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PreprintCC BY 4.0arXiv

Analytical solutions to the non-equilibrium Green's functions in large-q SYK models

  • Jan C. Louw
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Abstract

It is known that the Sachdev-Ye-Kitaev (SYK) model is exactly solvable at leading order in 1/q; specifically, the instantaneously thermal time block after the quench is known in closed form. Thus far the remaining (inherently out of equilibrium) blocks have only been numerically accessible. Here we provide their analytical solutions for a quench between non-commuting q/2-body SYK Hamiltonians. We obtain the Green's functions in closed form for every time block. We extract a simple relation between the pre- and post-quench energies ε1 ∝ ε0 leading to an exact temperature update rule. Via a Cauchy-Schwarz inequality, we show that heating is inevitable for the closed system; hence, the second law emerges geometrically. The solution is used in a companion paper to address what ``instantaneous thermalization'' means at finite q.

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Cite

BibTeXRIS
BibTeX
@misc{louw2026analytical,
  title = {{Analytical solutions to the non-equilibrium Green's functions in large-$q$ SYK models}},
  author = {Jan C. Louw},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16438},
  eprint = {2609.16438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16438},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Analytical solutions to the non-equilibrium Green's functions in large-q SYK models
AU  - Jan C. Louw
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16438
UR  - https://arxiv.org/abs/2609.16438
AB  - It is known that the Sachdev-Ye-Kitaev (SYK) model is exactly solvable at leading order in 1/q; specifically, the instantaneously thermal time block after the quench is known in closed form. Thus far the remaining (inherently out of equilibrium) blocks have only been numerically accessible. Here we provide their analytical solutions for a quench between non-commuting q/2-body SYK Hamiltonians. We obtain the Green's functions in closed form for every time block. We extract a simple relation between the pre- and post-quench energies ε_1 ∝ ε_0 leading to an exact temperature update rule. Via a Cauchy-Schwarz inequality, we show that heating is inevitable for the closed system; hence, the second law emerges geometrically. The solution is used in a companion paper to address what ``instantaneous thermalization'' means at finite q.
ER  -