Bibliographic Details
| Title: |
Schr\'odinger evolution in a low-density random potential: annealed convergence to the linear Boltzmann equation for general semiclassical Wigner measures |
| Authors: |
Mikkelsen, Søren |
| Publication Year: |
2023 |
| Collection: |
Mathematics
Mathematical Physics |
| Subject Terms: |
Mathematical Physics, Mathematics - Analysis of PDEs |
| More Details: |
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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2303.05176 |
| Accession Number: |
edsarx.2303.05176 |
| Database: |
arXiv |
