|
|
|
 |
Viscoelastic subdiffusion in nontrivial potentials: non-Markovian rate theory, fluctuating barriers, anomalous ratchets and all that.Igor Goychuk Tuesday, 14 September , 13.00, W2.19 The first theory of viscoelasticity was proposed by Maxwell [1] and corresponds in the modern language to a linear viscous friction with memory which exponentially decays in time. Complex viscoelastic media like e.g. cytosol of biological cells densely stuffed with macromolecules, biological membranes, or protein complexes serving themselves as media for e.g. long-range electron transfer, are generally characterized rather by a sum of exponentials and sometimes by a power law decaying memory kernel [2]. The corresponding frictional force leads to the Cole-Cole dielectric response of the overdamped particles trapped in harmonic potentials [3] and can be abbreviated using the notion of a fractional integro-differential [2]. The Newtonian equation of motion with a viscoelastic memory frictional force and a random thermal force related by the fluctuation dissipation theorem, termed the generalized Langevin equation (GLE) [4], provides a natural theoretical framework to treat anomalous Brownian motion, chemical reactions and transport processes in such complex media. I will discuss a stochastic approach based on a multi-dimensional Markovian embedding of such a strongly correlated in time, non-Markovian subdiffusive GLE dynamics which has a simple mechanistic interpretation and allows for an excellent approximation of the fractional Brownian dynamics (strict power law kernel) on practically any experimentally relevant time scale [5]. It leads naturally to the picture of slowly fluctuating non-Markovian rates for a bistable (e.g. conformational) dynamics. The limit of non-Markovian rate theory [6] is shown to be reproduced for very high activation barriers when the amplitude of rate fluctuations gradually vanishes with the barrier height. However, for a broad range of realistic barrier height and temperature the bistable subdiffusive dynamics is essentially non-exponential and can be characterized by slowly fluctuating rates. It exhibits bursting and anti-correlation of the residence time intervals in two potential wells, as well as a complex power spectrum with $1/f^\beta$ noise features. Surprisingly, in a periodic potential such a subdiffusion is asymptotically not sensitive to the presence of a periodic potential. The extremally long transients are, however, highly sensitive to the potential amplitude and temperature and this leads to a possibility of non-adiabatically rocking subdiffusive ratchets exhibiting a number of surprising features [7]. [1] J. C. Maxwell, Phil. Trans. R. Soc. London 157, 49 (1867). [2] A. Gemant, Physics 7, 311 (1936); W. Min, et al., Phys. Rev. Lett. 94, 198302 (2005); I. Goychuk and P. H\"anggi, Phys. Rev. Lett. 99, 200601 (2007). [3] K.S. Cole, R.H. Cole, J. Chem. Phys. 9, 341 (1941); I. Goychuk, Phys. Rev. E 76, 040102(R) (2007). [4] R. Kubo, Rep. Prog. Phys. 29, 255 (1966). [5] I. Goychuk, Phys. Rev. E 80, 046125 (2009). [6] P. H\"anggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). [7] I. Goychuk, Chem. Phys., doi:10.1016/j.chemphys.2010.04.009 (Special Issue on Stochastic Processes in Physics and Chemistry, in press) . |
||
|
|