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Universal Scaling Bounds on a Quantum Heat Current.

Shunsuke Kamimura1,2, Kyo Yoshida1, Yasuhiro Tokura1

  • 1Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japan.

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|September 18, 2023
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This summary is machine-generated.

This study establishes new upper bounds for heat current in quantum systems, showing it scales at most as L³ for large systems. A more feasible bound of L² is derived for specific quantum systems, aiding quantum thermodynamics device design.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Understanding heat transport in quantum systems is crucial for developing quantum technologies.
  • Previous studies have explored heat currents in various quantum models, but scaling laws for general systems are not fully established.

Purpose of the Study:

  • To derive new fundamental bounds on the heat current flowing into a quantum L-particle system coupled to a Markovian environment.
  • To investigate the scaling behavior of this heat current with system size L.
  • To explore implications for the performance of quantum thermodynamic devices.

Main Methods:

  • Derivation of theoretical bounds on heat current using system and system-environment Hamiltonians.
  • Analysis of scaling laws in the limit of large system size (L).
  • Consideration of specific system classes, including non-interacting particles and systems with restricted noise operator nondiagonal elements.

Main Results:

  • A universal upper bound of Θ(L³) is proven for the heat current's absolute value in large quantum systems.
  • An example saturating this bound is presented, though it requires complex many-body environmental interactions.
  • A tighter bound of Θ(L²) is derived for systems with specific noise operator properties, with superradiance as an example.

Conclusions:

  • The derived bounds provide critical insights into the maximum achievable heat current in quantum systems.
  • These findings are essential for optimizing the performance of quantum heat engines, refrigerators, and batteries.
  • The results offer a theoretical framework for designing and evaluating next-generation quantum thermodynamic devices.