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arXiv · 2610.06764

Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers

Simon Becker·Cambyse Rouzé·Robert Salzmann
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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 $L^2$-to-$L^p$ bound for any $p>2$.

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Simon Becker, Cambyse Rouzé, Robert Salzmann. 2026-10-05. Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers. https://arxiv.org/abs/2610.06764

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