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arXiv:2306.09094 · Physics Letters B

Universality of energy-momentum response in kinetic theories

Xiaojian Du, Stephan Ochsenfeld, Sören Schlichting

Published Aug 31, 2023• 8 citations
arXivHTMLPDF

Abstract

We study the response of the energy-momentum tensor in several kinetic theories, from the simple relaxation time approximation (RTA) to Quantum Chromodynamics (QCD). Irrespective of the differences in microscopic properties, we find a remarkable degree of universality in the response functions from conformal theories. We find that the response to scalar perturbations in kinetic theory can be effectively described by a pair of one hydrodynamic sound mode and one non-hydrodynamic mode. We find that even beyond the range of validity of hydrodynamics, the energy-momentum response in position space can be effectively described by one single mode with non-trivial dispersion relation and residue.

DOI
10.1016/j.physletb.2023.138161

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We study the response of the energy-momentum tensor in several kinetic theories, from the simple relaxation time approximation (RTA) to Quantum Chromodynamics (QCD). Irrespective of the differences in microscopic properties, we find a remarkable degree of universality in the response functions from conformal theories. We find that the response to scalar perturbations in kinetic theory can be effectively described by a pair of one hydrodynamic sound mode and one non-hydrodynamic mode. We find that even beyond the range of validity of hydrodynamics, the energy-momentum response in position space can be effectively described by one single mode with non-trivial dispersion relation and residue.
Nonequilibrium Green's functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early-time preequilibrium stage of high-energy heavy-ion collisions. Besides their practical relevance they also provide a meaningful way to address the question when and to what extent a hydrodynamic description of the system becomes applicable. Within the kinetic theory framework we derive a new method to calculate time-dependent nonequilibrium Green's functions describing the evolution of energy and momentum perturbations on top of an evolving far-from-equilibrium background. We discuss the approach toward viscous hydrodynamics along with the emergence of various scaling phenomena for conformal systems. By comparing our results obtained in the relaxation time approximation to previous calculations in Yang-Mills kinetic theory, we further address the question which macroscopic features of the energy-momentum tensor are sensitive to the underlying microscopic dynamics.
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A new approach to the dynamics of relaxation and kinetics of thermalization in a scalar field theory is presented that incorporates the relevant time scales through the resummation of hard thermal loops. An alternative derivation of the kinetic equations for the "quasiparticle" distribution functions is obtained that allows a clear understanding of the different "coarse-graining" approximations usually involved in a kinetic description. This method leads to a systematic perturbative expansion to obtain the kinetic equations including hard thermal loop resummation and to an improvement including renormalization, off-shell effects, and contributions that change chemical equilibrium on short time scales. As a by-product of these methods we establish the equivalence between the relaxation time scale in the linearized equation of motion of the quasiparticles and the thermalization time scale of the quasiparticle distribution function in the "relaxation time approximation" including hard thermal loop effects. Hard thermal loop resummation dramatically modifies the scattering rate for long wavelength modes as compared to the usual (semi)classical estimate. Relaxation and kinetics are studied both in the unbroken and broken symmetry phases of the theory. The broken symmetry phase also provides the setting to obtain the contribution to the kinetic equations from processes that involve decay of a heavy scalar into light scalar particles in the medium.
Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.
A remarkable feature of standard quantum mechanics is its analogy with classical fluid dynamics. This has motivated in the past efforts to formulate phase-space techniques based on various statistical models of quantum hydrodynamic equations. In this work an inverse kinetic theory for the Schr\"odinger equation has been constructed in order to formally describe the standard quantum dynamics by means of a classical dynamical system (to be denoted as phase-space Schr\"odinger dynamical system). It is shown that the inverse kinetic theory can be (non)uniquely determined under suitable mathematical prescriptions. In particular, when the quantum linear momentum is identified with a suitable linear kinetic momentum, it follows that the fluctuations of the position vector and the kinetic linear momentum satisfy identically the Heisenberg theorem.