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Chain mapping approach of Hamiltonian for FMO complex using associated, generalized and exceptional Jacobi polynomials. (English) Zbl 1344.82033

Summary: The excitation energy transfer (EET) in photosynthesis complex has been widely investigated in recent years. However, one of the main problems is simulation of this complex under realistic condition. In this paper by using the associated, generalized and exceptional Jacobi polynomials, firstly, we introduce the spectral density of Fenna-Matthews-Olson (FMO) complex. Afterward, we obtain a map that transforms the Hamiltonian of FMO complex as an open quantum system to a one-dimensional chain of oscillatory modes with only nearest neighbor interaction in which the system is coupled only to first mode of chain. The frequency and coupling strength of each mode can be analytically obtained from recurrence coefficient of mentioned orthogonal polynomials.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
81S22 Open systems, reduced dynamics, master equations, decoherence
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
33C90 Applications of hypergeometric functions

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