2002
DOI: 10.1103/physrevlett.89.210405
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Torus Quantization for Spinning Particles

Abstract: We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and classical spin precession. We determine the geometry of the invariant manifolds of this product dynamics which support semiclassical solutions of the wave equation. The semiclassical quantization conditions contain a new term, which is of the same order as the Maslov correction. Thi… Show more

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Cited by 11 publications
(17 citation statements)
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“…In this section, we demonstrate the general expression (16) of the main text for the spectrum of the Andreev bound states when the junction has some barriers. We first consider the scattering of particles and holes with E < ∆ at a single interface between a normal metal (left half space) and a superconductor (right half space).…”
Section: Appendix D: Junction With Barriersmentioning
confidence: 96%
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“…In this section, we demonstrate the general expression (16) of the main text for the spectrum of the Andreev bound states when the junction has some barriers. We first consider the scattering of particles and holes with E < ∆ at a single interface between a normal metal (left half space) and a superconductor (right half space).…”
Section: Appendix D: Junction With Barriersmentioning
confidence: 96%
“…(8). This precession preserves, as in the non-superconducting case [16,17], the latitude with respect to the local spin quantization axis n, which obeys a classical equation [Eq. (7)].…”
mentioning
confidence: 99%
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“…Next, it is suggested that the Fermi-Dirac (for electrons) and the Bose-Einstein (for photons) statistics used in the quantum mechanical description of the EPR-Bohm problem [16] seem to be a reminiscence of two consecutive steps. In the case of fermions that are ruled by the Dirac equation, the first step consists of the appearance of the generalized Einstein-Brillouin-Keller quantization conditions [17]. In the case of the free electromagnetic field that fulfills the Maxwell equations, the first step consists of the existence of the conserved generalized helicity [18].…”
Section: Introductionmentioning
confidence: 99%