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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Joint Pitt-CNA Colloquium
Irene Gamba
UT Austin
Title: The Cauchy Problem for the Quantum Boltzmann Equation for Bosons at Very Low Temperature

Abstract: This model approximates the evolution of quasiparticles in a dilute gas of bosons at very low temperature by a Boltzmann problem with a cubic kinetic transition probability kernel. The solution to this equation couples to the quantum density evolution of the condensate, modeled by a coupled system of Gross-Pitaevskii and quantum Boltzmann equation for bosons. At this first stage, we prove existence and uniqueness for the quantum Boltzmann model after deriving a priori qualitative properties including propagation and creation of polynomial moments, by means of of ODEs methods in Banach spaces by characterizing an invariant bounded, convex, closed solutions subset of integrable solutions with bounded mass differentiable in time. We also show the propagation and creation of Mittag-Leffler moments that characterize the exponential order of the tails decay. This is a work in collaboration with Ricardo J. Alonso and Minh Binh Tran.

Date: Friday, April 7, 2017
Time: 4:00 pm
Location: Frick Fine Arts auditorium 125
Submitted by:  Ian Tice
Note: Reception to follow 5:00, Frick Fine Arts Cloister