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Updated: Jun 25, 2026
10:35
Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Heat conduction in the disordered Fermi-Pasta-Ulam chain
1Raman Research Institute, Bangalore 560080, India. dabhi@rri.res.in
Summary
Disorder does not induce finite thermal conductivity in anharmonic chains. Instead, small systems show disorder effects, but large systems follow standard Fermi-Pasta-Ulam (FPU) scaling for heat conduction.
Area of Science:
- Condensed matter physics
- Nonlinear dynamics
- Statistical mechanics
Background:
- The Fermi-Pasta-Ulam (FPU) potential is a foundational model for studying heat conduction in nonlinear systems.
- The role of disorder in influencing thermal transport properties remains a key research question.
- Previous studies suggested disorder could lead to finite thermal conductivity at low temperatures.
Purpose of the Study:
- To investigate the effect of disorder on heat conduction in an anharmonic chain with FPU interactions.
- To re-evaluate claims of disorder-induced finite thermal conductivity at low temperatures.
- To analyze the system-size dependence of heat transport in disordered FPU chains.
Main Methods:
- Numerical simulations of heat conduction in anharmonic chains with varying degrees of disorder.
- Analysis of transport properties as a function of system size and temperature.
- Comparison of results with theoretical predictions and previous experimental findings.
Main Results:
- No evidence of a finite-temperature transition in conducting properties due to disorder was found.
- At low temperatures, transport properties in small systems are significantly influenced by disorder.
- The asymptotic system-size dependence of heat current follows the standard FPU result (J ~ 1/N^(2/3)).
Conclusions:
- Disorder does not fundamentally alter the conducting behavior of FPU chains towards finite conductivity at low temperatures.
- While disorder impacts small-scale transport, the macroscopic heat conduction remains governed by intrinsic FPU dynamics.
- The study also explored unique thermal transport characteristics in binary-mass ordered FPU chains.
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