Quantum thermal transport beyond second order with the reaction coordinate mapping

Standard quantum master equation techniques, such as the Redfield or Lindblad equations, are perturbative to second order in the microscopic system-reservoir coupling parameter lambda. As a result, the characteristics of dissipative systems, which are beyond second order in lambda, are not captured by such tools. Moreover, if the leading order in the studied effect is higher-than-quadratic in lambda, a second-order description fundamentally fails even at weak coupling. Here, using the reaction coordinate (RC) quantum master equation framework, we are able to investigate and classify higher-than-second-order transport mechanisms. This technique, which relies on the redefinition of the system-environment boundary, allows for the effects of system-bath coupling to be included to high orders. We study steady-state heat current beyond second-order in two models: The generalized spin-boson model with non-commuting system-bath operators and a three-level ladder system. In the latter model, heat enters in one transition and is extracted from a different one. Crucially, we identify two transport pathways: (i) System's current, where heat conduction is mediated by transitions in the system, with the heat current scaling as j(q) (sic) lambda(2) to the lowest order in lambda. (ii) Inter-bath current, with the thermal baths directly exchanging energy between them, facilitated by the bridging quantum system. To the lowest order in lambda, this current scales as j(q) & PROP; lambda(4). These mechanisms are uncovered and examined using numerical and analytical tools. We contend that the RC mapping brings, already at the level of the mapped Hamiltonian, much insight into transport characteristics. Published under an exclusive license by AIP Publishing

Automated summary

Standard quantum master equation techniques are limited to capturing second-order effects in the coupling between microscopic systems and reservoirs. The reaction coordinate (RC) quantum master equation framework allows for the investigation and classification of higher-order transport mechanisms.