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Anto-Sztrikacs N, Ivander F, Segal D. Quantum thermal transport beyond second order with the reaction coordinate mapping. J Chem Phys 2022; 156:214107. [DOI: 10.1063/5.0091133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Standard quantum master equation techniques, such as the Redfield or Lindblad equations, are perturbative to second order in the microscopic system–reservoir coupling parameter λ. As a result, the characteristics of dissipative systems, which are beyond second order in λ, are not captured by such tools. Moreover, if the leading order in the studied effect is higher-than-quadratic in λ, 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 ∝ λ2 to the lowest order in λ. (ii) Inter-bath current, with the thermal baths directly exchanging energy between them, facilitated by the bridging quantum system. To the lowest order in λ, this current scales as j q ∝ λ4. 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.
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Affiliation(s)
- Nicholas Anto-Sztrikacs
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Felix Ivander
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Dvira Segal
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
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