Stochastic Liouville equation Fokker-Planck equations

The Fokker-Planck equation to be assodated with Eqs. (4.1) belongs to the family of stochastic Liouville equations. Its expUcit expression is... 

The three-pulse EOM-PMA can be formulated not only in terms of density matrices and master equations but also in terms of wavefunctions and Schrodinger equations [29]. The EOM-PMA can therefore be straightforwardly incorporated into computer programs which provide the time evolution of the density matrix or the wavefunction of material systems. Besides the multilevel Redlield theory, the EOM-PMA can be combined with the Lindblad master equation [49], the surrogate Hamiltonian approach [49], the stochastic Liouville equation [18], the quantum Fokker-Planck equation [18], and the density matrix [50] or the wavefunction [14] multiconfigurational time-dependent Hartree (MCTDH) methods. When using the... 

Approach based on Stochastic Liouville equation in the Fokker-Planck form... 

There are two conceptually different theoretical approaches for simulation of motional CW EPR spectra. The first is based on the stochastic Liouville equation (SLE) in the Fokker-Planck (FP) form which was developed by Kubo in the early 1960s and the second is the so-called trajectory based approach (see later). 

In closing this section, we note that the stochastic master equation, Eq. (16), can be used to study the effect of boundary conditions on transport equations. If a(x, y, t) is sufficiently peaked as a function of x — y, that is if transitions occur from y to states in the near neighborhood of y, only, then the master equation can be approximated by a Fokker-Planck equation. The effects of the boundary on the master equation all appear in the properties of a(x, y, t). However, in the transition to the Fokker-Planck differential equation, these boundary effects appear as boundary conditions on the differential equation.7 These effects are prototypes for the study of how molecular boundary conditions imposed on the Liouville equation are reflected in the macroscopic boundary conditions imposed on the hydrodynamic equations. 

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