Abstract
From four non-stochastic rigorous theories leading to a set of equations for site-diagonal as well as site off-diagonal elements of the electron (carrier) density matrix (Time-Convolution Generalized Master Equation, Mori theory, Time-Convolutionless Generalized Master Equation and Tokuyama-Mori), the first two (time nonlocal) approaches were recently found to be disabled in the second order in the carrier-bath coupling. On the other hand, the latter two (time local) theories are argued here to lead, in the above order and any electronic system with a site-local coupling to bath, to completely identical and physically fully acceptable equations. The theory is applied to a periodic chain and asymmetric dimer. It is shown that, irrespective of problems with introducing\(\bar \gamma _{mn} \) or γ mn (m≠n) Haken-Strobl-Reineker parameters, the usual transition from the non-activated to activated (Arrhenius-type) ‘up-and-down’ asymmetric Marcus long-time reaction kinetics is obtained. The usual long-time markovian description of the population kinetics assumed in the standard theory is, however, found to be unjustified.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Primas, H.: Helv. Phys. Acta34, 36 (1961)
Haken, H., Strobl, G.: In: The Triplet State. Proc. Int. Symp., Amer. Univ. Beirut, Lebanon, 1967. Zahlan, A. B. (ed.). Cambridge: University Press 1967
Reineker, P.: In: Exciton Dynamics in Molecular Crystals and Aggregates. Springer Tracts in Modern Physics, Vol. 94. Höhler, G. (ed.), p. 111, Berlin, Heidelberg, New York: Springer (1982)
Čápek, V.: Z. Phys. B60, 101 (1985)
Čápek, V., Szöcs, V.: Phys. Status Solidi (b)131, 667 (1985)
Lindenberg, K., West, B. J.: The Nonequilibrium Statistical Mechanics of Open and Closed Systems. New York: VCH 1990
Čápek, V.: Physica A203, 495 (1994)
Fick, E., Sauermann, G.: The Quantum Statistics of Dynamic Processes. Springer Series in Solid-State Sciences Vol. 86. Fulde, P. (ed.). Berlin, Heidelberg, New York: Springer 1990
Čápek, V.: Z. Phys. B92, 523 (1993)
Čápek, V.: Physica A203, 520 (1994)
Fuliski, A.: Phys. Lett. A25, 13 (1967)
FuliXXXski, A., Kramarczyk, W. J.: Physica39, 575 (1968)
Hashitsume, N., Shibata, F., Shingu, M.: J. Stat. Phys.17, 155 (1977)
Shibata, F., Takahashi, Y., Hashitsume, N.: J. Stat. Phys.17, 171 (1977)
Gzyl, H.: J. Stat. Phys.26, 679 (1981)
Tokuyama, M., Mori, H.: Progr. Theor. Phys.55, 411 (1976)
Silinsh, E. A., Čápek, V.: Molecular Crystals. New York: Amer. Inst. of Physics (1994)
Marcus, R. A.: J. Chem. Phys.24, 966 (1956)
Marcus, R. A.: J. Chem. Phys.24, 979 (1956)
Mori, H.: Progr. Theor. Phys.33, 423 (1965)
Čápek, V.: Physica A203, 495 (1994)
Čápek, V.: Czech. J. Phys.43, 829 (1993)
P. Reineker, Z. Physik261, 187 (1973)
Einstein, A.: Verhandl. Deutch. Physik. Gesellschaft18, 318 (1916)
Einstein, A.: Mitt. Physik. Gesellschaft (Zürich)18, 47 (1916) (also Physik. Zeitschrift18, 121 (1917))
Marcus, R. A.: J. Chem. Phys.24, 979 (1956)
Zusman, L. D.: Chem. Phys.49, 295 (1980)
Rips, I., Jortner, J.: J. Chem. Phys.87, 2090 (1987)
Marcus, R. A., Sutin, N.: Biochim. Biophys. Acta811, 265 (1985)
Eyring, H., Lin, S. H., Lin, S. M.: Basic Chemical Kinetics. New York-Chichester-Brisbane-Toronto: John Wiley & Sons (1980)
Smith, Ian W. M.: Kinetics and dynamics of elementary gas reactions. London, Boston, Sydney: Butterworth 1980