"Rates of Convergence to Non-Equilibrium Steady States for the Chain of Oscillators"Menegaki, AngelikiA 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 for 1-dimensional weakly anharmonic homogeneous oscillator chains and on the optimal spectral gap for harmonic homogeneous or disordered oscillator chains in all dimensions. |
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