@article{2377,
abstract = {We prove that the critical temperature for the BCS gap equation is given by T c = μ ( 8\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting Euler's constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.},
author = {Hainzl, Christian and Robert Seiringer},
journal = {Letters in Mathematical Physics},
number = {2-3},
pages = {99 -- 107},
publisher = {Springer},
title = {{The BCS critical temperature for potentials with negative scattering length}},
doi = {10.1007/s11005-008-0242-y},
volume = {84},
year = {2008},
}
@article{2378,
abstract = {We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.},
author = {Robert Seiringer and Yin, Jun},
journal = {Journal of Statistical Physics},
number = {6},
pages = {1139 -- 1154},
publisher = {Springer},
title = {{Ground state energy of the low density hubbard model}},
doi = {10.1007/s10955-008-9527-x},
volume = {131},
year = {2008},
}
@article{2379,
author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer},
journal = {Journal of the American Mathematical Society},
number = {4},
pages = {925 -- 950},
publisher = {American Mathematical Society},
title = {{Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators}},
doi = {10.1090/S0894-0347-07-00582-6},
volume = {21},
year = {2008},
}
@article{2380,
abstract = {The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.},
author = {Hainzl, Christian and Hamza, Eman and Robert Seiringer and Solovej, Jan P},
journal = {Communications in Mathematical Physics},
number = {2},
pages = {349 -- 367},
publisher = {Springer},
title = {{The BCS functional for general pair interactions}},
doi = {10.1007/s00220-008-0489-2},
volume = {281},
year = {2008},
}
@article{2381,
abstract = {We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.},
author = {Frank, Rupert L and Robert Seiringer},
journal = {Journal of Functional Analysis},
number = {12},
pages = {3407 -- 3430},
publisher = {Academic Press},
title = {{Non-linear ground state representations and sharp Hardy inequalities}},
doi = {10.1016/j.jfa.2008.05.015},
volume = {255},
year = {2008},
}