[{"extern":1,"abstract":[{"lang":"eng","text":"We study the long time evolution of a quantum particle interacting with a random potential in the Boltzmann-Grad low density limit. We prove that the phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation. The Boltzmann collision kernel is given by the full quantum scattering cross-section of the obstacle potential."}],"status":"public","date_updated":"2019-04-26T07:22:19Z","doi":"10.1142/S0129055X0500242X","title":"The linear Boltzmann equation as the low density limit of a random Schrödinger equation","type":"journal_article","_id":"2744","intvolume":" 17","date_published":"2005-07-01T00:00:00Z","publist_id":"4148","issue":"6","publisher":"World Scientific Publishing","page":"669 - 743","date_created":"2018-12-11T11:59:22Z","publication":"Reviews in Mathematical Physics","publication_status":"published","citation":{"ieee":"D. Eng and L. Erdös, “The linear Boltzmann equation as the low density limit of a random Schrödinger equation,” *Reviews in Mathematical Physics*, vol. 17, no. 6, pp. 669–743, 2005.","mla":"Eng, David, and László Erdös. “The Linear Boltzmann Equation as the Low Density Limit of a Random Schrödinger Equation.” *Reviews in Mathematical Physics*, vol. 17, no. 6, World Scientific Publishing, 2005, pp. 669–743, doi:10.1142/S0129055X0500242X.","ista":"Eng D, Erdös L. 2005. The linear Boltzmann equation as the low density limit of a random Schrödinger equation. Reviews in Mathematical Physics. 17(6), 669–743.","chicago":"Eng, David, and László Erdös. “The Linear Boltzmann Equation as the Low Density Limit of a Random Schrödinger Equation.” *Reviews in Mathematical Physics* 17, no. 6 (2005): 669–743. https://doi.org/10.1142/S0129055X0500242X.","ama":"Eng D, Erdös L. The linear Boltzmann equation as the low density limit of a random Schrödinger equation. *Reviews in Mathematical Physics*. 2005;17(6):669-743. doi:10.1142/S0129055X0500242X","short":"D. Eng, L. Erdös, Reviews in Mathematical Physics 17 (2005) 669–743.","apa":"Eng, D., & Erdös, L. (2005). The linear Boltzmann equation as the low density limit of a random Schrödinger equation. *Reviews in Mathematical Physics*, *17*(6), 669–743. https://doi.org/10.1142/S0129055X0500242X"},"day":"01","volume":17,"month":"07","author":[{"last_name":"Eng","full_name":"Eng, David","first_name":"David"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"László Erdös"}],"quality_controlled":0,"_version":8,"year":"2005"}]