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Fourier law from a chain of coupled anharmonic oscillators under energy conserving noise

We analyze the transport of heat along a chain of particles interacting through anharmonic po- tentials consisting of quartic terms in addition to harmonic quadratic terms and subject to heat reservoirs at its ends. Each particle is also subject to an impulsive shot noise with exponentially distributed waiting times whose effect is to change the sign of its velocity, thus conserving the en- ergy of the chain. We show that the introduction of this energy conserving stochastic noise leads to Fourier law. The behavior of thels heat conductivity for small intensities of the shot noise and large system sizes are found to obey a finite-size scaling relation. We also show that the heat conductivity is not constant but is an increasing monotonic function of temperature.