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Fourier's law from Schrödinger dynamics.

Mathias Michel¹, Günter Mahler, Jochen Gemmer

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

Physical Review Letters

|December 31, 2005

Summary

Energy diffusion occurs in one-dimensional chains of many-level systems under specific Hamiltonian conditions. This study verifies the prediction through numerical simulations and analyzes heat conduction near equilibrium.

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Area of Science:

Quantum mechanics
Condensed matter physics
Statistical mechanics

Background:

One-dimensional chains of many-level systems are fundamental models in physics.
Understanding energy transport in such systems is crucial for various applications.
Previous studies have explored different aspects of energy dynamics in similar models.

Purpose of the Study:

To theoretically predict and numerically verify energy diffusion in one-dimensional chains of weakly coupled many-level systems.
To analyze the heat conduction properties of these chains near equilibrium.
To compute the heat conduction coefficient directly from the developed theory.

Main Methods:

Development of a theoretical framework for energy diffusion in many-level systems.
Numerical solution of the time-dependent Schrödinger equation to verify theoretical predictions.
Analysis of heat conduction by examining energy transport close to thermodynamic equilibrium.

Main Results:

A theory predicting energy diffusion for almost all initial states is presented, contingent on specific Hamiltonian conditions.
Numerical simulations confirm the occurrence of energy diffusion.
The heat conduction coefficient is computed directly from the theory for systems near equilibrium.

Conclusions:

Energy diffusion is a robust phenomenon in these one-dimensional quantum systems under specified conditions.
The study provides a theoretical and numerical basis for understanding heat transport in such chains.
The findings contribute to the broader understanding of energy dynamics in complex quantum systems.