Pairings of categories and spectra

K-theory and the bridge from motives to noncommutative motives

Classical algebraic K-theory: The functors K0, K1, K2

Excitation-energy transfer problems in molecular aggregates have attracted intensive research interests for their fundamental importance. It is usually supposed that the total density operator at time $t=0$ is a factorized product of single-excitation system state and thermal equilibrium bath state. The Franck-Condon principle ensures that it is a good approximation for a rapid photoexcitation. For natural photosynthesis, however, the transfer process in light-harvesting complexes mostly is initialized from an excited molecule, not direct absorption of a photon. Such intermolecular excitations span the same time scale as the transfer dynamics, and longer than the characteristic time of bath relaxation. Therefore, the initial system-bath correlations should be reconsidered. This work extends the coherent resonant energy transfer theory by including initial system-bath correlations. Within the approach of a second-order time-convolutionless quantum master equation in the polaron frame, a general time evolution equation for the reduced system density operator is obtained, including detailed expressions for both homogeneous and inhomogeneous terms. Two essentially distinct kinds of nonequilibrium are identified: one stems from subsistent initial system-bath correlations, while the other is from the theory of polaron transformation itself. The two kinds of nonequilibrium can accelerate or slow down the dynamical evolution for different energetic situations. Rate equations based on F\orster-Dexter theory with and without initial correlations are also derived for comparison. Besides, our conclusions provide a positive perspective accounting for the quantum coherence induced by initial system-bath correlations, which may help to clarify the long-lasting issue of whether quantum phenomenons might be observed under natural conditions of excitation by incoherent solar light, and deepen understandings of the physical mechanisms underlying the natural photosynthesis process.

On the algebraic K-theory of a∞-ring spaces