Mathematisches Kolloquium

Zusammenfassung: The peculiar quantum-mechanical properties of the ground state of quantum-mechanical many-body systems (bosons) at low density and temperature can now be examined experimentally; this continues to be an active and exciting topic. The mathematical derivation of these results is difficult because the problem is extremely quantum mechanical -- meaning that the mathematical subleties of the Schrödinger equation are richly displayed. The simplest question is the ground state energy (lowest eigenvalue) of the Schrödinger operator. Its value was "known", but it took 40 years to prove it. This will be reviewed, as well as the (different) solution which was found to hold in two dimensions. With the aid of the methodology developed to prove these results for the homogeneous gas, several other problems have been successfully addressed. One is the fact that the Gross-Pitaevskii differential equation correctly describes the ground state in the "traps" actually used in the experiments. Another is a recent proof that Foldy's 1961 theory (and Dyson's generalization) of the high density gas of charged particles correctly describes their ground state. (Joint work with R. Seiringer, J.-P. Solovej and J. Yngvason.)

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 19.00 Uhr wird noch bekannt gegeben.