Stochastic claster dynamics of macromolecules
A.Yu. Chikishev 
, W. Ebeling 
, L. Schimansky-Geier ,
A.V. Netrebko 
, N.V. Netrebko , Yu.M. Romanovsky ,
E.G. Shidlovskaya
Department of Physics, M.V. Lomonosov University, Moscow;
Physical Institute, Humboldt University, Berlin;
Institute of Mechanics, M.V. Lomonosov University, Moscow
Since the known paper of L. Pontryagin, A. Andronov, and A. Vitta (1933) a lot of problems were considered in nonlinear dynamics, associated with the study of the transition of a multistable system from one stable state to another under the influence of noise. In the recent years new problems emerged in the studies of complex vibrational systems. These problems deal with the transitions of the test particles (TP) in the 2D potential relieves with the fluctuating or periodically changing parameters. As a complex relief is a variant of Sinai billiard, the motions of TP therein become stochastic even without any external action. The examples of the cluster dynamics of macromolecules are considered. The dependencies are established of the transition time of a TP from the area of one minimum to the zone of attraction of another one on the frequency of the periodic changes of the parameters of the potential relief. The finite sizes of TPs are taken into account. A problem is considered of the quantum transitions of TP in case of the slow changes of parameters of potential relief. The study of these processes will allow us to get closer to the comprehension of the principles of molecular machines.
The work is supported by research grant N 95-02-05677a from Russian Foundation for Basic Investigations.