Representations of canonical commutation relations describing infinite coherent states (Alain Joye, University Grenoble Alpes)

10.12.2018 15:15 – 16:15

We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which are random as well and can be expressed with the help of Ito stochastic integrals. We analyze the dynamics of the infinite coherent state alone and that of open systems consisting of small quantum systems coupled to the infinite coherent state. Under the free field dynamics, the initial phase distribution is shown to be driven to the uniform distribution, and coherences in small quantum systems interacting with the infinite coherent state, are shown to exhibit Gaussian time decay, instead of the exponential decay caused by infinite thermal states.
Joint work with Marco Merkli.

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Room 17, Séminaire "Mathématique Physique"

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