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Heat conduction in the disordered harmonic chain revisited
1Raman Research Institute, Bangalore 560080, India.
Physical Review Letters
|June 21, 2001
Summary
This study introduces a general method to analyze heat conduction in disordered harmonic chains, revealing that thermal conductivity depends on both the system and its heat baths. Different boundary conditions lead to various power-law dependencies for heat current on system size.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Thermodynamics
Background:
- Heat conduction in disordered systems is complex.
- Understanding the influence of heat baths is crucial.
- Existing models often lack generality.
Purpose of the Study:
- Develop a general formulation for heat conduction in disordered harmonic chains.
- Investigate the role of arbitrary heat baths.
- Analyze the system-size dependence of heat current.
Main Methods:
- Developed a general theoretical formulation.
- Applied the fluctuation-dissipation theorem.
- Extracted asymptotic system-size dependence of heat current.
Main Results:
- Obtained a formal expression for heat current (J).
- Demonstrated that thermal conductivity depends on system and heat bath spectral properties.
- Recovered known results for fixed (J ~ 1/N^(3/2)) and free (J ~ 1/N^(1/2)) boundaries.
- Identified other power laws, including Fourier behavior (J ~ 1/N).
Conclusions:
- The developed formulation provides a unified framework for studying heat conduction in disordered systems.
- Heat bath properties significantly influence thermal transport.
- System-size dependence of heat current varies with boundary conditions and bath characteristics.