{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23954"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23954","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Theory of polaron mobility","abstract":"\"Two different methods for describing the polaron-phonon system are formulated 0 These are: (1) description in terms of quasiparticle states, (2) description in terms of thermodynamic GreenYs functions~ The first approach leads naturally to an S matrix formulation of polaron transport~ The second leads to the Kadanoff-Baym transport equations 0 It is shown that both approaches are equivalento By using the latter approach$ it is shown that the low-temperature polaron drift mObility is given rigorously by IJ. :; e'T/m * , where 'T is the polaron lifetime\"\" and m* its effective masso This relationship is verified explicitly to lowest nontrivial order in the coupling constant by using the Kubo formula. Various methods for calculating the low-temperature mobility for weak and intermediate coupling are discussed and critically compared~ These methods include: (1) perturbation theorYt (2) the Feynman model of the polaron as applied by 'osaka, or Feynman, Hellswarth, Iddings, and Platzman» or Schultz, (3) the Low-Pines intermediate coupling theory augmented by Lawus scattering theory 0 The low=temperature mobility is calculated in pertur- 02· bat ion theory to order a. 0 It is found that I-L = lJ.o (l=a/6 + 0(0, UJI where Il o is the weak~coupling mo. bilityo This result corresponds most closely with the expansion of Osakavs mobility formula o Certain improvements to the mobility calculations of Schultz~ and of Low and Pines are suggested 0 When these improvements are incorporated» both the Low~Pines and the Schultz theories come into much better agreement with the perturbation expansion for weak coupling, and wit.h OsakaBs theory for intermediate coupling.\"","abstract_html":""Two different methods for describing the polaron-phonon system are formulated 0 These are: (1) description in terms of quasiparticle states, (2) description in terms of thermodynamic GreenYs functions~ The first approach leads naturally to an S matrix formulation of polaron transport~ The second leads to the Kadanoff-Baym transport equations 0 It is shown that both approaches are equivalento By using the latter approach$ it is shown that the low-temperature polaron drift mObility is given rigorously by IJ. :; e'T/m * , where 'T is the polaron lifetime"" and m* its effective masso This relationship is verified explicitly to lowest nontrivial order in the coupling constant by using the Kubo formula. Various methods for calculating the low-temperature mobility for weak and intermediate coupling are discussed and critically compared~ These methods include: (1) perturbation theorYt (2) the Feynman model of the polaron as applied by 'osaka, or Feynman, Hellswarth, Iddings, and Platzman» or Schultz, (3) the Low-Pines intermediate coupling theory augmented by Lawus scattering theory 0 The low=temperature mobility is calculated in pertur- 02· bat ion theory to order a. 0 It is found that I-L = lJ.o (l=a/6 + 0(0, UJI where Il o is the weak~coupling mo. bilityo This result corresponds most closely with the expansion of Osakavs mobility formula o Certain improvements to the mobility calculations of Schultz~ and of Low and Pines are suggested 0 When these improvements are incorporated» both the Low~Pines and the Schultz theories come into much better agreement with the perturbation expansion for weak coupling, and wit.h OsakaBs theory for intermediate coupling."","abstract_has_math":false,"creators":["Langreth, David Chapman"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Kadanoff, L.P."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-18T20:46:28Z","date_published":"2011-05-18T20:46:28Z","updated_at":"2026-07-22T22:25:23Z","subjects":["polaron mobility","polaron-phonon system","quasiparticle states","Green's functions"],"languages":["en"],"rights":["1964 David Chapman Langreth"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["6146096"],"render_values":[{"text":"6146096","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23954","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kadanoff, L.P."]},{"key":"dc:creator","label":"Author","values":["Langreth, David Chapman"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-18T20:46:28Z","10000-01-01","1964"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["polaron mobility","polaron-phonon system","quasiparticle states","Green's functions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1964 David Chapman Langreth"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["6146096","http://hdl.handle.net/2142/23954"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"Two different methods for describing the polaron-phonon system are formulated 0 These are: (1) description in terms of quasiparticle states, (2) description in terms of thermodynamic GreenYs functions~ The first approach leads naturally to an S matrix formulation of polaron transport~ The second leads to the Kadanoff-Baym transport equations 0 It is shown that both approaches are equivalento By using the latter approach$ it is shown that the low-temperature polaron drift mObility is given rigorously by IJ. :; e'T/m * , where 'T is the polaron lifetime\"\" and m* its effective masso This relationship is verified explicitly to lowest nontrivial order in the coupling constant by using the Kubo formula. Various methods for calculating the low-temperature mobility for weak and intermediate coupling are discussed and critically compared~ These methods include: (1) perturbation theorYt (2) the Feynman model of the polaron as applied by 'osaka, or Feynman, Hellswarth, Iddings, and Platzman» or Schultz, (3) the Low-Pines intermediate coupling theory augmented by Lawus scattering theory 0 The low=temperature mobility is calculated in pertur- 02· bat ion theory to order a. 0 It is found that I-L = lJ.o (l=a/6 + 0(0, UJI where Il o is the weak~coupling mo. bilityo This result corresponds most closely with the expansion of Osakavs mobility formula o Certain improvements to the mobility calculations of Schultz~ and of Low and Pines are suggested 0 When these improvements are incorporated» both the Low~Pines and the Schultz theories come into much better agreement with the perturbation expansion for weak coupling, and wit.h OsakaBs theory for intermediate coupling.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T20:46:28Z No. of bitstreams: 1 1964_langreth.pdf: 5116633 bytes, checksum: 605e051a16245d9ceac84c15c7e0cd33 (MD5)","Made available in DSpace on 2011-05-18T20:46:28Z (GMT). No. of bitstreams: 1 1964_langreth.pdf: 5116633 bytes, checksum: 605e051a16245d9ceac84c15c7e0cd33 (MD5) Previous issue date: 1964","Restriction data tranferred 2014-07-01T11:16:09-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T20:46:28Z Item is restricted indefinitely.","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Theory of polaron mobility"]}]}],"canonical_facts":{"dc:contributor":["Kadanoff, L.P."],"dc:creator":["Langreth, David Chapman"],"dc:date":["2011-05-18T20:46:28Z","10000-01-01","1964"],"dc:description":["\"Two different methods for describing the polaron-phonon system are formulated 0 These are: (1) description in terms of quasiparticle states, (2) description in terms of thermodynamic GreenYs functions~ The first approach leads naturally to an S matrix formulation of polaron transport~ The second leads to the Kadanoff-Baym transport equations 0 It is shown that both approaches are equivalento By using the latter approach$ it is shown that the low-temperature polaron drift mObility is given rigorously by IJ. :; e'T/m * , where 'T is the polaron lifetime\"\" and m* its effective masso This relationship is verified explicitly to lowest nontrivial order in the coupling constant by using the Kubo formula. Various methods for calculating the low-temperature mobility for weak and intermediate coupling are discussed and critically compared~ These methods include: (1) perturbation theorYt (2) the Feynman model of the polaron as applied by 'osaka, or Feynman, Hellswarth, Iddings, and Platzman» or Schultz, (3) the Low-Pines intermediate coupling theory augmented by Lawus scattering theory 0 The low=temperature mobility is calculated in pertur- 02· bat ion theory to order a. 0 It is found that I-L = lJ.o (l=a/6 + 0(0, UJI where Il o is the weak~coupling mo. bilityo This result corresponds most closely with the expansion of Osakavs mobility formula o Certain improvements to the mobility calculations of Schultz~ and of Low and Pines are suggested 0 When these improvements are incorporated» both the Low~Pines and the Schultz theories come into much better agreement with the perturbation expansion for weak coupling, and wit.h OsakaBs theory for intermediate coupling.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T20:46:28Z No. of bitstreams: 1 1964_langreth.pdf: 5116633 bytes, checksum: 605e051a16245d9ceac84c15c7e0cd33 (MD5)","Made available in DSpace on 2011-05-18T20:46:28Z (GMT). No. of bitstreams: 1 1964_langreth.pdf: 5116633 bytes, checksum: 605e051a16245d9ceac84c15c7e0cd33 (MD5) Previous issue date: 1964","Restriction data tranferred 2014-07-01T11:16:09-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T20:46:28Z Item is restricted indefinitely.","Thesis","U of I Only"],"dc:identifier":["6146096","http://hdl.handle.net/2142/23954"],"dc:language":["en"],"dc:rights":["1964 David Chapman Langreth"],"dc:subject":["polaron mobility","polaron-phonon system","quasiparticle states","Green's functions"],"dc:title":["Theory of polaron mobility"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:23Z"}