Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile

Handle URI:
http://hdl.handle.net/10754/566116
Title:
Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile
Authors:
Bardos, Claude W.; Golse, François; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Paul, Thierry A.
Abstract:
Consider a monokinetic probability measure on the phase space (Formula presented.) , i.e. (Formula presented.) where Uin is a vector field on RN and ρin a probability density on RN. Let Φt be a Hamiltonian flow on RN × RN. In this paper, we study the structure of the transported measure (Formula presented.) and of its integral in the ξ variable denoted ρ(t). In particular, we give estimates on the number of folds in (Formula presented.) , on which μ(t) is concentrated. We explain how our results can be applied to investigate the classical limit of the Schrödinger equation by using the formalism of Wigner measures. Our formalism includes initial momentum profiles Uin with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis
Issue Date:
27-Dec-2014
DOI:
10.1007/s00205-014-0829-7
ARXIV:
arXiv:1207.5927v2
Type:
Article
ISSN:
00039527
Sponsors:
Peter Markowich thanks the Fondation des Sciences Mathematiques de Paris for its support during the preparation of this paper.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBardos, Claude W.en
dc.contributor.authorGolse, Françoisen
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorPaul, Thierry A.en
dc.date.accessioned2015-08-12T09:28:57Zen
dc.date.available2015-08-12T09:28:57Zen
dc.date.issued2014-12-27en
dc.identifier.issn00039527en
dc.identifier.doi10.1007/s00205-014-0829-7en
dc.identifier.urihttp://hdl.handle.net/10754/566116en
dc.description.abstractConsider a monokinetic probability measure on the phase space (Formula presented.) , i.e. (Formula presented.) where Uin is a vector field on RN and ρin a probability density on RN. Let Φt be a Hamiltonian flow on RN × RN. In this paper, we study the structure of the transported measure (Formula presented.) and of its integral in the ξ variable denoted ρ(t). In particular, we give estimates on the number of folds in (Formula presented.) , on which μ(t) is concentrated. We explain how our results can be applied to investigate the classical limit of the Schrödinger equation by using the formalism of Wigner measures. Our formalism includes initial momentum profiles Uin with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp.en
dc.description.sponsorshipPeter Markowich thanks the Fondation des Sciences Mathematiques de Paris for its support during the preparation of this paper.en
dc.publisherSpringer Natureen
dc.titleHamiltonian Evolution of Monokinetic Measures with Rough Momentum Profileen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalArchive for Rational Mechanics and Analysisen
dc.contributor.institutionLaboratoire J.-L. Lions, Université Paris-Diderot, 4 place Jussieu, BP187Paris Cedex 05, Franceen
dc.contributor.institutionEcole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS)Palaiseau Cedex, Franceen
dc.contributor.institutionCNRS and Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS)Palaiseau Cedex, Franceen
dc.identifier.arxividarXiv:1207.5927v2en
kaust.authorMarkowich, Peter A.en
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