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Heat transfer statistics in mixed quantum-classical systems.

Junjie Liu1, Chang-Yu Hsieh2, Dvira Segal3

  • 1Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada.

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Summary
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We present a mixed quantum-classical approach for modeling nanoscale heat transfer, crucial for energy harvesting and molecular electronics. This method accurately simulates heat flow, overcoming limitations of previous models.

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Area of Science:

  • Quantum thermodynamics
  • Nanoscale heat transfer
  • Molecular electronics

Background:

  • Accurate modeling of quantum heat transfer is essential for advancing energy harvesting and molecular electronic devices.
  • Existing models often rely on simplifying assumptions about bath timescales and subsystem-bath coupling strengths.

Purpose of the Study:

  • To develop a robust theoretical framework for simulating quantum heat transfer at the nanoscale.
  • To investigate heat transfer dynamics in systems using a mixed quantum-classical description.

Main Methods:

  • Employed a mixed quantum-classical (MQC) description, treating the subsystem quantum mechanically and heat baths classically.
  • Utilized the full counting statistics approach to derive a general expression for the moment generating function of heat.
  • Derived expressions for average heat and heat current dynamics solvable via numerical simulations.
  • Investigated the validity of steady-state fluctuation symmetry under the quantum-classical Liouville equation (QCLE).

Main Results:

  • The MQC approach allows for closed-system analysis of heat transfer, avoiding common simplifying assumptions.
  • Derived general expressions for heat and heat current dynamics.
  • Demonstrated that steady-state fluctuation symmetry holds up to order ℏ for non-bilinear/non-harmonic couplings.
  • Simulated time-dependent average heat and heat current for the nonequilibrium spin boson model.

Conclusions:

  • The developed MQC framework provides a powerful tool for studying nanoscale quantum heat transfer.
  • The approach offers improved accuracy by relaxing restrictive assumptions on system-bath interactions.
  • Numerical simulations based on this framework can effectively predict heat transfer dynamics in complex quantum systems.