# Regensburg 1998 – wissenschaftliches Programm

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# MP: Theoretische und Mathematische Grundlagen der Physik

## MP 4: Hauptvorträge IV

### MP 4.2: Hauptvortrag

### Freitag, 27. März 1998, 10:15–11:00, H46

**The ground state of the low density Bose gas** — •Elliott H. Lieb — Princeton University, USA

Now that the properties of low temperature Bose gases at low density,
ρ, can be examined experimentally it is appropriate to revisit some
of the formulas deduced by many authors 4-5 decades ago. One of these is
that the leading term in the energy/particle is 2π ℏ^{2} ρ *a*/*m*,
where *a* is the scattering length. Owing to the delicate and peculiar
nature of bosonic correlations, four decades of research had failed to
establish this plausible formula rigorously. The only previous lower
bound for the energy was found by Dyson in 1957, but it was 14 times too
small. The correct asymptotic formula has very recently been obtained
jointly with J. Yngvason and this work will be presented here. Another
problem of great interest is the existence of Bose-Einstein condensation,
and what little is known about this rigorously will also be discussed.