2015/02/13 by Jens Marklof, Marklof, Jens, Andreas Strömbergsson +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.1502.04134
arxiv created 2015/02/13 · arxiv updated 2015/02/17
The linear Boltzmann equation describes the macroscopic transport of a gas of non-interacting point particles in low-density matter. It has wide-ranging applications, including neutron transport, radiative transfer, semiconductors and ocean wave scattering. Recent research shows that the equation fails in highly-correlated media, where the distribution of free path lengths is non-exponential. We investigate this phenomenon in the case of polycrystals whose typical grain size is comparable to the mean free path length. Our principal result is a new generalized linear Boltzmann equation that captures the long-range memory effects in this setting. A key feature is that the distribution of free path lengths has an exponential decay rate, as opposed to a power-law distribution observed in a single crystal.