Theory of quantum energy transfer in spin chains: superexchange and ballistic motion

Quantum energy transfer in a chain of two-level (spin) units, connected at its ends to two thermal reservoirs, is analyzed in two limits: (i) in the off-resonance regime, when the characteristic subsystem excitation energy gaps are larger than the reservoirs frequencies, or the baths temperatures are low and (ii) in the resonance regime, when the chain excitation gaps match populated bath modes. In the latter case, the model is studied using a master equation approach, showing that the dynamics is ballistic for the particular chain model explored. In the former case, we analytically study the system dynamics utilizing the recently developed Energy-Transfer Born-Oppenheimer formalism [L.-A. Wu and D. Segal, Phys. Rev. E 83, 051114 (2011)], demonstrating that energy transfers across the chain in a superexchange (bridge assisted tunneling) mechanism, with the energy current decreasing exponentially with distance. This behavior is insensitive to the chain details. Since at low temperatures the excitation spectrum of molecular systems can be truncated to resemble a spin chain model, we argue that the superexchange behavior obtained here should be observed in widespread systems satisfying the off-resonance condition.