Some applications of stochastic averaging method for quasi Hamiltonian systems in physics

Many physical systems can be modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems can be applied to yield reasonable approximate response statistics. In the present paper, the basic idea and procedure of the stochastic averaging method for quasi Hamiltonian systems are briefly introduced. The applications of the stochastic averaging method in studying the dynamics of active Brownian particles, the reaction rate theory, the dynamics of breathing and denaturation of DNA, and the Fermi resonance and its effect on the mean transition time are reviewed. Supported by the National Natural Science Foundation of China (Grant Nos. 10772159 and 10802074), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060335125), and the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y7080070)