TY - JOUR
AU - Jakšić, Vojkan
AU - Pillet, Claude
AU - Seiringer, Robert
ID - 1822
IS - 7
JF - Journal of Mathematical Physics
TI - Introduction
VL - 55
ER -
TY - JOUR
AB - 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.
AU - Bräunlich, Gerhard
AU - Hainzl, Christian
AU - Seiringer, Robert
ID - 1889
IS - 7
JF - Reviews in Mathematical Physics
TI - Translation-invariant quasi-free states for fermionic systems and the BCS approximation
VL - 26
ER -
TY - JOUR
AB - 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.
AU - Frank, Rupert
AU - Lewin, Mathieu
AU - Lieb, Élliott
AU - Seiringer, Robert
ID - 1904
IS - 7
JF - Journal of the European Mathematical Society
TI - Strichartz inequality for orthonormal functions
VL - 16
ER -
TY - JOUR
AB - 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.
AU - Bellazzini, Jacopo
AU - Frank, Rupert
AU - Lieb, Élliott
AU - Seiringer, Robert
ID - 1918
IS - 1
JF - Reviews in Mathematical Physics
TI - Existence of ground states for negative ions at the binding threshold
VL - 26
ER -
TY - JOUR
AB - 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.
AU - Giuliani, Alessandro
AU - Lieb, Élliott
AU - Seiringer, Robert
ID - 1935
IS - 1
JF - Communications in Mathematical Physics
TI - Formation of stripes and slabs near the ferromagnetic transition
VL - 331
ER -