Trajectory based EPR simulation approach

1 Propagation of spin density matrix and simulation of EPR spectra 

The equation for the propagation of spin density matrix in (7) has the following formal solution  

Equivalently the propagation can be carried out in Hilbert space using the spin Hamiltonian  

The observed EPR spectrum is found as a Laplace-Fourier transform of the time dependent averaged transverse magnetisation into the frequency of field domain which is calculated according to the following equation  

In this case the associated Liouville superoperator L t) with 36x36 total matrix elements is diagonal and the expression for the transverse magnetisation can be cast into three contributions with formal solutions in a scalar form  

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