Transport Coefficients in a Transient State
We extended the linear response analysis to calculate the complex dynamic mobility/conductivity for a system in a transient state relaxing to equilibrium. This analysis has a meaning in the intermediate time and frequency region in solvation dynamics, for example, in electrolyte systems or in diffusion of an adatom adsorbed on a surface as well as in pump-probe experiments in the molecular and solid state area when laser field sources of high intensities axe used. As a test model, we assumed a single-particle one-dimensional random walk on a lattice in an inhomogeneous periodic potential, where the transient state is created by a nonequilibrium initial probability distribution. In the frame of this model, we derived formulas for the above mentioned dynamic quantities. A time- and frequency-dependent diffusion coefficient was also studied. The extension of the calculations to higher dimensions is straightforward although more tedious. As a striking effect, we found a non-monotonic frequency and time dependence of transport coefficients. To verify this effect, numerical simulations were performed by exact enumeration and by the Monte Carlo method for a one-dimensional random walk of a single ion in cutoff Coulomb potential wells.
KeywordsRandom Walk Transport Coefficient Dynamic Mobility State Initial Condition Fixed Initial Condition
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- 3.R. Kubo, M. Toda, and N. Hashitsume, “Statistical Physics II. Nonequilibrium Statistical Mechanics”, Solid State Sciences, Vol. 31, Springer-Verlag, Berlin, (1985).Google Scholar
- 4.R. Kutner, D. Knödler, P. Pendzig, R. Przenioslo, and W. Dieterich, in: “Diffusion Processes: Experiment, Theory, Simulations”, Lecture Notes in Physics, Vol. 438, A. Pçkalski, ed., Springer-Verlag, Berlin, (1994).Google Scholar