TY - JOUR
T1 - Energy transport in weakly anharmonic chains
AU - Aoki, Kenichiro
AU - Lukkarinen, Jani
AU - Spohn, Herbert
N1 - Funding Information:
KA was supported in part by Grant–in–Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan. JL and HS thank Jean Bricmont, Antti Kupiainen, Raphael Lefevere, and Alain Schenkel for most instructive discussions, which merged into the present study.
PY - 2006/9
Y1 - 2006/9
N2 - 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.
AB - 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.
KW - Fourier's law
KW - Molecular dynamics
KW - One-dimensional lattice dynamics
KW - Phonon Boltzmann equation
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U2 - 10.1007/s10955-006-9171-2
DO - 10.1007/s10955-006-9171-2
M3 - Article
AN - SCOPUS:33750088987
VL - 124
SP - 1105
EP - 1129
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 5
ER -