@article{1822,
author = {Jakšić, Vojkan and Pillet, Claude and Seiringer, Robert},
journal = {Journal of Mathematical Physics},
number = {7},
publisher = {American Institute of Physics},
title = {{Introduction}},
doi = {10.1063/1.4884877},
volume = {55},
year = {2014},
}
@article{1889,
abstract = {We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but also includes direct and exchange energies. We show that for suitable short-range interactions, these latter terms only lead to a renormalization of the chemical potential, with the usual properties of the BCS functional left unchanged. Our analysis thus represents a rigorous justification of part of the BCS approximation. We give bounds on the critical temperature below which the system displays superfluidity.},
author = {Bräunlich, Gerhard and Hainzl, Christian and Seiringer, Robert},
journal = {Reviews in Mathematical Physics},
number = {7},
publisher = {World Scientific Publishing},
title = {{Translation-invariant quasi-free states for fermionic systems and the BCS approximation}},
doi = {10.1142/S0129055X14500123},
volume = {26},
year = {2014},
}
@article{1904,
abstract = {We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation with a time-dependent potential and we show the existence of the wave operator in Schatten spaces.},
author = {Frank, Rupert and Lewin, Mathieu and Lieb, Élliott and Seiringer, Robert},
journal = {Journal of the European Mathematical Society},
number = {7},
pages = {1507 -- 1526},
publisher = {European Mathematical Society},
title = {{Strichartz inequality for orthonormal functions}},
doi = {10.4171/JEMS/467},
volume = {16},
year = {2014},
}
@article{1918,
abstract = {As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition. We investigate whether the electrons remain bound and whether the radius of the system stays finite as the critical value Zc is approached. Existence of a ground state at Zc is shown under the condition Zc < N-K, where K is the maximal number of electrons that can be removed at Zc without changing the energy.},
author = {Bellazzini, Jacopo and Frank, Rupert and Lieb, Élliott and Seiringer, Robert},
journal = {Reviews in Mathematical Physics},
number = {1},
publisher = {World Scientific Publishing},
title = {{Existence of ground states for negative ions at the binding threshold}},
doi = {10.1142/S0129055X13500219},
volume = {26},
year = {2014},
}
@article{1935,
abstract = {We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.},
author = {Giuliani, Alessandro and Lieb, Élliott and Seiringer, Robert},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {333 -- 350},
publisher = {Springer},
title = {{Formation of stripes and slabs near the ferromagnetic transition}},
doi = {10.1007/s00220-014-1923-2},
volume = {331},
year = {2014},
}