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Energy transport and detailed verification of Fourier heat law in a chain of colliding harmonic oscillators
Prosen, Tomaž, 1970- ; Robnik, Marko, 1954-
We study a simple nonlinear classical Hamiltonian system with positive K-entropy, a model for heat conduction, and we find that it obeys the Fourier heat law. Numerical simulation of its dynamics can ...be performed very efficiently, so we are able to explore it in detail. We verify the Fourier heat law and calculate the coefficient of thermal conductivity K by three independent methods. The first is direct simulation, i.e. simulating the dynamics of the chain between two heat reservoirs. The second is Green-Kubo formalism which is derived in a self-contained manner. The third method - the one-sided heating of semi-infinite cold chain - is new and gives the best results. It yields the entire temperature dependence K(T) in a single numerical simulation and definitely demonstrates the validity of the Fourier heat law at all temperatures for the given system. We believe that this method can also be useful for other systems. We derive analytically the asymptotic behaviour of the coefficient of thermal conductivity at low temperatures T ▫$\to$▫ 0 and observe that it agrees with numerical results obtained by the Green-Kubo formalism, which gives by far the best results at very low temperatures
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