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 - Seiringer, Robert ID - 2345 IS - 9 JF - Journal of Physics A: Mathematical and General SN - 0305-4470 TI - On the maximal ionization of atoms in strong magnetic fields VL - 34 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 - Seiringer, Robert ID - 2341 IS - 1 JF - Annales Henri Poincare SN - 1424-0637 TI - Atoms with bosonic "electrons" in strong magnetic fields VL - 2 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 - Seiringer, Robert ID - 2346 IS - 2 JF - Letters in Mathematical Physics SN - 0377-9017 TI - Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics VL - 55 ER - 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 - Seiringer, Robert ED - Demuth, Michael ED - Schultze, Bert ID - 2340 SN - 9783034894838 TI - Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state energy formula VL - 126 ER - TY - JOUR AB - In this Note we present pairs of hyperkähler orbifolds which satisfy two different versions of mirror symmetry. On the one hand, we show that their Hodge numbers (or more precisely, stringy E-polynomials) are equal. On the other hand, we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a Calabi-Yau and its mirror should fiber over the same real manifold, with special Lagrangian fibers which are tori dual to each other. Our examples arise as moduli spaces of local systems on a curve with structure group SL(n); the mirror is the corresponding space with structure group PGL(n). The special Lagrangian tori come from an algebraically completely integrable Hamiltonian system: the Hitchin system. AU - Hausel, Tamas AU - Thaddeus, Michael ID - 1452 IS - 4 JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics SN - 0764-4442 TI - Examples of mirror partners arising from integrable systems VL - 333 ER -