Preprints
https://doi.org/10.5194/mr-2021-26
https://doi.org/10.5194/mr-2021-26

  12 Mar 2021

12 Mar 2021

Review status: this preprint is currently under review for the journal MR.

Hyperpolarization and the Physical Boundary of Liouville Space

Malcolm H. Levitt and Christian Bengs Malcolm H. Levitt and Christian Bengs
  • School of Chemistry, University of Southampton, SO17 1BJ, UK

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.

Malcolm H. Levitt and Christian Bengs

Status: open (until 15 Apr 2021)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on mr-2021-26', Anonymous Referee #1, 25 Mar 2021 reply
    • AC1: 'Reply on RC1', Malcolm Levitt, 25 Mar 2021 reply
  • CC1: 'Comment on mr-2021-26', Tom Barbara, 25 Mar 2021 reply
    • AC2: 'Reply on CC1', Malcolm Levitt, 25 Mar 2021 reply
  • RC2: 'Comment on mr-2021-26', Anonymous Referee #2, 13 Apr 2021 reply
    • CC2: 'Reply on RC2', Tom Barbara, 13 Apr 2021 reply

Malcolm H. Levitt and Christian Bengs

Malcolm H. Levitt and Christian Bengs

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Short summary
Magnetic resonance experiments are described using a mathematical object called the spin density operator. The article explores the regions of an abstract space called Liouville space which may be occupied by the density operator. The study is of particular relevance to hyperpolarized magnetic resonance, which is capable of generating greatly enhanced NMR signals which may be used, amongst other things, for imaging of metabolism in the human body.