Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic dynamics, as well as the starting semiclassical...

The task of quantization consists of forming a quantum mechanical system from a given classical system. Thereby, classical observables are replaced by quantum mechanical observables. We carry out this procedure with Gibbs’ canonical ensemble. Therefrom, we obtain a density matrix which...

Langevin equation for the macrovariable is derived at the level of the generating functional starting from the field theoretical microscopic Hamiltonian. The macrovariable is precisely defined first, and then the generating functional is written by the path integral over the macrovariable. For...

Taking into account the random scatterings due to random eigenfrequencies and random hopping matrices, we obtain the correlation functions for phonon and sound density fluctuations, which yield three and one entropy fluctuation modes at high frequencies, and three and one thermal conductivity at...