We report on two possible physically justified situations concerning the evolution of polycrystalline microstructures. The first is an observation that a polycrystalline microstructure formation process, considered as a random walk in the space of the crystallites’ sizes, can be equivalent to...

In this paper we analyze the double Caldeira–Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: (i) when each oscillator is coupled to its own...

The thermal relaxation of a relativistic particle diffusing in a fluid at equilibrium is investigated through a numerical study of the Relativistic Ornstein–Uhlenbeck Process. The spectrum of the relaxation operator has both a discrete and a continuous component. Both components are fully...

Explicit propagators are given for a diffusing particle (motor) moving on a linear chain of either infinity or finite length with reflecting ends. Each chain contains a number of thermally accessible barriers and/or potential wells (active sites). All particle interactions with its environment...