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Dressed coherent states in finite quantum systems: A cooperative game theory approach
Publication Date
2017
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(c) 2017 Elsevier. Reproduced in accordance with the publisher's self-archiving policy. This manuscript version is made available under the CC-BY-NC-ND 4.0 license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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Accepted for publication
2016-12-01
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Abstract
A quantum system with variables in Z(d) is considered. Coherent density matrices and coherent projectors of rank n are introduced, and their properties (e.g., the resolution of the identity) are discussed. Cooperative game theory and in particular the Shapley methodology, is used to renormalize coherent states, into a particular type of coherent density matrices (dressed coherent states). The Q-function of a Hermitian operator, is then renormalized into a physical analogue of the Shapley values. Both the Q-function and the Shapley values, are used to study the relocation of a Hamiltonian in phase space as the coupling constant varies, and its effect on the ground state of the system. The formalism is also generalized for any total set of states, for which we have no resolution of the identity. The dressing formalism leads to density matrices that resolve the identity, and makes them practically useful.
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Accepted Manuscript
Citation
Vourdas A (2017) Dressed coherent states in finite quantum systems: A cooperative
game theory approach. Annals of Physics. 376: 153-181.
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Article