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Quantum thermal transport beyond second order with the reaction coordinate mapping.

Nicholas Anto-Sztrikacs1, Felix Ivander2, Dvira Segal1

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Standard quantum master equations fail for higher-order system-bath coupling effects. The reaction coordinate quantum master equation framework reveals two new heat transport mechanisms, one scaling with λ² and another with λ⁴.

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Area of Science:

  • Quantum physics
  • Thermodynamics
  • Condensed matter theory

Background:

  • Standard quantum master equations (e.g., Redfield, Lindblad) are limited to second-order perturbation in system-reservoir coupling (λ).
  • These methods fail to capture dissipative system characteristics and transport mechanisms beyond second-order in λ, even at weak coupling.

Purpose of the Study:

  • To investigate and classify heat transport mechanisms beyond second-order in system-reservoir coupling (λ).
  • To utilize the reaction coordinate (RC) quantum master equation framework for analyzing higher-order transport phenomena.

Main Methods:

  • Application of the reaction coordinate (RC) quantum master equation framework.
  • Analysis of steady-state heat current in two models: a generalized spin-boson model and a three-level ladder system.
  • Numerical and analytical examination of transport pathways.

Main Results:

  • Identification of two distinct heat transport pathways: system's current (jq ∝ λ²) and inter-bath current (jq ∝ λ⁴) to the lowest order in λ.
  • Demonstration that the RC mapping provides significant insights into transport characteristics even at the mapped Hamiltonian level.
  • Characterization of heat flow mediated by system transitions versus direct energy exchange between baths facilitated by the quantum system.

Conclusions:

  • The reaction coordinate quantum master equation framework enables the study of higher-than-second-order transport mechanisms in dissipative quantum systems.
  • Two distinct heat transport mechanisms, with different scaling behaviors in system-reservoir coupling, have been identified and classified.
  • The RC mapping offers a powerful tool for understanding complex quantum transport phenomena beyond perturbative approximations.