Transport Coefficients in a Transient State

  • R. Kutner
  • P. Pendzig
  • D. Knödler
Part of the NATO ASI Series book series (NSSB, volume 360)


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.


Random Walk Transport Coefficient Dynamic Mobility State Initial Condition Fixed Initial Condition 
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  1. 1.
    B. Heiner, Linear response for systems far off equilibrium, Physica A 223:391 (1996).ADSCrossRefGoogle Scholar
  2. 2.
    R. Kutner, Susceptibility and transport coefficients in a transient state on a one-dimensional lattice. I. Extended linear response and diffusion, Physica A 224:558 (1996).ADSCrossRefGoogle Scholar
  3. 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. 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
  5. 5.
    I. Majid, D. Ben-Avraham, S. Havlin, and H. E. Stanley, Exact-enumeration approach to random walks on percolation clusters in two dimensions, Phys. Rev. B 30:1626 (1984).ADSCrossRefGoogle Scholar
  6. 6.
    K. Binder, Introduction: theory and “technical” aspects of Monte Carlo simulations, in: “Monte Carlo Methods in Statistical Physics”, Topics in Current Physics, Vol.7, K. Binder, ed., Springer-Verlag, Berlin, (1979).CrossRefGoogle Scholar
  7. 7.
    R. L. Stratonovich, “Nonlinear Nonequilibrium Thermodynamic. I. Linear and Nonlinear Fluctuation-Dissipation Theorems”, Springer-Verlag, Berlin, (1992).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • R. Kutner
    • 1
  • P. Pendzig
    • 2
  • D. Knödler
    • 2
  1. 1.Department of PhysicsWarsaw UniversityWarsawPoland
  2. 2.Fakultät für PhysikUniversität KonstanzKonstanzGermany

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