Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons
In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symm...
Gespeichert in:
| Veröffentlicht in: | Archive for rational mechanics and analysis 2019-01, Vol.231 (1), p.63-89 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 89 |
|---|---|
| container_issue | 1 |
| container_start_page | 63 |
| container_title | Archive for rational mechanics and analysis |
| container_volume | 231 |
| creator | Nguyen, Toan T. Tran, Minh-Binh |
| description | In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time. |
| doi_str_mv | 10.1007/s00205-018-1271-z |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2161379194</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2161379194</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-1444d414d4f064617c045ed993ea73d678af47d7268a0d2d45a1877fad2d79ed3</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWKs_wFvAczSTZJPdo5b6AQsibc8hNFnZ0k3aZBexv94sK3jyMMzX887Ai9At0HugVD0kShktCIWSAFNATmdoBoIzQqXi52hGKeWkKpi6RFcp7caWcTlDq41vmxA73Hq8bjuH6_DlIn4Kg7c4L_Aq7Ie-DT7hPmCDPwbj-6HLwL4_dcZ7vDwOZgRwaPI0ZfIaXTRmn9zNb56jzfNyvXgl9fvL2-KxJlsOsicghLACcjRUCglqS0XhbFVxZxS3UpWmEcoqJktDLbOiMFAq1Zhcq8pZPkd3091DDMfBpV7vwhB9fqkZSOCqgkpkCiZqG0NK0TX6ENvOxG8NVI_e6ck7nb3To3f6lDVs0qTM-k8X_y7_L_oBqzxxFw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2161379194</pqid></control><display><type>article</type><title>Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons</title><source>Springer Nature - Complete Springer Journals</source><creator>Nguyen, Toan T. ; Tran, Minh-Binh</creator><creatorcontrib>Nguyen, Toan T. ; Tran, Minh-Binh</creatorcontrib><description>In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.</description><identifier>ISSN: 0003-9527</identifier><identifier>EISSN: 1432-0673</identifier><identifier>DOI: 10.1007/s00205-018-1271-z</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Boltzmann transport equation ; Bosons ; Classical Mechanics ; Complex Systems ; Fluid- and Aerodynamics ; Gaussian distribution ; Lower bounds ; Mathematical analysis ; Mathematical and Computational Physics ; Normal distribution ; Particle energy ; Physics ; Physics and Astronomy ; Theoretical</subject><ispartof>Archive for rational mechanics and analysis, 2019-01, Vol.231 (1), p.63-89</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-1444d414d4f064617c045ed993ea73d678af47d7268a0d2d45a1877fad2d79ed3</citedby><cites>FETCH-LOGICAL-c316t-1444d414d4f064617c045ed993ea73d678af47d7268a0d2d45a1877fad2d79ed3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00205-018-1271-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00205-018-1271-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Nguyen, Toan T.</creatorcontrib><creatorcontrib>Tran, Minh-Binh</creatorcontrib><title>Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons</title><title>Archive for rational mechanics and analysis</title><addtitle>Arch Rational Mech Anal</addtitle><description>In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.</description><subject>Boltzmann transport equation</subject><subject>Bosons</subject><subject>Classical Mechanics</subject><subject>Complex Systems</subject><subject>Fluid- and Aerodynamics</subject><subject>Gaussian distribution</subject><subject>Lower bounds</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Normal distribution</subject><subject>Particle energy</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Theoretical</subject><issn>0003-9527</issn><issn>1432-0673</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wFvAczSTZJPdo5b6AQsibc8hNFnZ0k3aZBexv94sK3jyMMzX887Ai9At0HugVD0kShktCIWSAFNATmdoBoIzQqXi52hGKeWkKpi6RFcp7caWcTlDq41vmxA73Hq8bjuH6_DlIn4Kg7c4L_Aq7Ie-DT7hPmCDPwbj-6HLwL4_dcZ7vDwOZgRwaPI0ZfIaXTRmn9zNb56jzfNyvXgl9fvL2-KxJlsOsicghLACcjRUCglqS0XhbFVxZxS3UpWmEcoqJktDLbOiMFAq1Zhcq8pZPkd3091DDMfBpV7vwhB9fqkZSOCqgkpkCiZqG0NK0TX6ENvOxG8NVI_e6ck7nb3To3f6lDVs0qTM-k8X_y7_L_oBqzxxFw</recordid><startdate>20190101</startdate><enddate>20190101</enddate><creator>Nguyen, Toan T.</creator><creator>Tran, Minh-Binh</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20190101</creationdate><title>Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons</title><author>Nguyen, Toan T. ; Tran, Minh-Binh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-1444d414d4f064617c045ed993ea73d678af47d7268a0d2d45a1877fad2d79ed3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Boltzmann transport equation</topic><topic>Bosons</topic><topic>Classical Mechanics</topic><topic>Complex Systems</topic><topic>Fluid- and Aerodynamics</topic><topic>Gaussian distribution</topic><topic>Lower bounds</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Normal distribution</topic><topic>Particle energy</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nguyen, Toan T.</creatorcontrib><creatorcontrib>Tran, Minh-Binh</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Archive for rational mechanics and analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nguyen, Toan T.</au><au>Tran, Minh-Binh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons</atitle><jtitle>Archive for rational mechanics and analysis</jtitle><stitle>Arch Rational Mech Anal</stitle><date>2019-01-01</date><risdate>2019</risdate><volume>231</volume><issue>1</issue><spage>63</spage><epage>89</epage><pages>63-89</pages><issn>0003-9527</issn><eissn>1432-0673</eissn><abstract>In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00205-018-1271-z</doi><tpages>27</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-9527 |
| ispartof | Archive for rational mechanics and analysis, 2019-01, Vol.231 (1), p.63-89 |
| issn | 0003-9527 1432-0673 |
| language | eng |
| recordid | cdi_proquest_journals_2161379194 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Boltzmann transport equation Bosons Classical Mechanics Complex Systems Fluid- and Aerodynamics Gaussian distribution Lower bounds Mathematical analysis Mathematical and Computational Physics Normal distribution Particle energy Physics Physics and Astronomy Theoretical |
| title | Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-10T12%3A57%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Uniform%20in%20Time%20Lower%20Bound%20for%20Solutions%20to%20a%20Quantum%20Boltzmann%20Equation%20of%20Bosons&rft.jtitle=Archive%20for%20rational%20mechanics%20and%20analysis&rft.au=Nguyen,%20Toan%20T.&rft.date=2019-01-01&rft.volume=231&rft.issue=1&rft.spage=63&rft.epage=89&rft.pages=63-89&rft.issn=0003-9527&rft.eissn=1432-0673&rft_id=info:doi/10.1007/s00205-018-1271-z&rft_dat=%3Cproquest_cross%3E2161379194%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2161379194&rft_id=info:pmid/&rfr_iscdi=true |