Abstract
Fourier's law, which states that the energy flow in a system subjected to a temperature gradient is proportional to the gradient, has been known since the 19th century. This law, which is at the origin of the heat and diffusion equation, is phenomenological, as are several laws of the same type (Fick's law for particle transport, Ohm's law for charge transport). Trying to understand it from first principles, i.e. from microscopic models, remains a hot topic since simulations on chains of coupled oscillators have shown that in low dimensions (dimension 1 or 2) it is not verified. For these low-dimensional systems, we observe an anomalous Fourier law with a heat equation in which the Laplacian is replaced by a fractional Laplacian. In her seminar, Marielle Simon described a family of models studied over the last ten years, simpler than chains of coupled oscillators, but which allow us to rigorously establish the anomalous Fourier law.
