Mean-field dynamics in a class of open quantum systems

Rafiyi, Alireza (2017) Mean-field dynamics in a class of open quantum systems. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

We consider a system of N identical quantum particles coupled to an environment. The coupling is scaled in a mean-field way, and particles interact indirectly through the environment. There is no direct interaction between particles. The time evolution of the mean-field-scaled particles is called the mean-field dynamics and the limit of the evolution as N → ∞ is called the mean-field limit. The study of mean-field limits is an active topic of research in many-body quantum theory. Previously, almost all research in this area has been carried out for directly interacting particles without interaction with an environment. In this thesis, we prove that under a suitable condition on the initial system states the mean-field limit in the above indirectly interacting particle system does exist. The condition is satisfied in particular for spin ½ (qubit) systems. Assuming this condition, we show that the system dynamics is the free dynamics in the mean-field limit N → ∞, and we find the first and second correction terms. We show that the particles have a collective effect on the dynamics of the environment (reservoir) which we derive analytically. We give examples to illustrate our results.

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