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Summary

This study analyzes heat conduction in disordered harmonic chains. We derived an exact formula for heat current fluctuations, revealing system size dependencies crucial for understanding thermal transport in such materials.

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Area of Science:

Condensed matter physics
Statistical mechanics
Thermal transport

Background:

Understanding heat conduction in disordered systems is crucial for materials science.
Non-equilibrium steady states (NESS) present unique challenges for theoretical analysis.
Harmonic chains serve as fundamental models for studying thermal properties.

Purpose of the Study:

To investigate heat conduction in a one-dimensional mass-disordered harmonic chain.
To obtain an exact expression for the heat current-current autocorrelation function in NESS.
To determine the system size dependence of current fluctuations under various boundary conditions.

Main Methods:

Utilizing nonequilibrium phonon Green's functions.
Calculating the boundary heat current-current autocorrelation function.
Analyzing the time integral of the correlation function.

Main Results:

An exact expression for the boundary heat current-current autocorrelation function in NESS was derived.
The system size dependence of current fluctuations was found to be N(-α) for different boundary conditions.
Specific values of α were determined: 1/2 for free, 3/2 for fixed, and exponential decay for pinned boundary conditions.

Conclusions:

The derived formula accurately predicts heat current in both equilibrium and non-equilibrium cases.
The study elucidates the distinct asymptotic behaviors of current fluctuations based on boundary conditions.
Results provide insights into thermal transport properties of disordered one-dimensional systems.