Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains

TL;DR

This paper investigates how sinusoidal temperature distributions equilibrate in nonlinear chains, revealing the transition from ballistic to diffusive heat conduction and how initial conditions and wavelength affect equilibration dynamics.

Contribution

It provides a detailed analysis of temperature equilibration in nonlinear chains, including the effects of nonlinearity degree, wavelength, and initial conditions, with comparison to analytical solutions.

Findings

Equilibration time varies with anharmonicity and wavelength.

Ballistic and diffusive regimes exhibit distinct temperature dynamics.

Optimal anharmonicity maximizes equilibration speed.

Abstract

The equilibration of sinusoidally modulated distribution of the kinetic temperature is analyzed in the $\beta$-Fermi-Pasta-Ulam-Tsingou chain with different degrees of nonlinearity and for different wavelengths of temperature modulation. Two different types of initial conditions are used to show that either one gives the same result as the number of realizations increases and that the initial conditions that are closer to the state of thermal equilibrium give faster convergence. The kinetics of temperature equilibration is monitored and compared to the analytical solution available for the linear chain in the continuum limit. The transition from ballistic to diffusive thermal conductivity with an increase in the degree of anharmonicity is shown. In the ballistic case, the energy equilibration has an oscillatory character with an amplitude decreasing in time, and in the diffusive case, it is monotonous in time. For smaller wavelength of temperature modulation, the oscillatory character of temperature equilibration remains for a larger degree of anharmonicity. For a given wavelength of temperature modulation, there is such a value of the anharmonicity parameter at which the temperature equilibration occurs most rapidly.