TY - JOUR
AB - Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.
AU - Frank, Rupert L
AU - Laptev, Ari
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2366
IS - 3
JF - Letters in Mathematical Physics
TI - Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
VL - 77
ER -
TY - CHAP
AB - The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases.
AU - Robert Seiringer
ED - Dereziński, Jan
ED - Siedentop, Heinz
ID - 2368
T2 - Large Coulomb Systems
TI - Dilute, trapped Bose gases and Bose-Einstein condensation
VL - 695
ER -
TY - CHAP
AB - One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.
AU - Aizenman, Michael
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
AU - Yngvason, Jakob
ED - Asch, Joachim
ED - Joye, Alain
ID - 2369
T2 - Mathematical Physics of Quantum Mechanics
TI - Bose-Einstein condensation as a quantum phase transition in an optical lattice
VL - 690
ER -
TY - CHAP
AU - Bang-Jensen, Jørgen
AU - Reed, Bruce
AU - Schacht, Bruce
AU - Šámal, Robert
AU - Toft, Bjarne
AU - Uli Wagner
ID - 2416
T2 - Topics in Discrete Mathematics
TI - On six problems posed by Jarik Nešetřil
VL - 26
ER -
TY - JOUR
AB - We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane.
AU - Matoušek, Jiří
AU - Sharir, Micha
AU - Smorodinsky, Shakhar
AU - Uli Wagner
ID - 2429
IS - 2
JF - Discrete & Computational Geometry
TI - K-sets in four dimensions
VL - 35
ER -