On the relaxation dynamics of non-equilibrium quantum systems
Abstract
We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak B+L washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.
Related
- Out-of-equilibrium relaxation dynamics of the superconducting order parameter in CsV3Sb5
- Critical aging and relaxation dynamics in long-range systems
- Algebraic criteria for complete relaxation in autonomous and periodically driven open quantum systems
- Equilibrium propagation in non-equilibrium quantum systems
- Quantum electrodynamics of equilibrium systems: A rigorous Maxwell-regularized functional-theoretic formulation
BibTeX
@misc{carosi2026relaxation,
title = {{On the relaxation dynamics of non-equilibrium quantum systems}},
author = {Matthias Carosi and Björn Garbrecht and Silvia Pla and Nils Wagner and Edward Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17447},
eprint = {2609.17447},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17447},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the relaxation dynamics of non-equilibrium quantum systems
AU - Matthias Carosi
AU - Björn Garbrecht
AU - Silvia Pla
AU - Nils Wagner
AU - Edward Wang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17447
UR - https://arxiv.org/abs/2609.17447
AB - We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak B+L washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.
ER -