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Renormalization Group Limit Cycles in Quantum Mechanical Problems

2004/03/10 by Erich J. Mueller, Mueller, Erich J., Tin-Lun Ho +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #Quantum chaos and dynamical systems #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0403283

5 pages, 2 figures (1 BW, 1 color), RevTeX4; ver2: updated references; Due to strong overlap with [Kolomeisky and Straley, Phys. Rev. B 46, 12664 (1992)] this paper is no longer being considered for publication

arxiv created 2004/03/31 · arxiv updated 2009/12/01

Abstract

We formulate a renormalization group (RG) for the interaction parameters of the general two-body problem and show how a limit cycle emerges in the RG flow if the interaction approaches an inverse square law. This limit cycle generates a scaling structure in the energy spectrum. Our demonstration is relevant to the Efimov problem in nuclear physics where similar scaling appears.

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