Non-Markovian open quantum systems

Zinterl, Maike Gail (2019) Non-Markovian open quantum systems. Masters thesis, Memorial University of Newfoundland.

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We examine different nonlinear open quantum systems and calculate the non-Markovianity based on the distinguishability between two density matrices. We show that for a single spin (qubit) coupled to a bosonic field the non-Markovianity depends on the spectral density function and can take on any number N with 0 ≤ N ≤ 1, meaning the dynamics can be Markovian or highly non-Markovian. For the main result we consider a system of Ntot identical spins coupled to an environment in the mean-field way. Each spin is coupled to a local and the common reservoir. There are only indirect interactions between the spins through the common reservoir. In limit Ntot → 1 the subsystem consisting of a fixed set of n particles reduces to a factorized state in which each factor is a single spin evolving according to a nonlinear Hartree-Lindblad equation which is exactly solvable. For non-stationary initial spin states the non-Markovianity diverges. In this instance we can never approximate the dynamics of the quantum system by a Markovian master equation and this implies that in the mean field models, memory effects are significant.

Item Type: Thesis (Masters)
Item ID: 13967
Additional Information: Includes bibliographical references (pages 82-84).
Keywords: Open Quantum System, Quantum dynamics, Non-Markovian measure, Mean-field
Department(s): Science, Faculty of > Mathematics and Statistics
Date: July 2019
Date Type: Submission
Library of Congress Subject Heading: Quantum systems--Mathematical models; Mean field theory--Mathematical models

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