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Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator


Alexander Karabanov

Grzegorz Kwiatkowski


Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided how the Lindblad-Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad-Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition we provide a summary of different relaxation mechanism that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation.


Karabanov, A., Kwiatkowski, G., & Köckenberger, W. (2014). Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator. Molecular Physics, 112(14),

Journal Article Type Article
Acceptance Date Jan 10, 2014
Online Publication Date Feb 14, 2014
Publication Date Jul 18, 2014
Deposit Date Jul 15, 2016
Publicly Available Date Jul 15, 2016
Journal Molecular Physics
Print ISSN 0026-8976
Electronic ISSN 0026-8976
Publisher Taylor & Francis Open
Peer Reviewed Peer Reviewed
Volume 112
Issue 14
Keywords Lindblad–Kossakowski master equation, Liouville space, solid effect dynamic nuclear polarisation, relaxation superoperator, spin dynamics
Public URL
Publisher URL
Additional Information The Version of Record of this manuscript has been published and is available in Molecular Physics c2014


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