TY - CONF
AB -
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in external potentials and interacting via repulsive short range forces are usually described by means of the Gross-Pitaevskii energy functional. In joint work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for the quantum mechanical many-body ground state problem has recently been rigorously clarified. We present a summary of this work, for both the two-and three-dimensional case.
AU - Robert Seiringer
ED - Demuth, Michael
ED - Schultze, Bert-Wolfgang
ID - 2340
TI - Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula
VL - 126
ER -
TY - JOUR
AB - We study the ground state properties of an atom with nuclear charge Z and N bosonic "electrons" in the presence of a homogeneous magnetic field B. We investigate the mean field limit N→∞ with N / Z fixed, and identify three different asymptotic regions, according to B≪Z2,B∼Z2,andB≫Z2 . In Region 1 standard Hartree theory is applicable. Region 3 is described by a one-dimensional functional, which is identical to the so-called Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with fermionic electrons in the region B≫Z3 ; i.e., for very strong magnetic fields the ground state properties of atoms are independent of statistics. For Region 2 we introduce a general magnetic Hartree functional, which is studied in detail. It is shown that in the special case of an atom it can be restricted to the subspace of zero angular momentum parallel to the magnetic field, which simplifies the theory considerably. The functional reproduces the energy and the one-particle reduced density matrix for the full N-particle ground state to leading order in N, and it implies the description of the other regions as limiting cases.
AU - Baumgartner, Bernhard
AU - Robert Seiringer
ID - 2341
IS - 1
JF - Annales Henri Poincare
TI - Atoms with bosonic "electrons" in strong magnetic fields
VL - 2
ER -
TY - JOUR
AB - We give upper bounds for the number of spin-1/2 particles that can be bound to a nucleus of charge Z in the presence of a magnetic field B, including the spin-field coupling. We use Lieb's strategy, which is known to yield Nc < 2Z + 1 for magnetic fields that go to zero at infinity, ignoring the spin-field interaction. For particles with fermionic statistics in a homogeneous magnetic field our upper bound has an additional term of the order of Z × min {(B/Z3)2/5, 1 + | 1n(B/Z3)|2}.
AU - Robert Seiringer
ID - 2345
IS - 9
JF - Journal of Physics A: Mathematical and General
TI - On the maximal ionization of atoms in strong magnetic fields
VL - 34
ER -
TY - JOUR
AB - By means of a generalization of the Fefferman - de la Llave decomposition we derive a general lower bound on the interaction energy of one-dimensional quantum systems. We apply this result to a specific class of lowest Landau band wave functions.
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2346
IS - 2
JF - Letters in Mathematical Physics
TI - Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics
VL - 55
ER -
TY - JOUR
AB - We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number N is large but ρ̄a2 is small, where ρ̄ is the average particle density and a the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional with a coupling constant g ∼ 1/| 1n(ρ̄a2)|. In contrast to the 3D case the coupling constant depends on N through the mean density. The GP energy per particle depends only on Ng. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a Thomas-Fermi type functional is adequate.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2347
IS - 1
JF - Communications in Mathematical Physics
TI - A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
VL - 224
ER -