TY - JOUR
AB - We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation.
AU - Robert Seiringer
ID - 2364
IS - 3
JF - Reviews in Mathematical Physics
TI - A correlation estimate for quantum many-body systems at positive temperature
VL - 18
ER -
TY - JOUR
AB - We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.
AU - Robert Seiringer
ID - 2365
IS - 3
JF - Communications in Mathematical Physics
TI - The thermodynamic pressure of a dilute fermi gas
VL - 261
ER -
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 -