A semiclassical analysis of the Efimov energy spectrum in the unitary limit

Details A semiclassical analysis of the Efimov energy spectrum in the unitary limit A semiclassical analysis of the Efimov energy spectrum in the unitary limit

2011-03-09

arxiv.org/abs/1103.1737v2

Phys. Ref. A 83, 063612 (2011)

Physics

Quantum Physics

LaTeX (revtex 4), 18pp., 4 Figs., revised version; to be published in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.83.063612

We demonstrate that the (s-wave) geometric spectrum of the Efimov energy levels in the unitary limit is generated by the radial motion of a primitive periodic orbit (and its harmonics) of the corresponding classical system. The action of the primitive orbit depends logarithmically on the energy. It is shown to be consistent with an inverse-squared radial potential with a lower cut-off radius. The lowest-order WKB quantization, including the Langer correction, is shown to reproduce the geometric scaling of the energy spectrum. The (WKB) mean-squared radii of the Efimov states scale geometrically like the inverse of their energies. The WKB wavefunctions, regularized near the classical turning point by Langer's generalized connection formula, are practically indistinguishable from the exact wave functions even for the lowest ($n=0$) state, apart from a tiny shift of its zeros that remains constant for large $n$.

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