Energy Transport in Weakly Anharmonic Chains |
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Authors: | Kenichiro Aoki Jani Lukkarinen Herbert Spohn |
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Institution: | (1) Department of Physics, Keio University, 4–1–1 Hiyoshi, Kouhoku–ku, Yokohama 223–8521, Japan;(2) Zentrum Mathematik, TU München, D-85747 Garching, Germany |
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Abstract: | We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier’s law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed. |
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Keywords: | Fourier’ s law phonon Boltzmann equation molecular dynamics one-dimensional lattice dynamics |
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