Universal Equilibration Condition for Heavy Quarks
arXiv:2504.21139 · doi:10.1103/m2d2-9sdb
Abstract
Kinetic equilibration at late times is physically required for heavy particles in a finite temperature medium. In Fokker-Planck dynamics, it is ensured by the Einstein relation between the drag and longitudinal momentum diffusion coefficients. However, in certain gauge field theories, this relation is violated at any nonzero heavy quark velocity. Recent work in strongly coupled SYM gauge theory shows that the Kolmogorov equation for the heavy quark phase space distribution (that reduces to Fokker-Planck form upon truncating the momentum transfer probability distribution to second moments) does equilibrate even though the Fokker-Planck equation does not. Going beyond these (to date theory-specific) insights, we derive a universal equilibration condition for the kernel of the Kolmogorov equation and, consequently, for the momentum transfer probability distribution that holds in any quantum field theory with any coupling strength. This condition, which is the generalization of the Einstein relation to quantum field theories which feature non-Gaussian fluctuations, reveals that the asymmetry between energy loss and energy gain in the momentum transfer probability distribution takes a simple, theory-independent, form.
6 pages
References in corpus (34)
- Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
- How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?
- Drag force in AdS/CFT
- Heavy Quark Diffusion in Strongly Coupled Yang Mills
- Real-time gauge/gravity duality: Prescription, Renormalization and Examples
- Real-time gauge/gravity duality
- Extraction of Heavy-Flavor Transport Coefficients in QCD Matter
- Momentum fluctuations of heavy quarks in the gauge-string duality
- Transverse Momentum Broadening of a Fast Quark in a Yang Mills Plasma
- Heavy Quark Momentum Diffusion Coefficient from Lattice QCD
- Heavy quark diffusion in perturbative QCD at next-to-leading order
- Open Heavy Flavor in QCD Matter and in Nuclear Collisions
- Towards the determination of heavy-quark transport coefficients in quark-gluon plasma
- Transverse Momentum Broadening and the Jet Quenching Parameter, Redux
- A data-driven analysis for the temperature and momentum dependence of the heavy quark diffusion coefficient in relativistic heavy-ion collisions
- Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order
- Heavy Quark Diffusion from the Lattice
- Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
- A linearized Boltzmann--Langevin model for heavy quark transport in hot and dense QCD matter
- Lattice QCD constraints on the heavy quark diffusion coefficient
- A way to estimate the heavy quark thermalization rate from the lattice
- Heavy-Quark Diffusion in the Quark-Gluon Plasma
- Real-time gauge/gravity duality and ingoing boundary conditions
- Heavy Quark Diffusion from 2+1 Flavor Lattice QCD with 320 MeV Pion Mass
- Momentum Broadening in Weakly Coupled Quark-Gluon Plasma (with a view to finding the quasiparticles within liquid quark-gluon plasma)
- Heavy quark momentum diffusion from the lattice using gradient flow
- Cracking the difference of estimating heavy quark transport coefficients in a Quark-Gluon Plasma
- Stochastic trailing string and Langevin dynamics from AdS/CFT
- Dynamical collisional energy loss and transport properties of on- and off-shell heavy quarks in vacuum and in the Quark Gluon Plasma
- Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD
- Heavy quark diffusion coefficient with gradient flow
- Stochastic String Motion Above and Below the World Sheet Horizon
- Schwinger-Keldysh effective action for relativistic Brownian particle in AdS-CFT
- Dynamics of Heavy Quarks in Strongly Coupled SYM Plasma