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 - Spin-wave theory is a key ingredient in our comprehension of quantum spin systems, and is used successfully for understanding a wide range of magnetic phenomena, including magnon condensation and stability of patterns in dipolar systems. Nevertheless, several decades of research failed to establish the validity of spin-wave theory rigorously, even for the simplest models of quantum spins. A rigorous justification of the method for the three-dimensional quantum Heisenberg ferromagnet at low temperatures is presented here. We derive sharp bounds on its free energy by combining a bosonic formulation of the model introduced by Holstein and Primakoff with probabilistic estimates and operator inequalities.
AU - Correggi, Michele
AU - Giuliani, Alessandro
AU - Seiringer, Robert
ID - 2029
IS - 2
JF - EPL
TI - Validity of spin-wave theory for the quantum Heisenberg model
VL - 108
ER -
TY - JOUR
AB - We present an overview of mathematical results on the low temperature properties of dilute quantum gases, which have been obtained in the past few years. The presentation includes a discussion of Bose-Einstein condensation, the excitation spectrum for trapped gases and its relation to superfluidity, as well as the appearance of quantized vortices in rotating systems. All these properties are intensely being studied in current experiments on cold atomic gases. We will give a description of the mathematics involved in understanding these phenomena, starting from the underlying many-body Schrödinger equation.
AU - Seiringer, Robert
ID - 2297
IS - 2
JF - Japanese Journal of Mathematics
TI - Hot topics in cold gases: A mathematical physics perspective
VL - 8
ER -
TY - JOUR
AB - We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long-range, power law decaying, antiferromagnetic interactions. If the strength of the ferromagnetic coupling J is larger than a critical value Jc, then the ground state is homogeneous and ferromagnetic. As the critical value is approached from smaller values of J, it is believed that the ground state consists of a periodic array of stripes (d=2) or slabs (d=3), all of the same size and alternating magnetization. Here we prove rigorously that the ground state energy per site converges to that of the optimal periodic striped or slabbed state, in the limit that J tends to the ferromagnetic transition point. While this theorem does not prove rigorously that the ground state is precisely striped or slabbed, it does prove that in any suitably large box the ground state is striped or slabbed with high probability.
AU - Giuliani, Alessandro
AU - Lieb, Élliott
AU - Seiringer, Robert
ID - 2300
IS - 6
JF - Physical Review B
TI - Realization of stripes and slabs in two and three dimensions
VL - 88
ER -
TY - JOUR
AB - We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential.
AU - Seiringer, Robert
ID - 2318
IS - 3
JF - Journal of Spectral Theory
TI - Absence of bound states implies non-negativity of the scattering length
VL - 2
ER -