Instructor: Rowan Killip, 6935 Math Sciences Building.
Grading: There will be homework, but no exams.
Topics: After a brief introduction to the mathematical formulation of single- and many-body quantum mechanics, we will focus the rigourous analysis of Bose-Einstein condensation and the behaviour of waves in such condensates.
Prerequisites: The target audience is math grad students in their second year and beyond. The 245 sequence is highly recommended; additional exposure to functional analysis (e.g. 255) or PDE (e.g. 266 or 251) would be beneficial. No prior physics knowledge will be assumed.
References: The lectures will include material from the following:
Laszlo Erdos, Benjamin Schlein, and Horng-Tzer Yau,
Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate.
Annals of Math. 172 (2010) 291--370
and arXiv:math-ph/0606017.
Elliott H. Lieb, Robert Seiringer, Jan Philip Solovej, and Jakob Yngvason,
The Mathematics of the Bose Gas and its Condensation. Oberwolfach Seminar Series, Vol. 34,
and arXiv:cond-mat/0610117.
Benjamin Schlein, Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics.
Clay Math. Proc., 17, and arXiv:0807.4307.
Robert M. Ziff, George E. Uhlenbeck, and Mark Kac, The ideal Bose-Einstein gas, revisited.
Physics Reports 32 (1977) 169--248.
Homework: Problems. Due Friday May 2nd.