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The multilevel pairing Hamiltonian versus the degenerate case. (English) Zbl 1138.81561

Summary: We study the pairing Hamiltonian in a set of non-degenerate levels. First, we review in the path integral framework the spontaneous breaking of the \(U(1)\) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.

MSC:

81V35 Nuclear physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R40 Symmetry breaking in quantum theory
81Q15 Perturbation theories for operators and differential equations in quantum theory
81S40 Path integrals in quantum mechanics
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References:

[1] Barbaro, M. B.; Molinari, A.; Palumbo, F.; Quaglia, M. R., Phys. Rev. C, 70, 034309 (2004)
[2] Barbaro, M. B.; Cenni, R.; Molinari, A.; Quaglia, M. R., Eur. Phys. J. A, 22, 377 (2004)
[3] Barbaro, M.; Cenni, R.; Molinari, A.; Quaglia, M. R., Phys. Rev. C, 66, 034310 (2002)
[4] Haag, R., Nuovo Cim., 25, 287 (1962)
[5] M.C. Cambiaggio, A.M.F. Rivas, M. Saraceno, arXiv:nucl-th/9708031; M.C. Cambiaggio, A.M.F. Rivas, M. Saraceno, arXiv:nucl-th/9708031
[6] Richardson, R. W., J. Math. Phys., 6, 1034 (1965)
[7] Roman, M.; Sierra, G.; Dukelsky, J., Nucl. Phys. B, 634, 483 (2002)
[8] Negele, J. W.; Orland, H., Quantum many-particle systems (1988), Addison-Wesley Pub. Co.: Addison-Wesley Pub. Co. Redwood City, CA
[9] Weinberg, S., The Quantum Theory of Fields, Vol.2 (1996), Cambridge University Press
[10] M.B. Barbaro and M.R. Quaglia, “Bosonization of the pairing hamiltonian,” contribution to the book Progress in Boson Research, Nova Science Publishers (NY), arXiv:nucl-th/0506085; M.B. Barbaro and M.R. Quaglia, “Bosonization of the pairing hamiltonian,” contribution to the book Progress in Boson Research, Nova Science Publishers (NY), arXiv:nucl-th/0506085 · Zbl 1037.81638
[11] Palumbo, F., Phys. Rev. C, 72, 014303 (2005)
[12] Anderson, P. W., J. Phys. Chem. Solids, 11, 28 (1959)
[13] Yuzbashyan, E.; Baytin, A.; Altshuler, B., Phys. Rev. B, 68, 214509 (2003)
[14] M.B. Barbaro, R. Cenni, A. Molinari, M.R. Quaglia, submitted for publication.; M.B. Barbaro, R. Cenni, A. Molinari, M.R. Quaglia, submitted for publication.
[15] Gaudin, M., Modeles Exactement Resolus (1995), les Editions de Physique: les Editions de Physique France
[16] Gorkov, L. P.; Melik-Barkhudarov, T. K., Sov. Phys. JEPT, 13, 1018 (1961)
[17] Heiselberg, H.; Pethick, C. J.; Smith, H.; Viverit, L., Phys. Rev. Lett., 85, 2418 (2000)
[18] T. Papenbrock, A. Bhattacharyya, arXiv:nucl-th/0609084; T. Papenbrock, A. Bhattacharyya, arXiv:nucl-th/0609084
[19] Rombouts, S.; Van Deck, D.; Dukelsky, J., Phys. Rev. C, 69, 061303 (2004), (R)
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