@article{1267,
abstract = {We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result.},
author = {Frank, Rupert and Killip, Rowan and Nam, Phan},
journal = {Letters in Mathematical Physics},
number = {8},
pages = {1033 -- 1036},
publisher = {Springer},
title = {{Nonexistence of large nuclei in the liquid drop model}},
doi = {10.1007/s11005-016-0860-8},
volume = {106},
year = {2016},
}
@article{1704,
abstract = {Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.},
author = {Deuchert, Andreas and Hainzl, Christian and Seiringer, Robert},
journal = {Letters in Mathematical Physics},
number = {10},
pages = {1449 -- 1466},
publisher = {Springer},
title = {{Note on a family of monotone quantum relative entropies}},
doi = {10.1007/s11005-015-0787-5},
volume = {105},
year = {2015},
}
@article{1807,
abstract = {We study a double Cahn-Hilliard type functional related to the Gross-Pitaevskii energy of two-components Bose-Einstein condensates. In the case of large but same order intercomponent and intracomponent coupling strengths, we prove Γ-convergence to a perimeter minimisation functional with an inhomogeneous surface tension. We study the asymptotic behavior of the surface tension as the ratio between the intercomponent and intracomponent coupling strengths becomes very small or very large and obtain good agreement with the physical literature. We obtain as a consequence, symmetry breaking of the minimisers for the harmonic potential.},
author = {Goldman, Michael and Royo-Letelier, Jimena},
journal = {ESAIM - Control, Optimisation and Calculus of Variations},
number = {3},
pages = {603 -- 624},
publisher = {EDP Sciences},
title = {{Sharp interface limit for two components Bose-Einstein condensates}},
doi = {10.1051/cocv/2014040},
volume = {21},
year = {2015},
}
@article{1880,
abstract = {We investigate the relation between Bose-Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder},
author = {Könenberg, Martin and Moser, Thomas and Seiringer, Robert and Yngvason, Jakob},
journal = {New Journal of Physics},
publisher = {IOP Publishing Ltd.},
title = {{Superfluid behavior of a Bose-Einstein condensate in a random potential}},
doi = {10.1088/1367-2630/17/1/013022},
volume = {17},
year = {2015},
}
@article{1939,
author = {Dereziński, Jan and Napiórkowski, Marcin M},
journal = {Annales Henri Poincare},
number = {7},
pages = {1709 -- 1711},
publisher = {Birkhäuser},
title = {{Erratum to: Excitation spectrum of interacting bosons in the Mean-Field Infinite-Volume limit}},
doi = {10.1007/s00023-014-0390-9},
volume = {16},
year = {2015},
}
@article{2085,
abstract = {We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. },
author = {Nam, Phan and Seiringer, Robert},
journal = {Archive for Rational Mechanics and Analysis},
number = {2},
pages = {381 -- 417},
publisher = {Springer},
title = {{Collective excitations of Bose gases in the mean-field regime}},
doi = {10.1007/s00205-014-0781-6},
volume = {215},
year = {2015},
}
@article{473,
abstract = {We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction strength behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schrödinger functional on a finite interval, as well as smoother interactions in dimensions d 2.},
author = {Lewin, Mathieu and Phan Thanh, Nam and Rougerie, Nicolas},
journal = {Journal de l'Ecole Polytechnique - Mathematiques},
pages = {65 -- 115},
publisher = {Ecole Polytechnique},
title = {{Derivation of nonlinear gibbs measures from many-body quantum mechanics}},
doi = {10.5802/jep.18},
volume = {2},
year = {2015},
}
@article{1572,
abstract = {We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error term. It uses in an essential way the bosonic formulation of the model in terms of the Holstein-Primakoff representation. In this language, the model describes interacting bosons with a hard-core on-site repulsion and a nearest-neighbor attraction. This attractive interaction makes the lower bound on the free energy particularly tricky: the key idea there is to prove a differential inequality for the two-particle density, which is thereby shown to be smaller than the probability density of a suitably weighted two-particle random process on the lattice.
},
author = {Correggi, Michele and Giuliani, Alessandro and Seiringer, Robert},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {279 -- 307},
publisher = {Springer},
title = {{Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet}},
doi = {10.1007/s00220-015-2402-0},
volume = {339},
year = {2015},
}
@article{1573,
abstract = {We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in ℝ3. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdos, Schlein, and Yau.},
author = {Chen, Thomas and Hainzl, Christian and Pavlović, Nataša and Seiringer, Robert},
journal = {Communications on Pure and Applied Mathematics},
number = {10},
pages = {1845 -- 1884},
publisher = {Wiley},
title = {{Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti}},
doi = {10.1002/cpa.21552},
volume = {68},
year = {2015},
}
@inproceedings{8044,
abstract = {Many questions concerning models in quantum mechanics require a detailed analysis of the spectrum of the corresponding Hamiltonian, a linear operator on a suitable Hilbert space. Of particular relevance for an understanding of the low-temperature properties of a system is the structure of the excitation spectrum, which is the part of the spectrum close to the spectral bottom. We present recent progress on this question for bosonic many-body quantum systems with weak two-body interactions. Such system are currently of great interest, due to their experimental realization in ultra-cold atomic gases. We investigate the accuracy of the Bogoliubov approximations, which predicts that the low-energy spectrum is made up of sums of elementary excitations, with linear dispersion law at low momentum. The latter property is crucial for the superfluid behavior the system.},
author = {Seiringer, Robert},
booktitle = {Proceeding of the International Congress of Mathematicans},
isbn = {9788961058063},
location = {Seoul, South Korea},
pages = {1175--1194},
publisher = {Kyung Moon SA},
title = {{Structure of the excitation spectrum for many-body quantum systems}},
volume = {3},
year = {2014},
}