Perturbative Semiclassical Trace Formulae for Harmonic Oscillators

Jakob Møller-Andersen, Magnus Ögren

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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.
Original languageEnglish
JournalReports on Mathematical Physics
Issue number3
Pages (from-to)359-382
Number of pages24
Publication statusPublished - 2015


  • Perturbative trace formula
  • Semiclassical density of states
  • Radially perturbed harmonic oscillators


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