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Updated: May 9, 2026
05:20
Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Size effects in long-term quasistatic heat transport
George Y Panasyuk1, Kirk L Yerkes
1Aerospace Systems Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, USA. George.Panasyuk.ctr@wpafb.af.mil
Summary
Finite-size quantum reservoirs affect heat transfer. Heat current shows unique behavior at specific times and vanishes nonmonotonically, challenging Fourier
Area of Science:
- Quantum Thermodynamics
- Condensed Matter Physics
- Statistical Mechanics
Background:
- Understanding heat transfer in quantum systems is crucial.
- Finite-size effects in thermal reservoirs can alter energy dynamics.
- The Drude-Ullersma model is a standard for describing thermal reservoirs.
Purpose of the Study:
- To investigate finite-size effects on heat transfer between quantum thermal reservoirs.
- To analyze the validity of Fourier's law in finite-size systems.
- To derive and solve equations governing temperature relaxation and heat current.
Main Methods:
- Generalized quantum Langevin equation.
- Drude-Ullersma model for thermal reservoirs.
- Analysis of long-time quasistatic heat transfer regime.
Main Results:
- A general expression for heat current in the long-time quasistatic regime was obtained.
- Time dependencies of reservoir temperatures and heat current exhibit peculiarities at specific time intervals (t=2πm/Δ).
- Fourier's law validity is questioned at short characteristic times (order of Δ(-1)) due to mode temperature deviations.
Conclusions:
- Finite-size quantum reservoirs introduce unique dynamics to heat transfer.
- The heat current vanishes nonmonotonically as time approaches infinity.
- While Fourier's law may not hold at short times, asymptotic temperatures align with its predictions for small initial temperature deviations.
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