation rate for both finite and infinite volumes. Furthermore, we conduct a finite-size scaling analysis to calculate the dynamic critical exponent z. Our extracted value closely matches existing values from the literature.