TY - CONF
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2333
TI - Ground-state energy of a dilute Fermi gas
VL - 412
ER -
TY - CONF
AU - Robert Seiringer
AU - Lieb, Élliott H
AU - Yngvason, Jakob
ED - Zambrini, Jean-Claude
ID - 2334
TI - One-dimensional behavior of dilute, trapped Bose gases in traps
ER -
TY - GEN
AB - We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2363
IS - 2
T2 - Communications in Mathematical Physics
TI - Derivation of the Gross-Pitaevskii equation for rotating Bose gases
VL - 264
ER -
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 -