An Egorov Theorem for Wasserstein Distances

• URL: http://arxiv.org/abs/2509.07185v1
• Date: Mon, 08 Sep 2025 20:03:38 GMT
• Title: An Egorov Theorem for Wasserstein Distances
• Authors: Jordan Cotler, Felipe Hernández,
• Abstract summary: We prove a new version of Egorov's theorem formulated in the Schr"odinger picture of quantum mechanics.<n>The special case $p=1$ corresponds to a "low-regularity" Egorov theorem, while larger values $p>1$ yield progressively stronger estimates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove a new version of Egorov's theorem formulated in the Schr\"{o}dinger picture of quantum mechanics, using the $p$-Wasserstein metric applied to the Husimi functions of quantum states. The special case $p=1$ corresponds to a "low-regularity" Egorov theorem, while larger values $p>1$ yield progressively stronger estimates. As a byproduct of our analysis, we prove an optimal transport inequality analogous to a result of Golse and Paul in the context of mean-field many-body quantum mechanics.

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