@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},
}
@article{2029,
abstract = {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.},
author = {Correggi, Michele and Giuliani, Alessandro and Seiringer, Robert},
journal = {EPL},
number = {2},
publisher = {IOP Publishing Ltd.},
title = {{Validity of spin-wave theory for the quantum Heisenberg model}},
doi = {10.1209/0295-5075/108/20003},
volume = {108},
year = {2014},
}
@article{2186,
abstract = {We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ℝ3. Moreover, we show that an exponential energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs.},
author = {Chen, Thomas and Hainzl, Christian and Pavlović, Nataša and Seiringer, Robert},
journal = {Letters in Mathematical Physics},
number = {7},
pages = {871 -- 891},
publisher = {Springer},
title = {{On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti}},
doi = {10.1007/s11005-014-0693-2},
volume = {104},
year = {2014},
}
@inproceedings{1516,
abstract = {We present a rigorous derivation of the BCS gap equation for superfluid fermionic gases with point interactions. Our starting point is the BCS energy functional, whose minimizer we investigate in the limit when the range of the interaction potential goes to zero.
},
author = {Bräunlich, Gerhard and Hainzl, Christian and Seiringer, Robert},
booktitle = {Proceedings of the QMath12 Conference},
location = {Berlin, Germany},
pages = {127 -- 137},
publisher = {World Scientific Publishing},
title = {{On the BCS gap equation for superfluid fermionic gases}},
doi = {10.1142/9789814618144_0007},
year = {2014},
}
@article{2297,
abstract = {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.},
author = {Seiringer, Robert},
journal = {Japanese Journal of Mathematics},
number = {2},
pages = {185 -- 232},
publisher = {Springer},
title = {{Hot topics in cold gases: A mathematical physics perspective}},
doi = {10.1007/s11537-013-1264-5},
volume = {8},
year = {2013},
}