Bounds for the state-modulated resolvent of a linear Boltzmann generator

Details Bounds for the state-modulated resolvent of a linear Boltzmann generator Bounds for the state-modulated resolvent of a linear Boltzmann generator

2011-10-04

arxiv.org/abs/1110.0689v1

Physics

Mathematical Physics

31 pages

Scientific paper

We study a generalized resolvent for the generator of a Markovian semigroup. The Markovian generator appears in a linear Boltzmann equation modeling a one-dimensional test particle in a periodic potential and colliding elastically with particles from an ideal background gas. We obtain bounds for the state-modulated resolvent which are relevant in the regime where the mass ratio between the test particle and a particle from the gas is large. These bounds relate to the typical amount of time that the particle spends in different regions of phase space before arriving to a region around the origin.

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