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Representations of canonical commutation relations describing infinite coherent states

Banff International Research Station for Mathematical Innovation and Discovery

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 state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution, and we demonstrate that coherencesin small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay, in contrast with the decay caused byinfinite thermal states, which is known to be exponentially rapid only. Work in collaboration with M. Merkli

Mathematics; Quantum theory; Partial differential equations; Applied computer science

video/mp4

Author affiliation: Institut Fourier, Université Grenoble 1

2016-07-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58559

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/