Heat conduction in a weakly anharmonic chain : an analytical approach.
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2006
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The analytical study of heat conduction in an anharmonic chain is considered
here. We investigate an one-dimensional system (directly related to the
Frenkel–Kontorova model) with anharmonic cosine on-site potential and
harmonic interparticle interaction. We start with a stochastic thermal reservoir
connected to each site of the system, and analyse the behaviour of the
conductivity in the steady state with all the heat baths as we turn off the interior
reservoirs, i.e., as we keep the heat baths at the boundaries only. For a weak
interparticle potential and small anharmonicity, in a perturbative computation,
we derive an analytic expression for the heat conductivity which indicates
that the Fourier’s law holds only when each site is connected to a heat bath.
To show the trustworthiness of our perturbative computation, we also derive
an expression for the conductivity by starting from the exact solution of the
linear part of the dynamics and compare with the result which comes from the
previous perturbative analysis.
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FRANCISCO NETO, A.; LEMOS, H. C. F.; PEREIRA, E. Heat conduction in a weakly anharmonic chain: an analytical approach. Journal of Physics. A, Mathematical and General, v. 39, p. 9399-9410, 2006. Disponível em: <http://iopscience.iop.org/article/10.1088/0305-4470/39/30/002>. Acesso em: 20 jul. 2017.