Lionville equation

Phase space, the classical distribution function, and the Lionville equation... 

This is the classical Lionville equation. An alternative derivation of this equation that sheds additional light on the nature of the phase space distribution function /(r, p / Z) is given in Appendix 1 A. 

The quantum analogs of the phase space distribution function and the Lionville equation discussed in Section 1.2.2 are the density operator and the quantum Lionville equation discussed in Chapter 10. Here we mention for future reference the particularly simple results obtained for equilibrium systems of identical noninteracting particles. If the particles are distinguishable, for example, atoms attached to their lattice sites, then the canonical partitions function is, for a system of N particles... 

Appendix lA Derivation of the classical Lionville equation as a conservation law... 

For slower motions in more viscous media where XrAco > 1, the ESR spectrum depends dramatically on the combined influence of molecnlar motion and magnetic interactions. The slow-motional ESR line shapes, in principle, provide a more detailed picture of rotational dynamics compared with fast-motional line shapes, and can be fully analyzed using a theoretical approach based on numerical solution of the stochastic Lionville equation. The theoretical approach resulting in the Schneider-Freed set of programs enables the calculation of theoretical line shapes of ESR spectra of nitroxides subjected to anisotropic rotational... 

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