Dressed coherent states in finite quantum systems: A cooperative game theory approach

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• 作者：A. Vourdas ^{a.vourdas@bradford.ac.uk}
• 关键词：Coherent states ; Finite quantum systems
• 刊名：Annals of Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：376
• 期：Complete
• 页码：153-181
• 全文大小：553 K
• 卷排序：376

文摘

A quantum system with variables in Z(d)Z(d) is considered. Coherent density matrices and coherent projectors of rank nn 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 QQ-function of a Hermitian operator, is then renormalized into a physical analogue of the Shapley values. Both the QQ-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.