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Uniform semiclassic...
Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking
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- Brack, M. (författare)
- Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany
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- Ögren, Magnus, 1977- (författare)
- Lund University,Lunds universitet,Matematisk fysik,Fysiska institutionen,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH
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- Yu, Yongle (författare)
- Lund University,Lunds universitet,Matematisk fysik,Fysiska institutionen,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH
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- Reimann, Stephanie (författare)
- Lund University,Lunds universitet,Matematisk fysik,Fysiska institutionen,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Physics,Department of Physics,Departments at LTH,Faculty of Engineering, LTH
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(creator_code:org_t)
- 2005-11-02
- 2005
- Engelska.
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 0305-4470 .- 1361-6447. ; 38:46, s. 9941-9967
- Relaterad länk:
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http://arxiv.org/pdf...
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http://dx.doi.org/10...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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https://lup.lub.lu.s...
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Abstract
Ämnesord
Stäng
- We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term . This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term for small ε in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold which is covered by the parameters describing their four-fold degeneracy. Then, we obtain an analytical uniform trace formula for arbitrary ε which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit ε (or energy) →0 restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios ωr:ωφ ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r4.
Ämnesord
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
- NATURVETENSKAP -- Fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences (hsv//eng)
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