1:00 pm Friday, October 2, 2015
Analysis: The Gross-Pitaevskii hierarchy on periodic domains by
Vedran Sohinger (ETH Zurich) in RLM 10.176
The Gross-Pitaevskii hierarchy is a system of infinitely many linear PDEs which occurs in the derivation of the nonlinear Schrodinger equation from the dynamics of many-body quantum systems. We will study this problem in the periodic setting. Even though the hierarchy is linear, it is non-closed, in the sense that the equation for the k^th density matrix in the system depends on the (k+1)^st density matrix. This structure poses its challenges in the study of the problem, in particular in the understanding of uniqueness of solutions. Moreover, by randomizing in the collision operator, it is possible to use probabilistic techniques to study related hierarchies at low regularities. I will summarize some recent results obtained on these problems, partly in joint work with Philip Gressman, Sebastian Herr, and Gigliola Staffilani. Submitted by
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