1:00 pm Wednesday, August 24, 2016
Analysis: Quantum Kinetic Problems by Minh Binh Tran (U Wisconsin at Madison and ICES) in RLM 10.176
After the production of the first Bose-Einstein condensates by Eric Cornell, Wolfgang Ketterle and Carl Wieman and its first kinetic model by Kirkpartrick and Dorfman, the physics and mathematics communities have introduced a large body of research on the kinetic theory for quantum gases. More specifically, on the physics side, Peter Zoller and collaborators derived a Master Quantum Kinetic Equation, and introduced the terminology ‘quantum kinetic theory’ in 2001; and more recently (2012), Linda Reichl and collaborators made a breakthrough in discovering a new collision operator, which had been missing in the previous works. On the mathematical side, a very recent important result is the work of Miguel Escobedo and Juan JL Velazquez (2015), in which they proved that the Uehling-Ulenbeck equation has a blow-up solution. In this talk, I will describe our recent results on quantum kinetic theory. The talk is based on the joint works with Ricardo Alonso, Irene Gamba (existence and uniqueness), Linda Reichl (derivation), Miguel Escobedo, Gheorghe Craciun (convergence to equilibrium), Toan Nguyen (Maxwellian lower bound), Avy Soffer (stability of the coupling cubic nonlinear Schrodinger–quantum Boltzmann). Submitted by
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