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Adiabatic invariants for the regular region of the Dicke model

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Bastarrachea Magnani A.; R, M. A. and Relaño Pérez, Armando and Lerma Hernández, S. and López del Carpio, B. and Chávez Carlos, J. and Hirsch, J. G. (2017) Adiabatic invariants for the regular region of the Dicke model. Journal of physics A: Mathematical and theoretical, 50 (14). ISSN 1751-8113

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Official URL: http://dx.doi.org/10.1088/1751-8121/aa6162


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http://iopscience.iop.org/Publisher


Abstract

Adiabatic invariants for the non-integrable Dicke model are introduced. They are shown to provide approximate second integrals of motion in the energy region where the system exhibits a regular dynamics. This low-energy region, present for any set of values of the Hamiltonian parameters is described both with a semiclassical and a full quantum analysis in a broad region of the parameter space. Peres lattices in this region exhibit that many observables vary smoothly with energy, along distinct lines which beg for a formal description. It is demonstrated how the adiabatic invariants provide a rationale to their presence in many cases. They are built employing the Born-Oppenheimer approximation, valid when a fast system is coupled to a much slower one. As the Dicke model has one bosonic and one fermionic degree of freedom, two versions of the approximation are used, depending on which one is the faster. In both cases a noticeably accord with exact numerical results is obtained. The employment of the adiabatic invariants provides a simple and clear theoretical framework to study the physical phenomenology associated to these regimes, far beyond the energies where a quadratic approximation around the minimal energy configuration can be used.


Item Type:Article
Additional Information:

© 2017 IOP Publishing Ltd. AR is supported by Spanish Grants No. FIS2012-35316 and FIS2015-63770-P (MINECO/FEDER), MAB-M, SL-H, BLC, JC-C and JGH acknowledge financial support from Mexican CONACyT project CB166302 and DGAPA-UNAM project IN109417. SL-H acknowledges financial support from Mexican CONACyT project CB2015-01/255702 and from CONACyT fellowship program for sabbatical leaves.

Uncontrolled Keywords:Superradiant phase-transition; No-go theorem; Numerical-solutions; Space quantization; Radiation-field; Quantum rabi; Lipkin model; Systems; Spin; Integrability
Subjects:Sciences > Physics > Thermodynamics
ID Code:44709
Deposited On:22 Nov 2017 12:20
Last Modified:11 Dec 2017 11:33

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