What does "instant thermalization" in large-q SYK models mean?
Abstract
Motivated by the Planckian thermalization rate Γ∼ T observed in the two-body interacting SYK model, we study thermalization in the q/2-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in 1/q. It was conjectured that the thermalization may still be Planckian but with a divergent rate Γ∼ T q, explaining the ``instantaneous'' part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time t = 0 and indeed find a Planckian rate, albeit with the unexpected decaying behavior $Γ\sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function 𝒢(t1, t2), which instantly acquires a thermal form in the two-time plane block t1, t2 > 0. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks t1 · t2 < 0 are inherently non-thermal at any q. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.
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BibTeX
@misc{osterkorn2026what,
title = {{What does "instant thermalization" in large-$q$ SYK models mean?}},
author = {Alexander Osterkorn and Jan C. Louw},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17794},
eprint = {2609.17794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17794},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - What does "instant thermalization" in large-q SYK models mean?
AU - Alexander Osterkorn
AU - Jan C. Louw
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17794
UR - https://arxiv.org/abs/2609.17794
AB - Motivated by the Planckian thermalization rate Γ∼ T observed in the two-body interacting SYK model, we study thermalization in the q/2-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in 1/q. It was conjectured that the thermalization may still be Planckian but with a divergent rate Γ∼ T q, explaining the ``instantaneous'' part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time t = 0 and indeed find a Planckian rate, albeit with the unexpected decaying behavior $Γ\sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function 𝒢(t_1, t_2), which instantly acquires a thermal form in the two-time plane block t_1, t_2 > 0. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks t_1 · t_2 < 0 are inherently non-thermal at any q. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.
ER -