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Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

Bonet Luz, Esther and Tronci, C (2015) Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states .

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The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical operators are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the `Ehrenfest group'. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie-Poisson structure associated to another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models previously appeared in the chemical physics literature.

Item Type: Other
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bonet Luz,
Date : 9 July 2015
Uncontrolled Keywords : math-ph, math-ph, math.MP, physics.chem-ph, quant-ph
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 13:39
Last Modified : 06 Jul 2019 05:23

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