1,187 research outputs found
On the number of electrons that a nucleus can bind
We review some results on the ionization conjecture, which says that a
neutral atom can bind at most one or two extra electrons.Comment: Contribution to the Proceedings of ICMP12, Aalborg, Denmark, August
6--11, 201
Bogoliubov correction to the mean-field dynamics of interacting bosons
We consider the dynamics of a large quantum system of identical bosons in
3D interacting via a two-body potential of the form . For fixed and large , we obtain a norm
approximation to the many-body evolution in the -particle Hilbert space. The
leading order behaviour of the dynamics is determined by Hartree theory while
the second order is given by Bogoliubov theory.Comment: Final version, to appear in ATM
Ground states of large bosonic systems: The gross-pitaevskii limit revisited
We study the ground state of a dilute Bose gas in a scaling limit where the
Gross-Pitaevskii functional emerges. This is a repulsive non-linear
Schr\"odinger functional whose quartic term is proportional to the scattering
length of the interparticle interaction potential. We propose a new derivation
of this limit problem, with a method that bypasses some of the technical
difficulties that previous derivations had to face. The new method is based on
a combination of Dyson's lemma, the quantum de Finetti theorem and a second
moment estimate for ground states of the effective Dyson Hamiltonian. It
applies equally well to the case where magnetic fields or rotation are present
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