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A master equation for spin systems far from equilibrium

A master equation for spin systems far from equilibrium
A master equation for spin systems far from equilibrium
The quantum dynamics of spin systems is often treated by a differential equation known as the master equation, which describes the trajectories of spin observables such as magnetization components, spin state populations, and coherences between spin states. The master equation describes how a perturbed spin system returns to a state of thermal equilibrium with a finite-temperature environment. The conventional master equation, which has the form of an inhomogeneous differential equation, applies to cases where the spin system remains close to thermal equilibrium, which is well satisfied for a wide variety of magnetic resonance experiments conducted on thermally polarized spin systems at ordinary temperatures. However, the conventional inhomogeneous master equation may fail in the case of hyperpolarized spin systems, when the spin state populations deviate strongly from thermal equilibrium, and in general where there is a high degree of nuclear spin order. We highlight a simple case in which the inhomogeneous master equation clearly fails, and propose an alternative master equation based on Lindblad superoperators which avoids most of the deficiencies of previous proposals. We discuss the strengths and limitations of the various formulations of the master equation, in the context of spin systems which are far from thermal equilibrium. The method is applied to several problems in nuclear magnetic resonance and to spin-isomer conversion.
Lindblad, Master equation, Relaxation, Spin isomers, Superoperator
1090-7807
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.
bcc5a80a-e5c5-4e0e-9a9a-249d036747c3

Bengs, Christian and Levitt, Malcolm H. (2020) A master equation for spin systems far from equilibrium. Journal of Magnetic Resonance, 310, [106645]. (doi:10.1016/j.jmr.2019.106645).

Record type: Article

Abstract

The quantum dynamics of spin systems is often treated by a differential equation known as the master equation, which describes the trajectories of spin observables such as magnetization components, spin state populations, and coherences between spin states. The master equation describes how a perturbed spin system returns to a state of thermal equilibrium with a finite-temperature environment. The conventional master equation, which has the form of an inhomogeneous differential equation, applies to cases where the spin system remains close to thermal equilibrium, which is well satisfied for a wide variety of magnetic resonance experiments conducted on thermally polarized spin systems at ordinary temperatures. However, the conventional inhomogeneous master equation may fail in the case of hyperpolarized spin systems, when the spin state populations deviate strongly from thermal equilibrium, and in general where there is a high degree of nuclear spin order. We highlight a simple case in which the inhomogeneous master equation clearly fails, and propose an alternative master equation based on Lindblad superoperators which avoids most of the deficiencies of previous proposals. We discuss the strengths and limitations of the various formulations of the master equation, in the context of spin systems which are far from thermal equilibrium. The method is applied to several problems in nuclear magnetic resonance and to spin-isomer conversion.

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Accepted/In Press date: 8 November 2019
e-pub ahead of print date: 19 November 2019
Published date: January 2020
Keywords: Lindblad, Master equation, Relaxation, Spin isomers, Superoperator

Identifiers

Local EPrints ID: 436191
URI: http://eprints.soton.ac.uk/id/eprint/436191
ISSN: 1090-7807
PURE UUID: db1ddafe-40f0-4f49-972b-f1e747ca4978
ORCID for Malcolm H. Levitt: ORCID iD orcid.org/0000-0001-9878-1180

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Date deposited: 03 Dec 2019 17:30
Last modified: 17 Mar 2021 02:37

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