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An Egorov Theorem for Wasserstein Distances (2509.07185v1)
Published 8 Sep 2025 in quant-ph, math-ph, math.AP, and math.MP
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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