Abstract
The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effects of interaction with a reservoir. One stems from the randomization of phases and the other from phase space considerations. Even the meaning of the word ‘phase’ differs drastically in the two instances in which it appears in the previous statement. In the first case it normally refers to quantum phases whereas in the second it describes the multiplicity of reservoir states that corresponds to each system state. The generalized master equation theory for the time evolution of such systems is here developed in a transparent manner and both effects of reservoir interactions are addressed in a unified fashion. The formalism is illustrated in simple cases including in the standard spin-boson situation wherein a quantum dimer is in interaction with a bath consisting of harmonic oscillators. The theory has been constructed for application in energy transfer in molecular aggregates and in photosynthetic reaction centers.
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References
R.S. Knox, Excitation energy transfer and migration: Theoretical considerations in Bioenergetics of Photosynthesis (Academic Press, New York, 1975)
R.V. Grondelle, J. Amesz, Excitation energy transfer in photosynthetic systems in Light Emission by Plants and Bacteria (Academic Press, New York, 1986)
G. Govindjee, R. Govindjee, Sci. Am. 231, 68 (1974)
R.K. Clayton, J. Theor. Biol. 14, 173 (1967)
R.K. Clayton, Photosynthesis Physical Mechanisms and Chemical Patterns, (Cambridge University Press, 1980)
E. Collini, C.Y. Wong, K.E. Wilk, P.M.G. Curmi, P. Brumer, G.D. Scholes, Nature 463, 644 (2010)
A. Ishizaki, G.R. Fleming, Proc. Natl. Acad. Sci. 106, 17255 (2009)
T. Förster, Ann. Phys. 437, 55 (1948)
V.M. Kenkre, R.S. Knox, Phys. Rev. B 9, 5279 (1974)
M. Grover, R. Silbey, J. Chem. Phys. 54, 4843 (1971)
I.I. Abram, R. Silbey, J. Chem. Phys. 63, 2317 (1975)
S. Rackovsky, R. Silbey, Mol. Phys. 25, 61 (1973)
V.M. Kenkre, Phys. Rev. B 11, 1741 (1975)
V.M. Kenkre, Phys. Rev. B 12, 2150 (1975)
R. Zwanzig, Statistical Mechanics of Irreversibility in lectures in Theoretical Physics (Interscience Publisher New york, 1961), Vol. 3
R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, 2001)
V.M. Kenkre, in Stastical Mechanics and Statistical Methods in Theory and Application, edited by U. Landman (Plenum, New York, 1977), pp. 441–461
V.M. Kenkre, T.S. Rahman, Phys. Lett. A 50, 170 (1974)
V.M. Kenkre, AIP Conf. Proc. 658, 63 (2003)
M. Bonitz, D. Kremp, D.C. Scott, R. Binder, W.D. Kraeft, H.S. Köhler, J. Phys. Condens. Matter 8, 6057 (1996)
D. Kremp, M. Bonitz, W.D. Kraeft, M. Schlanges, Ann. Phys. 258, 320 (1997)
M. Moeckel, S. Kehrein, New J. Phys. 12, 055016 (2010)
M. Kollar, F.A. Wolf, M. Eckstein, Phys. Rev. B 84, 054304 (2011)
S. Genway, A.F. Ho, D.K.K. Lee, Phys. Rev. Lett. 111, 130408 (2013)
S. Goldstein, T. Hara, H. Tasaki, Phys. Rev. Lett. 111, 140401 (2013)
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Tiwari, M., Kenkre, V. Approach to equilibrium of a nondegenerate quantum system: decay of oscillations and detailed balance as separate effects of a reservoir. Eur. Phys. J. B 87, 86 (2014). https://doi.org/10.1140/epjb/e2014-40891-0
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DOI: https://doi.org/10.1140/epjb/e2014-40891-0