Eigenfield expansion technique for efficient computation of field-swept fixed-frequency spectra from relaxation master equations

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Abstract
If the Hamiltonian and Liouville operators of a spectral intensity problem are functions of a field parameter x computation of the intensity as a function of x requires, in effect, inversion of a different large matrix for each value of x. Here we show that when the Liouville operator is a polynomial in x, with operator coefficients, solution of one generalized eigenvalue problem followed by a single solution of a system of linear equations yields the intensity for all x. This formulation promises to save large amounts of computational time, particularly for electron paramagnetic resonance problems involving large zero-field splittings.

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