{"article_processing_charge":"No","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.","citation":{"short":"L. Erdös, Journal of Statistical Physics 107 (2002) 1043–1127.","mla":"Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” <i>Journal of Statistical Physics</i>, vol. 107, no. 5–6, Springer, 2002, pp. 1043–127, doi:<a href=\"https://doi.org/10.1023/A:1015157624384\">10.1023/A:1015157624384</a>.","ama":"Erdös L. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. <i>Journal of Statistical Physics</i>. 2002;107(5-6):1043-1127. doi:<a href=\"https://doi.org/10.1023/A:1015157624384\">10.1023/A:1015157624384</a>","ieee":"L. Erdös, “Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field,” <i>Journal of Statistical Physics</i>, 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.","chicago":"Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” <i>Journal of Statistical Physics</i>. Springer, 2002. <a href=\"https://doi.org/10.1023/A:1015157624384\">https://doi.org/10.1023/A:1015157624384</a>.","apa":"Erdös, L. (2002). Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1023/A:1015157624384\">https://doi.org/10.1023/A:1015157624384</a>"},"date_created":"2018-12-11T11:59:20Z","month":"06","page":"1043 - 1127","status":"public","external_id":{"arxiv":["math-ph/0108025"]},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","volume":107,"date_updated":"2023-07-18T09:08:45Z","type":"journal_article","extern":"1","publication_identifier":{"issn":["0022-4715"]},"doi":"10.1023/A:1015157624384","author":[{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"}],"_id":"2738","publication":"Journal of Statistical Physics","publication_status":"published","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."}],"publisher":"Springer","year":"2002","article_type":"original","day":"01","date_published":"2002-06-01T00:00:00Z","publist_id":"4154","intvolume":"       107","language":[{"iso":"eng"}],"title":"Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field","quality_controlled":"1","scopus_import":"1","issue":"5-6","oa_version":"Submitted Version"}