Understanding thermalization in a non-Abelian gauge theory in terms of its soft modes

Abstract

We measure the maximal Lyapunov exponent ${\lambda }_L$ of physical states in a SU(2) gauge theory consisting of soft momentum modes both in and out-of-thermal equilibrium conditions using ab-initio lattice techniques. We have implemented different algorithms to appropriately describe the dynamics of soft-modes for a wide range of temperatures and under non-equilibrium conditions. The non-equilibrium state has been realized starting from an over-occupied initial condition for low momentum soft gluons whereas the thermal state comprises of strongly interacting soft gluons at temperatures where these are well separated from the hard momentum modes. Spectra of positive Lyapunov exponents is observed in both these states, similar to a chaotic dynamical system. From the Kolmogorov-Sinai entropy rate measured in terms of this spectrum, we estimate a typical time-scale of $\sim 0.50(3)$ fm/c to achieve thermalization at $T\sim 600$ MeV starting from the non-thermal state. We also measure, for the first time, the ${\lambda }_L$ for long wavelength critical modes of SU(2) using the out-of-time-ordered correlator of a classical $Z_2$ scalar field theory, which shares the same universal behavior with SU(2), near the deconfinement phase transition. The ${\lambda }_L$ is observed to maximize at the transition temperature.

arXiv commentv2: minor changes in the text and the title to match the published version

References in corpus (37)

• A bound on chaos
• Decoding the phase structure of QCD via particle production at high energy
• Transport coefficients in high temperature gauge theories: (I) Leading-log results
• Bottom-up thermalization in heavy ion collisions
• Viscosity, Black Holes, and Quantum Field Theory
• Collective Modes of an Anisotropic Quark-Gluon Plasma
• Introduction to Nonequilibrium Quantum Field Theory
• Basics of thermal field theory -- a tutorial on perturbative computations
• Scaling and Asymptotic Scaling in the SU(2) Gauge Theory
• Effective dynamics of soft non-abelian gauge fields at finite temperature
• QCD Plasma Instabilities and Bottom-Up Thermalization
• Out-of-time-order correlators in quantum mechanics
• Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
• Universal Charge Diffusion and the Butterfly Effect
• Universal attractor in a highly occupied non-Abelian plasma
• Apparent Thermalization due to Plasma Instabilities in Quark-Gluon Plasma
• Hard-Loop Dynamics of Non-Abelian Plasma Instabilities
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Kolmogorov-Sinai entropy-rate vs. physical entropy
• Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Thermalization at RHIC
• Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
• Color Diffusion and Conductivity in a Quark-Gluon Plasma
• Off-equilibrium sphaleron transitions in the Glasma
• Does parton saturation at high density explain hadron multiplicities at RHIC ?
• High temperature color conductivity at next-to-leading log order
• Temperature dependence of butterfly effect in a classical many-body system
• Turbulent thermalization of weakly coupled non-abelian plasmas
• The Sphaleron Rate: Bodeker's Leading Log
• Classical many-body chaos with and without quasiparticles
• Can Thermalization in Heavy Ion Collisions be Described by QCD Diagrams?
• Large N_c confinement and turbulence
• Lyapunov Exponent and Plasmon Damping Rate in Nonabelian Gauge Theories
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• Lyapunov Spectra in SU(2) Lattice Gauge Theory
• Many-body chaos near a thermal phase transition

Cited by in corpus (5)

• Entanglement Properties of SU(2) Gauge Theory
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• Revisiting the sphaleron and axion production rates in QCD at high temperatures
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• Anisotropy effects on heavy quark dynamics in Gribov modified gluon plasma