Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

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Séminaire de groupe

Fourier's law in one-dimensional chains under energy conserving noise
Gabriel Landi
Université de Sao Paulo, Brésil
jeudi 20 février 2014 , 10h25
Salle de séminaire du groupe de Physique Statistique

Fourier's law of heat conduction is a macroscopic law describing non-equilibrium systems. A question of current scientific relevance is whether it can be derived from a microscopic model. Indeed, despite being over 200 years old, to this day no such derivation exists. In this seminar we will discuss the reasons behind some of the difficulties in this derivation. Moreover, we will argue that in a simplified model (i.e., one that does not take into account all types of interactions present in a real material) an extra ingredient is necessary, which should take the form of an energy-conserving stochastic noise. As a particular model we will consider the one-dimensional harmonic chain where each ion is modelled by a classical particle connected to its nearest neighbours by harmonic springs. The first and last particles are connected to heat baths at different temperatures, described by Langevin equations. This system does not satisfy Fourier's law. We then introduce a new stochastic noise that randomly changes the direction of the velocity vector of each particle, while maintaining the magnitude unchanged. Hence, this noise conserves the total energy of the chain. It will be shown that the presence of this noise, irrespective of its intensity, correctly leads to Fourier's law. The physical reasons behind this result will also be discussed.

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