Abstract
Recently, time integrals of memory functions from Time-Convolution Generalized Master Equations (TCGME) with the Peier projector were calculated exactly. Similar procedure is applied in detail to the Argyres-Kelley projector yielding, in the Nakajima-Zwanzig projector formalism, TC-GME for the density matrix of the system. Specifying properly the meaning of the memory, the integral (if finite) is argued to yield exact zero in the interacting system-bath case provided that no approximations get involved and the thermodynamic limit of the bath is performed as usual before time-integration. This implies limitations on a simple-minded Born-Markov approximation often used in descriptions of kinetics of open systems and predicts slower-than-exponential relaxation to equilibrium in the long-time asymptotics. Origin of long-time tails of memories and reason for deviation from the usual correspondence with the Golden Rule are discussed.
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Čápek, V. Exact memory integral in Time-Convolution Generalized Master Equations: Argyres-Kelley projector. Zeitschrift für Physik B Condensed Matter 104, 323–331 (1997). https://doi.org/10.1007/s002570050457
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DOI: https://doi.org/10.1007/s002570050457