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dc.contributor.authorDatchev, Kiril
dc.contributor.authorGell-Redman, Jesse
dc.contributor.authorHassell, Andrew
dc.contributor.authorHumphries, Peter
dc.date.accessioned2016-10-21T19:27:54Z
dc.date.available2016-10-21T19:27:54Z
dc.date.issued2013-11
dc.date.submitted2012-12
dc.identifier.issn0010-3616
dc.identifier.issn1432-0916
dc.identifier.urihttp://hdl.handle.net/1721.1/104921
dc.description.abstractConsider a semiclassical Hamiltonian H[subscript V,h]:=h[superscript 2] Δ + V − E, where h > 0 is a semiclassical parameter, Δ is the positive Laplacian on R[superscript d],V is a smooth, compactly supported central potential function and E > 0 is an energy level. In this setting the scattering matrix S[subscript h](E) is a unitary operator on L[superscript 2](S[superscript d−1]), hence with spectrum lying on the unit circle; moreover, the spectrum is discrete except at 1. We show under certain additional assumptions on the potential that the eigenvalues of S[subscript h](E) can be divided into two classes: a finite number ∼c[subscript d](R√E/h)[superscript d−1], as h→0, where B(0, R) is the convex hull of the support of the potential, that equidistribute around the unit circle, and the remainder that are all very close to 1. Semiclassically, these are related to the rays that meet the support of, and hence are scattered by, the potential, and those that do not meet the support of the potential, respectively. A similar property is shown for the obstacle problem in the case that the obstacle is the ball of radius R.en_US
dc.description.sponsorshipNational Science Foundation (U.S.). (Postdoctoral Fellowship)en_US
dc.publisherSpringer Berlin Heidelbergen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00220-013-1841-8en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleApproximation and Equidistribution of Phase Shifts: Spherical Symmetryen_US
dc.typeArticleen_US
dc.identifier.citationDatchev, Kiril et al. “Approximation and Equidistribution of Phase Shifts: Spherical Symmetry.” Communications in Mathematical Physics 326.1 (2014): 209–236.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorDatchev, Kiril
dc.relation.journalCommunications in Mathematical Physicsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-08-18T15:24:04Z
dc.language.rfc3066en
dc.rights.holderSpringer-Verlag Berlin Heidelberg
dspace.orderedauthorsDatchev, Kiril; Gell-Redman, Jesse; Hassell, Andrew; Humphries, Peteren_US
dspace.embargo.termsNen
mit.licensePUBLISHER_POLICYen_US


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