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arXiv · 2303.05176

Schr\"odinger evolution in a low-density random potential: annealed convergence to the linear Boltzmann equation for general semiclassical Wigner measures

Søren Mikkelsen
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Abstract

We consider solutions of the time-dependent Schr\"odinger equation for a potential localised at the points of a Poisson process. We prove convergence of the phase-space distribution in the annealed Boltzmann-Grad limit to a semiclassical Wigner (or defect) measure and show that it is a solution of the linear Boltzmann equation. Our results hold for a large class of square-integrable initial data associated to Wigner measures, including Langragian states, WKB states and coherent states. This extends important previous work by Eng and Erd\H{o}s.

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Søren Mikkelsen. 2023-03-09. Schr\"odinger evolution in a low-density random potential: annealed convergence to the linear Boltzmann equation for general semiclassical Wigner measures. https://arxiv.org/abs/2303.05176

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