1516171819202120 of 21

Cite
Citation style
• apa
• harvard1
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
Discrete quantum Boltzmann equation
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0003-1232-3272
2019 (English)In: AIP Conference Proceedings, American Institute of Physics (AIP), 2019, Vol. 2132, p. 1-9, article id 130011Conference paper, Published paper (Refereed)
##### Abstract [en]

In this work, we consider a Boltzmann equation for anyons. In particular, we study a general discrete velocity model of the equation, where the velocity variable is assumed to only take values from a given finite-such that the (finite) number of velocities is arbitrary-set of velocities. Included, as two limiting cases, is the discrete quantum Boltzmann equation (Nordheim-Boltzmann/Uehling-Uhlenbeck equation) for bosons and fermions. Mass, momentum, and energy are assumed to be conserved during collisions, and considering suitable discrete velocity models, they will also be the only collision invariants. The equilibrium distributions will be given by a transcendental equation, and only in some few cases-including the two limiting cases where they are Planckians-they will be explicitly expressed. However, there is an H-theorem, and therefore one can prove that for the spatially homogeneous equation, as time tends to infinity, as well as, for the steady equation in a half-space with slab-symmetry, as the space variable tends to infinity, the distribution function converges to an equilibrium distribution. Linearizing around an equilibrium distribution in a suitable way, we find that the obtained linearized operator has similar properties as the corresponding linearized operator for the discrete Boltzmann equation: E.g. it is symmetric and positive semi-definite. Hence, previously obtained results for the spatially homogeneous Cauchy problem and the steady half-space problem in a slab symmetry for the discrete Boltzmann equation, can be applied also in the considered quantum case.

##### Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2019. Vol. 2132, p. 1-9, article id 130011
##### Series
AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616
Mathematics
Mathematics
##### Identifiers
Scopus ID: 2-s2.0-85070692522ISBN: 9780735418745 (print)OAI: oai:DiVA.org:kau-75689DiVA, id: diva2:1369679
##### Conference
31st International Symposium on Rarefied Gas Dynamics, RGD 2018, 23 July 2018 through 27 July 2018
Available from: 2019-11-12 Created: 2019-11-12 Last updated: 2019-11-21Bibliographically approved

#### Open Access in DiVA

##### File information
File name FULLTEXT01.pdfFile size 389 kBChecksum SHA-512
6540e6bee3ca86101d77a2ae6c25c0ed14b018fde54c3ee7c098be298a9f03e8e36faa6cf6a623f068ec4d51867761e52fb2f1144b9fb66fa1a83130c5c00c43
Type fulltextMimetype application/pdf

Scopus

Bernhoff, Niclas

#### Search in DiVA

Bernhoff, Niclas
##### By organisation
Department of Mathematics and Computer Science (from 2013)
Mathematics

#### Search outside of DiVA

The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available
doi
isbn
urn-nbn

#### Altmetric score

doi
isbn
urn-nbn
Total: 9 hits
1516171819202120 of 21

Cite
Citation style
• apa
• harvard1
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf