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Title: Investigation of the stochastic representation of quantum evolutions
Author: Brown, Matthew Francis
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2013
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ABSTRACT. This work begins with an informal deduction of quantum stochastic calculus from a basic assumption about the nature of evolution. This is achieved using Belavkin's development of the theory introduced by Hudson and Parthasarathy. The Belavkin formalism is presented here as part of the thesis. Following this, the author uses the Belavkin formalism to construct a theory of Q-adaptcd quantum stochastic calculus and also to study the equations of coupled quantum stochastic processes. The Q-adapted calculus is a natural. generalization of the adapted calculus. It describes a Markovian flow, but in contrast to the adapted calculus one may obtain non-Markovian flows as linear combinations of Q-adapted flows. It is shown that the Q-free single-integrals satisfy the bosonic and fermionic field equations when Q is respectively an embedding of + 1 and -1, a. result bearing much resemblance to the identifications made by Hudson and Parthasarathy. In addition to this, details about the structure of Q-adapted Maassan-Mayer kernels is presented, and a Q-adapted Lindblad equation is even derived. The theory of coupled quantum stochastic processes, developed. here in the Belavkin formalism, proves very powerful as the author is able to prove an important conjecture of Hudson, a pioneer of the study of coupled quantum stochastic systems. The theory is built from a discussion of the solutions of homogeneous QSDEs (quantum stochastic differential equations), in parallel to Bclavkin's work, and these principles are carried over to the study of coupled systems. The study of QSDEs in the Belavkin formalism is also used to obtain interesting results regarding the presentation of quantum Hamiltonian dynamics as the expectation of an interaction dynamics of a quantum system with a canonical quantization of the clock.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available