On the spectrum of linear transport operator

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dc.contributorVirginia Techen
dc.contributor.authorLarsen, E. W.en
dc.contributor.authorZweifel, Paul F.en
dc.contributor.departmentPhysicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:27Zen
dc.date.available2014-04-09T18:12:27Zen
dc.date.issued1974-11en
dc.description.abstractIn this paper, spectral properties of the time_independent linear transport operator A are studied. This operator is defined in its natural Banach space L 1(D _ V), where D is the bounded space domain and V is the velocity domain. The collision operator K accounts for elastic and inelastic slowing down, fission, and low energy elastic and inelastic scattering. The various cross sections in K and the total cross section are piecewise continuous functions of position and speed. The two cases _0>0 and _0=0 are treated, where _0 is the minimum neutron speed. For _0=0, it is shown that _(A) consists of a full half_plane plus, in an adjoining strip, point eigenvalues and curves. For _0>0, _(A) consists just of point eigenvalues and curves in a certain half_space. In both cases, the curves are due to purely elastic ``Bragg'' scattering and are absent if this scattering does not occur. Finally the spectral differences between the two cases _0>0 and _0=0 are discussed briefly, and it is proved that A is the infinitesimal generator of a strongly continuous semigroup of operators.en
dc.identifier.citationLarsen, E. W., Zweifel, P. F., "On the spectrum of linear transport operator," J. Math. Phys. 15, 1987 (1974); http://dx.doi.org/10.1063/1.1666570en
dc.identifier.doihttps://doi.org/10.1063/1.1666570en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47086en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/15/11/10.1063/1.1666570en
dc.language.isoen_USen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectelasticityen
dc.subjecteigenvaluesen
dc.subjecttransport propertiesen
dc.subjectelastic collisionsen
dc.subjectinelastic scatteringen
dc.subjectneutronsen
dc.subjectspectral propertiesen
dc.titleOn the spectrum of linear transport operatoren
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden

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