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Physics Colloquium - Friday, September 4th, 2009, 4:00 P.M.

E300 Math/Science Center; Refreshments at 3:30 P.M. in Room E200

Nikolai Sinitsyn
Center of Non-Linear Studies
Los Alamos National Laboratory

Geometric phases in stochastic kinetics: new design principles in nano-mechanics

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 Berry phase in quantum mechanics. Its discovery leads to an elegant unifying quantitative theory for a plethora of effects in non-equilibrium statistical physics [2]. Importantly, the theory of geometric phases in stochastic kinetics provides a new theoretical/computational approach to quantify the performance of nano-mechanical devices and their control in stochastic environments. I will review this theory, including recent exact results [3,4], and outline future applications to the problem of molecular motor design and spin polarization control in semiconductor spintronics.

[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] N. A. Sinitsyn, and I. Nemenman, "Universal geometric theory of stochastic pump and reversible ratchets", Phys. Rev. Lett. 99, 220408 (2007)
[3] V. Y. Chernyak, and N. A. Sinitsyn, "Pumping-Restriction Theorem for Stochastic Networks", Phys. Rev. Lett. 101, 160601 (2008)
[4] V. Y. Chernyak, and N. A. Sinitsyn, "Robust quantization of molecular motor motion in a stochastic environment", arXiv:0906.3032