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

Abstract

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. (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 [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.

Quantum Thermal Transport Beyond Second Order with the Reaction Coordinate Mapping

“…It captures the main physics: Heat is exchanged in the σ x − σ z model due to the two reaction coordinates becoming effectively coupled through the spin, an effect reminiscent of "superexchange" for charge current 60,61 . Since the RCs are in fact part of the heat baths, this term corresponds to the direct, inter-bath current as described by Eq.…”

“…As a result, the model manifests the emergence of two distinct transport regimes 56 : (i) The current flows sequentially from the hot to the cold reservoir mediated by the excitation of the central spin. (ii) Heat flows directly from the hot to the cold reservoir, apparently without exciting the central spin, in a manner reminiscent of the tunneling-superexchange behavior 60,61 . This direct bath-to-bath current between reservoirs in the generalized, non-commutative spin-boson model is an example of a transport phenomenon that emerges beyond second order in perturbation theory in the system-bath coupling energy.…”