ABSTRACT
The term dynamics in the broad sense refers to any problem involving time. Stochastic dynamics is the study of fluctuating quantities and their statistical characteristics. In the real world stochasticity is generated by causes internal to a system: random collisions between molecules owing to thermal Brownian motion, the spontaneous appearance and interaction of vortices in a turbulent flow, and so on. At present it is difficult or impossible to rigorously describe such processes mathematically. Therefore, the stochastic dynamics are usually modeled phenomenologically by introducing random “noise” into the dynamical equations — either random forces or other random parameters with a simple (usually Gaussian) distribution. The Gaussian distribution is specified by the noise correlator, which is selected on the basis of physical considerations. In particular, models of critical dynamics have been constructed in this manner in order to study the critical singularities of relaxation times and various kinetic coefficients. Critical dynamics is based on stochastic equations of a particular form, the Langevin equations. Here the noise corresponds to thermal fluctuations, and the noise correlator is uniquely determined by the requirement that the dynamics and statics be mutually consistent.
