Title: Thermalization in harmonic particle chains with velocity flips
Abstract:
I will discuss the thermalization of the pinned harmonic chain with
velocity flips. This is a stochastic model whose energy transport is
known to satisfy the dynamic Fourier's law in the sense of macroscopic
averages if the initial state is close enough to a local equilibrium
state. Here, by introducing a new mathematical tool for the analysis of
the moment generating function, it is possible to strengthen the result
to a law which holds microscopically, at every lattice site, and for
essentially arbitrary initial data. This way also explicit estimates
can be given for the size of the correction terms. The estimates imply
that the Fourier's law is a valid approximation for the temperature
profile as soon as a thermalization time period, which is at most of the
order L^(2/3), L denoting the number of particles in the chain, has
passed.