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Universality of the quantum boundary layer for a Maxwellian gas
Istanbul Technical University, Energy Institute.
Istanbul Technical University, Energy Institute.ORCID iD: 0000-0002-7431-5115
2009 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 79, article id 065002Article in journal (Refereed) Published
Abstract [en]

For an ideal gas confined in a rectangular domain, it has been shown that the density is not homogenous even in thermodynamic equilibrium and it goes to zero within a layernear to the boundaries due to the wave character of particles. This layer has been called the quantum boundary layer (QBL). In literature, an analytical expression for the thickness of QBL has been given for only a rectangular domain since both energy eigenvalues andeigenfunctions of the Schrödinger equation can analytically be obtained for only a rectangulardomain. In this study, ideal Maxwellian gases confined in spherical and cylindrical domainsare considered to investigate whether the thickness of QBL is independent of the domain shape. Although the energy eigenvalues are the roots of Bessel functions and there is noanalytical expression giving the roots, the thickness of QBL is expressed analytically by considering the density distributions and using some simplifications based on the numerical calculations. It is found that QBL has the same thickness for the domains of different shapes.Therefore, QBL seems to have a universal thickness independent of the domain shape for anideal Maxwellian gas.

Place, publisher, year, edition, pages
2009. Vol. 79, article id 065002
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:uu:diva-380299OAI: oai:DiVA.org:uu-380299DiVA, id: diva2:1299086
Available from: 2019-03-26 Created: 2019-03-26 Last updated: 2019-03-26

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