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

The Journal of Chemical Physics
D L Goodwin, Ilya Kuprov

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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Citations

May 6, 2016·The Journal of Organic Chemistry·Tharindi Dayara PanduwawalaTimothy D W Claridge
Jun 3, 2016·The Journal of Chemical Physics·D L Goodwin, Ilya Kuprov
Jul 30, 2016·Journal of Magnetic Resonance·Ilya Kuprov
Aug 16, 2016·The Journal of Physical Chemistry Letters·Octavi E SemoninJonathan S Owen
Jun 28, 2017·Physical Chemistry Chemical Physics : PCCP·Ludmilla GuduffIlya Kuprov
Sep 6, 2017·Magnetic Resonance in Chemistry : MRC·Ilya Kuprov
Mar 31, 2019·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Mads Sloth VindingTorben Ellegaard Lund
Mar 17, 2020·Magnetic Resonance in Chemistry : MRC·Maria Grazia Concilio
Jan 15, 2021·Journal of Magnetic Resonance·Ilya KuprovJames H Prestegard
Apr 18, 2021·Journal of Magnetic Resonance·Maria Grazia ConcilioIlya Kuprov

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