March 2010 April 2010 May 2010 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 1 2 3 1 7 8 9 10 11 12 13 4 5 6 7 8 9 10 2 3 4 5 6 7 8 14 15 16 17 18 19 20 11 12 13 14 15 16 17 9 10 11 12 13 14 15 21 22 23 24 25 26 27 18 19 20 21 22 23 24 16 17 18 19 20 21 22 28 29 30 31 25 26 27 28 29 30 23 24 25 26 27 28 29 30 31 |

4:00 pm Wednesday, April 21, 2010 Geometry-Analysis Seminar: Mean Field Limits for Interacting Bose Gases and the Cauchy Problem for Gross-Pitaevskii Hierarchiesby
Thomas Chen (University of Texas at Austin) in HB 227- This talk surveys some recent results, all based on joint work with Natasa Pavlovic, related to the dynamics of Bose gases, and the Cauchy problem for the Gross-Pitaevskii (GP) hierarchy. The GP hierarchy is a system of infinitely many coupled partial differential equations describing the interacting Bose gas in a mean field limit. First, we explain how the quintic nonlinear Schrodinger equation is derived from an N-body Schrodinger system with 3-body interactions and an associated GP hierarchy. Then, the local well-posedness theory for more general GP hierarchies is addressed, for focusing, defocusing, cubic and quintic interactions. In particular, the occurrence of blowup solutions is discussed (joint work with N. Pavlovic and N. Tzirakis). Furthermore, we present new conserved energy functionals which allow us to enhance local to global well-posedness in several crucial situations.
Submitted by damanik@rice.edu |