Fourier's law from Schrödinger dynamics

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.