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Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains
Elena A Korznikova1,2, Vitaly A Kuzkin3,4, Anton M Krivtsov3,4
1Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa 450054, Russia.
Physical Review. E
|January 20, 2021
Summary
This study analyzes temperature equilibration in nonlinear chains, finding that faster convergence occurs with initial conditions closer to equilibrium. The transition from ballistic to diffusive thermal conductivity depends on anharmonicity and modulation wavelength.
Area of Science:
- Nonlinear dynamics
- Statistical mechanics
- Condensed matter physics
Background:
- The Fermi-Pasta-Ulam-Tsingou (FPUT) chain is a fundamental model for studying heat transport in solids.
- Understanding thermal equilibration is crucial for predicting material properties and designing nanoscale devices.
- Nonlinearity plays a critical role in energy transport and thermalization dynamics.
Purpose of the Study:
- To investigate the kinetics of temperature equilibration in the nonlinear FPUT chain under sinusoidal temperature modulation.
- To explore the influence of nonlinearity, modulation wavelength, and initial conditions on thermalization dynamics.
- To compare simulation results with analytical solutions for the linear chain.
Main Methods:
- Simulations of the FPUT chain with varying degrees of nonlinearity and temperature modulation wavelengths.
- Analysis of temperature equilibration using different initial conditions, including those closer to thermal equilibrium.
- Comparison of the observed kinetics with the analytical solution for the linear chain in the continuum limit.
Main Results:
- The transition from ballistic to diffusive thermal conductivity is observed with increasing anharmonicity.
- Energy equilibration exhibits oscillatory behavior in the ballistic regime and monotonic behavior in the diffusive regime.
- Faster convergence to thermal equilibrium is achieved with initial conditions closer to the equilibrium state.
- For a fixed modulation wavelength, a specific anharmonicity parameter optimizes the speed of temperature equilibration.
Conclusions:
- Initial conditions significantly affect the rate of temperature equilibration, with states closer to equilibrium converging faster.
- The degree of anharmonicity and the wavelength of temperature modulation are key factors governing the transition between ballistic and diffusive heat transport.
- The FPUT model provides insights into fundamental heat transport mechanisms in nonlinear systems.
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