We show that if (J,,} is a sequence of uniformly LI-bounded functions on a measure space, and if.f, -fpointwise a.e., then lim,,_(I{lf,, 1 -IIf,, fII) If I,' for all 0 < p < oc. This result is alsoâ€¦ (More)

The ground state properties of interacting Bose gases in external potentials, as considered in recent experiments, are usually described by means of the Gross-Pitaevskii energy functional. We presentâ€¦ (More)

For neutral atoms and molecules and positive ions and radicals, we prove the existence of solutions of the Hartree-Fock equations which minimize the Hartree-Fock energy. We establish some propertiesâ€¦ (More)

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interactionâ€¦ (More)

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state â€” one thatâ€¦ (More)

We show that any measure on IR" possessing the Lee-Yang property retains that property when multiplied by a ferromagnetic pair interaction. Newman's Lee-Yang theorem for one-component ferromagnetsâ€¦ (More)

We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is Î¦p,q(A1, A2, . . . , Am) = (

We give a proof of the Lieb-Thirring inequality in the critical case d = 1, 7 = 1/2, which yields the best possible constant. e-print archive: http://xxx.lanl.gov/abs/hep-th/9806012 On leave of NWF Iâ€¦ (More)