Large fluctuations, although infrequent, play a fundamental role in a broad range of processes, from nucleation to failure of electronic devices. The proposed research aims to reach understanding of the dynamics of systems which perform large fluctuations, to investigate new large-fluctuation phenomena, and to find optimal ways of controlling fluctuations by external fields. For classical systems, the problem of the optimal (most probable) fluctuational paths will be formulated in terms of physically observable characteristics of the system and the driving noise. Generic singular features of the pattern of optimal paths will be revealed and analyzed as well as the related critical behavior of the distribution of fluctuational paths. Optimal paths in real time will be used to investigate quantum rates of escape from metastable periodic states and their singular behavior - the problem which is of topical interest for experiments and to which the standard notion of tunneling at a nearly constant energy does not apply.
