PreprintCC BY 4.0arXiv
Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers
Abstract
We derive rates of exponential relative-entropy decay for a broad class of infinite-dimensional quantum Gibbs samplers. A key technical ingredient is a perturbative stability theory for hypercontractive estimates and logarithmic Sobolev inequalities. For suitably chosen dissipative couplings, we obtain exponential entropy decay for full multimode Bose-Hubbard samplers with arbitrary hopping and repulsive density interactions. For harmonically confined quantum Coulomb gases and molecular systems, we prove exponential entropy decay for every fixed finite-rank low-energy truncation of the interaction. Finally, we exhibit a periodic charging model with a positive spectral gap but no finite-time L2-to-Lp bound for any p>2.
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BibTeX
@misc{becker2026hypercontractivity,
title = {{Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers}},
author = {Simon Becker and Cambyse Rouzé and Robert Salzmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06764},
eprint = {2610.06764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06764},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers
AU - Simon Becker
AU - Cambyse Rouzé
AU - Robert Salzmann
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06764
UR - https://arxiv.org/abs/2610.06764
AB - We derive rates of exponential relative-entropy decay for a broad class of infinite-dimensional quantum Gibbs samplers. A key technical ingredient is a perturbative stability theory for hypercontractive estimates and logarithmic Sobolev inequalities. For suitably chosen dissipative couplings, we obtain exponential entropy decay for full multimode Bose-Hubbard samplers with arbitrary hopping and repulsive density interactions. For harmonically confined quantum Coulomb gases and molecular systems, we prove exponential entropy decay for every fixed finite-rank low-energy truncation of the interaction. Finally, we exhibit a periodic charging model with a positive spectral gap but no finite-time L^2-to-L^p bound for any p>2.
ER -