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Hyperpolarization and the physical boundary of Liouville space

Hyperpolarization and the physical boundary of Liouville space
Hyperpolarization and the physical boundary of Liouville space

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I=1/2, I=1, I=3/2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.
395-407
Levitt, Malcolm H.
bcc5a80a-e5c5-4e0e-9a9a-249d036747c3
Bengs, Christian
6d086f95-d3e8-4adc-86a5-6b255aee4dd1
Levitt, Malcolm H.
bcc5a80a-e5c5-4e0e-9a9a-249d036747c3
Bengs, Christian
6d086f95-d3e8-4adc-86a5-6b255aee4dd1

Levitt, Malcolm H. and Bengs, Christian (2021) Hyperpolarization and the physical boundary of Liouville space. Magnetic Resonance, 2 (1), 395-407. (doi:10.5194/mr-2-395-2021).

Record type: Article

Abstract


The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I=1/2, I=1, I=3/2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

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More information

Accepted/In Press date: 3 May 2021
Published date: 8 June 2021

Identifiers

Local EPrints ID: 449783
URI: http://eprints.soton.ac.uk/id/eprint/449783
PURE UUID: df4231d1-9f07-41ba-b6c9-4b2404ce6063
ORCID for Malcolm H. Levitt: ORCID iD orcid.org/0000-0001-9878-1180

Catalogue record

Date deposited: 17 Jun 2021 16:30
Last modified: 29 Jun 2021 01:38

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