Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems

@misc{ye2026semiclassical,
  title = {{Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems}},
  author = {Yaoqi Ye and Xiao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20052},
  eprint = {2609.20052},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20052},
}

TY  - UNPB
TI  - Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems
AU  - Yaoqi Ye
AU  - Xiao Wang
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20052
UR  - https://arxiv.org/abs/2609.20052
AB  - We study the off-diagonal matrix elements of real-space observables in time-reversal-invariant single-particle chaotic systems. By analyzing the semiclassical expression for the off-diagonal variance derived from Berry's conjecture, we show that the banded structure of the observable matrix emerges naturally. For local observables, we identify a characteristic bandwidth associated with a late-time timescale inversely proportional to the particle velocity. We further show that, for systems with steep-wall confinement, the predicted magnitude follows the entropy scaling of the eigenstate thermalization hypothesis (ETH), multiplied by an additional kinetic-energy-dependent factor that is independent of spatial dimension and is not captured by conventional many-body ETH. We illustrate these results through a case study of quantum billiards and verify the semiclassical scaling numerically in a generalized quarter-Sinai billiard. Our results elucidate the dynamical implications of Berry's conjecture and provide a comparison between single-particle eigenstate thermalization and many-body ETH.
ER  -