Nonlinear Partial Differential Equations

Date: February 2, 2021

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Angeliki Menegaki, University of Cambridge

Title: Quantitative Rates of Convergence to Non-Equilibrium Steady States for the Chain of Oscillators

Abstract: A long-standing open problem in the study of out-of-equilibrium systems in statistical mechanics is the validity of Fourier's law. In this talk we will present a family of models, the atom chains, introduced for this purpose, i.e. to describe properly heat diffusion. The model we will focus on is the so-called chain of oscillators coupled at its boundaries to heat baths at different temperatures. We will present new results on the exponential convergence to the non-equilibrium steady state in several distances with explicit rates of convergence for 1-dimensional weakly anharmonic homogeneous oscillator chains and harmonic homogeneous or disordered oscillator chains in all dimensions.