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Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories
Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.
0021-9606
1-7
Goodwin, David
349b642d-bc15-4a8d-b1d7-98691a39e069
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065
Goodwin, David
349b642d-bc15-4a8d-b1d7-98691a39e069
Kuprov, Ilya
bb07f28a-5038-4524-8146-e3fc8344c065

Goodwin, David and Kuprov, Ilya (2015) Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories. The Journal of Chemical Physics, 143 (8), 1-7. (doi:10.1063/1.4928978). (PMID:26328824)

Record type: Article

Abstract

Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.

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Accepted/In Press date: 10 August 2015
Published date: 25 August 2015
Organisations: Computational Systems Chemistry, Magnetic Resonance

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Local EPrints ID: 395546
URI: https://eprints.soton.ac.uk/id/eprint/395546
ISSN: 0021-9606
PURE UUID: 9270181e-3a24-4fc7-acb9-9026da2ee516
ORCID for Ilya Kuprov: ORCID iD orcid.org/0000-0003-0430-2682

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Date deposited: 31 May 2016 15:56
Last modified: 20 Jul 2019 00:42

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Contributors

Author: David Goodwin
Author: Ilya Kuprov ORCID iD

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