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

2015/06/30 by D. L. Goodwin, Ilya Kuprov · 71 citations
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Exponential function #Formalism (music) #Hamiltonian (control theory) #Laser-Matter Interactions and Applications #Matrix (chemical analysis) #Matrix exponential #R-matrix #Representation (politics) #Scaling #Simple (philosophy) #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.1063/1.4928978

published in The Journal of Chemical Physics 143(8), 084113 (American Institute of Physics)

arxiv created 2015/07/24 · openalex publication_date 2015/08/25 · arxiv updated 2015/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Quantum mechanical NMR simulation algorithm for protein-size spin systems
• Computing multiple integrals involving matrix exponentials
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Spin-selective reactions of radical pairs act as quantum measurements

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