{"title":"Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation","quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication":"Proceedings of the 7th QMath Conference","doi":"10.1007/978-3-0348-8745-8_20","_id":"2711","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783034897549"]},"abstract":[{"lang":"eng","text":"We study the long time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to the solution of a linear Boltzmann equation globally in time. The Boltzmann collision kernel is given by the Born approximation of the quantum scattering cross section."}],"date_published":"1999-01-01T00:00:00Z","page":"233 - 242","month":"01","publication_status":"published","date_updated":"2022-09-13T08:02:52Z","day":"01","oa_version":"None","volume":108,"publisher":"World Scientific Publishing","intvolume":"       108","alternative_title":["Operator Theory: Advances and Applications"],"scopus_import":"1","extern":"1","publist_id":"4185","date_created":"2018-12-11T11:59:12Z","year":"1999","conference":{"location":"Prague, Czech Republik","end_date":"1999-09-26","start_date":"1998-06-22","name":"QMath: Mathematical Results in Quantum Physics"},"citation":{"mla":"Erdös, László. “Linear Boltzmann Equation as the Weak Coupling Limit of the Random Schrödinger Equation.” <i>Proceedings of the 7th QMath Conference</i>, vol. 108, World Scientific Publishing, 1999, pp. 233–42, doi:<a href=\"https://doi.org/10.1007/978-3-0348-8745-8_20\">10.1007/978-3-0348-8745-8_20</a>.","ieee":"L. Erdös, “Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation,” in <i>Proceedings of the 7th QMath Conference</i>, Prague, Czech Republik, 1999, vol. 108, pp. 233–242.","ama":"Erdös L. Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation. In: <i>Proceedings of the 7th QMath Conference</i>. Vol 108. World Scientific Publishing; 1999:233-242. doi:<a href=\"https://doi.org/10.1007/978-3-0348-8745-8_20\">10.1007/978-3-0348-8745-8_20</a>","apa":"Erdös, L. (1999). Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation. In <i>Proceedings of the 7th QMath Conference</i> (Vol. 108, pp. 233–242). Prague, Czech Republik: World Scientific Publishing. <a href=\"https://doi.org/10.1007/978-3-0348-8745-8_20\">https://doi.org/10.1007/978-3-0348-8745-8_20</a>","short":"L. Erdös, in:, Proceedings of the 7th QMath Conference, World Scientific Publishing, 1999, pp. 233–242.","chicago":"Erdös, László. “Linear Boltzmann Equation as the Weak Coupling Limit of the Random Schrödinger Equation.” In <i>Proceedings of the 7th QMath Conference</i>, 108:233–42. World Scientific Publishing, 1999. <a href=\"https://doi.org/10.1007/978-3-0348-8745-8_20\">https://doi.org/10.1007/978-3-0348-8745-8_20</a>.","ista":"Erdös L. 1999. Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation. Proceedings of the 7th QMath Conference. QMath: Mathematical Results in Quantum Physics, Operator Theory: Advances and Applications, vol. 108, 233–242."},"type":"conference","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"status":"public","article_processing_charge":"No"}