--- _id: '2738' abstract: - lang: eng text: We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes. acknowledgement: "This work initially was a joint project with H.-T. Yau and several ideas\r\npresented here have been developed in collaboration with him. I would like\r\nto thank him for the invaluable discussions and encouragement through\r\nthe entire work. Part of this project was completed during several visits at\r\nthe Erwin Schrödinger Institute, Vienna, and at the Center of Theoretical\r\nStudies, Hsinchu, Taiwan. The author is grateful for the hospitality and\r\nfinancial support. This work was partially supported by NSF Grant DMS9970323." article_processing_charge: No article_type: original author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 citation: ama: Erdös L. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. 2002;107(5-6):1043-1127. doi:10.1023/A:1015157624384 apa: Erdös, L. (2002). Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. Springer. https://doi.org/10.1023/A:1015157624384 chicago: Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” Journal of Statistical Physics. Springer, 2002. https://doi.org/10.1023/A:1015157624384. ieee: L. Erdös, “Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field,” Journal of Statistical Physics, vol. 107, no. 5–6. Springer, pp. 1043–1127, 2002. ista: Erdös L. 2002. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. 107(5–6), 1043–1127. mla: Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” Journal of Statistical Physics, vol. 107, no. 5–6, Springer, 2002, pp. 1043–127, doi:10.1023/A:1015157624384. short: L. Erdös, Journal of Statistical Physics 107 (2002) 1043–1127. date_created: 2018-12-11T11:59:20Z date_published: 2002-06-01T00:00:00Z date_updated: 2023-07-18T09:08:45Z day: '01' doi: 10.1023/A:1015157624384 extern: '1' external_id: arxiv: - math-ph/0108025 intvolume: ' 107' issue: 5-6 language: - iso: eng month: '06' oa_version: Submitted Version page: 1043 - 1127 publication: Journal of Statistical Physics publication_identifier: issn: - 0022-4715 publication_status: published publisher: Springer publist_id: '4154' quality_controlled: '1' scopus_import: '1' status: public title: Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 107 year: '2002' ...