Center for Functional Nanomaterials Seminar

The analysis of time-scale separation of fast and slow variables in purely classical stochastic (i.e. influenced by random noise) processes uncovers an unusual phenomenon [1], which is analogous to the quantum mechanical Berry phase. Its discovery leads to an elegant unifying quantitative theory for a plethora of effects in non-equilibrium statistical physics. Importantly, the theory of geometric phases in stochastic kinetics provides a new theoretical/computational approach to quantify performance of nano-mechanical devices and their control in stochastic environments. I will review this theory, including recent exact results [2-3], and outline future applications to modeling of nanoscale systems.

References
[1] N. A. Sinitsyn, and I. Nemenman, "The Berry phase and the pump flux in stochastic chemical kinetics", Euro. Phys. Lett. 77, 58001 (2007).
[2] V. Y. Chernyak, and N. A. Sinitsyn, "Pumping-Restriction Theorem for Stochastic Networks", Phys. Rev. Lett. 101, 160601 (2008).
[3] V. Y. Chernyak, and N. A. Sinitsyn, "Robust quantization of a molecular motor motion in a stochastic environment", J. Chem. Phys. 131, 181101, 2009.