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Application of the Hilbert space average method on heat conduction models.

Mathias Michel1, Jochen Gemmer, Günter Mahler

  • 1Institute of Theoretical Physics I, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany. mathias@theo1.physik.uni-stuttgart.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
Summary

This study shows energy diffusion and heat transport in one-dimensional chains using the Hilbert space average method. It demonstrates that reversible quantum dynamics can explain macroscopic heat conduction and Fourier

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Quantum dynamics

Background:

  • Understanding heat transport in complex quantum systems is crucial.
  • Macroscopic laws like Fourier's law often emerge from microscopic reversible dynamics.
  • One-dimensional systems offer a tractable model for studying transport phenomena.

Purpose of the Study:

  • To investigate energy diffusion and heat transport in one-dimensional chains of many-level systems.
  • To connect microscopic reversible dynamics to macroscopic heat conduction.
  • To derive the heat conduction coefficient from fundamental principles.

Main Methods:

  • Analysis of closed one-dimensional chains of weakly coupled many-level systems.
  • Application of the Hilbert space average method (HAM).

Related Experiment Videos

  • Investigation of energy diffusion and heat transport near equilibrium.

    • Main Results:

    • The Hilbert space average method predicts energy diffusion for almost all initial states under specific Hamiltonian conditions.
    • Heat transport behavior and the heat conduction coefficient are derived.
    • Energy diffusion and Fourier's law are shown to be compatible with reversible Schrödinger dynamics.

    Conclusions:

    • Reversible quantum dynamics at the microscopic level can lead to diffusive energy transport and obey Fourier's law macroscopically.
    • The Hilbert space average method provides a theoretical framework for understanding emergent heat transport.
    • This work bridges the gap between quantum mechanics and classical thermodynamics.