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Heat conduction in systems with Kolmogorov-Arnold-Moser phase space structure
I F Herrera-González1, H I Pérez-Aguilar, A Mendoza-Suárez
1Facultad de Ciencias Físico-Matemáticas, UMSNH, Avenida Francisco J. Mújica S/N, 58060, Morelia, Michoacán, México.
Summary
This study explores heat conduction and particle diffusion in sinusoidal channels. It reveals regular dynamics for small ripples and a transition to chaos with increasing ripple amplitude, impacting particle displacement.
Area of Science:
- Physics
- Statistical Mechanics
- Nonlinear Dynamics
Background:
- Heat conduction and particle diffusion are fundamental transport phenomena.
- Billiard systems with complex geometries offer insights into classical and quantum dynamics.
- Sinusoidal channel walls introduce geometric complexity affecting particle trajectories and heat transport.
Purpose of the Study:
- To investigate heat conduction and particle diffusion in a channel with sinusoidal walls.
- To analyze the transition from regular to chaotic dynamics as a function of ripple amplitude.
- To derive analytical results for temperature profiles and heat flux and propose a general formula.
Main Methods:
- Analytical calculations using an effective potential for small ripple amplitudes.
- Numerical simulations and analysis of Poincaré plots to study the dynamics.
- Investigation of particle mean square displacement for chaotic regimes.
Main Results:
- Analytical solutions for temperature profile and heat flux in the regular dynamics regime.
- Identification of ballistic conductance and ballistic diffusion for regular dynamics.
- Demonstration of a generic transition to chaos with increasing ripple amplitude.
- Asymptotic growth of mean square displacement as tln(t) in chaotic regimes without KAM curves.
Conclusions:
- The study provides a comprehensive understanding of heat and particle transport in sinusoidal channels.
- It highlights the crucial role of ripple amplitude in governing the system's dynamics, from regular to chaotic behavior.
- The findings contribute to the study of transport phenomena in complex geometries and the physics of chaos.
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