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Proof of Bose-Einstein Condensation for Dilute Trapped Gases
Elliott H. Lieb, Robert Seiringer
The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body rep…
Phase separation due to quantum mechanical correlations
J. K. Freericks, E. H. Lieb, D. Ueltschi
Can phase separation be induced by strong electron correlations? We present a theorem that affirmatively answers this question in the Falicov-Kimball model away from half-filling,…
A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics
Elliott H. Lieb, Michael Loss
We study three well known models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativi…
Stability of a Model of Relativistic Quantum Electrodynamics
Elliott H. Lieb, Michael Loss
The relativistic ``no pair'' model of quantum electrodynamics uses the Dirac operator, D(A), for the electron dynamics together with the usual self-energy of the quantized ultravio…
Convex Multivariable Trace Functions
Elliott H. Lieb, Gert K. Pedersen
For any densely defined, lower semi-continuous trace τon a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a…