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PreprintCC BY 4.0arXiv

Lyapunov-controlled thermalization: an exact real-time example

  • Jonas Loy
  • Jan C. Louw
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Abstract

A verified Kubo-Martin-Schwinger (KMS) relation, after a drive has ceased, is not sufficient evidence to prove equilibrium. We demonstrate this in a large-N large-q Sachdev-Ye-Kitaev (SYK) quench protocol. Although all post-quench fermion correlators are exactly thermal, a second quench back to the initial Hamiltonian reveals hidden memory of the initial state. It is encoded in correlators connecting to times before the first quench. This memory is an extensive nonequilibrium (NEQ) witness with its decay rate being the Lyapunov exponent λL. Thus λL sets the rate at which the state becomes effectively indistinguishable from a Gibbs state. Despite being a unitary interacting many-body system, the complete NEQ real-time evolution is obtained exactly in the large-N, large-q limit, making the setup ideal for analytically studying thermalization.

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Cite

BibTeXRIS
BibTeX
@misc{loy2026lyapunovcontrolled,
  title = {{Lyapunov-controlled thermalization: an exact real-time example}},
  author = {Jonas Loy and Jan C. Louw},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20597},
  eprint = {2609.20597},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20597},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Lyapunov-controlled thermalization: an exact real-time example
AU  - Jonas Loy
AU  - Jan C. Louw
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20597
UR  - https://arxiv.org/abs/2609.20597
AB  - A verified Kubo-Martin-Schwinger (KMS) relation, after a drive has ceased, is not sufficient evidence to prove equilibrium. We demonstrate this in a large-N large-q Sachdev-Ye-Kitaev (SYK) quench protocol. Although all post-quench fermion correlators are exactly thermal, a second quench back to the initial Hamiltonian reveals hidden memory of the initial state. It is encoded in correlators connecting to times before the first quench. This memory is an extensive nonequilibrium (NEQ) witness with its decay rate being the Lyapunov exponent λ_L. Thus λ_L sets the rate at which the state becomes effectively indistinguishable from a Gibbs state. Despite being a unitary interacting many-body system, the complete NEQ real-time evolution is obtained exactly in the large-N, large-q limit, making the setup ideal for analytically studying thermalization.
ER  -