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Perturbative semiclassical trace formulae for harmonic oscillators
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
Örebro University, School of Science and Technology. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark; Nano Science Center, Department of Chemistry, University of Copenhagen, København, Denmark. (matematik)ORCID iD: 0000-0002-2630-7479
2015 (English)In: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 75, no 3, 359-382 p.Article in journal (Refereed) Published
Abstract [en]

In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn the conclusion that the gross structure of the quantum spectrum is determined from only classical circular and diameter orbits for this class of systems.

Place, publisher, year, edition, pages
2015. Vol. 75, no 3, 359-382 p.
Keyword [en]
Perturbative trace formula; Radially perturbed harmonic oscillators; Semiclassical density of states
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Other Physics Topics
Research subject
Physics
Identifiers
URN: urn:nbn:se:oru:diva-44859DOI: 10.1016/S0034-4877(15)30011-2ISI: 000356748400003Scopus ID: 2-s2.0-84930856149OAI: oai:DiVA.org:oru-44859DiVA: diva2:818497
Available from: 2015-06-09 Created: 2015-06-09 Last updated: 2017-12-04Bibliographically approved

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Ögren, Magnus

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