@article{6002,
abstract = {The Bogoliubov free energy functional is analysed. The functional serves as a model of a translation-invariant Bose gas at positive temperature. We prove the existence of minimizers in the case of repulsive interactions given by a sufficiently regular two-body potential. Furthermore, we prove the existence of a phase transition in this model and provide its phase diagram.},
author = {Napiórkowski, Marcin M and Reuvers, Robin and Solovej, Jan Philip},
issn = {0003-9527},
journal = {Archive for Rational Mechanics and Analysis},
number = {3},
pages = {1037--1090},
publisher = {Springer Nature},
title = {{The Bogoliubov free energy functional I: Existence of minimizers and phase diagram}},
doi = {10.1007/s00205-018-1232-6},
volume = {229},
year = {2018},
}
@article{154,
abstract = {We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is stable, i.e., the energy is bounded from below, for m∈[m2,m2−1]. So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system.},
author = {Moser, Thomas and Seiringer, Robert},
issn = {15729656},
journal = {Mathematical Physics Analysis and Geometry},
number = {3},
publisher = {Springer},
title = {{Stability of the 2+2 fermionic system with point interactions}},
doi = {10.1007/s11040-018-9275-3},
volume = {21},
year = {2018},
}
@inproceedings{11,
abstract = {We report on a novel strategy to derive mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. The technique combines the method of counting and the coherent state approach to study the growth of the correlations among the particles and in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon system of equations from the Nelson model with ultraviolet cutoff and possibly massless scalar field. In particular, we prove the convergence of the reduced density matrices (of the nonrelativistic particles and the field bosons) associated with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon equations in trace norm. Furthermore, we derive explicit bounds on the rate of convergence of the one-particle reduced density matrix of the nonrelativistic particles in Sobolev norm.},
author = {Leopold, Nikolai K and Pickl, Peter},
location = {Munich, Germany},
pages = {185 -- 214},
publisher = {Springer},
title = {{Mean-field limits of particles in interaction with quantised radiation fields}},
doi = {10.1007/978-3-030-01602-9_9},
volume = {270},
year = {2018},
}
@article{399,
abstract = {Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm.},
author = {Napiórkowski, Marcin M and Reuvers, Robin and Solovej, Jan},
journal = {EPL},
number = {1},
publisher = {IOP Publishing Ltd.},
title = {{Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation}},
doi = {10.1209/0295-5075/121/10007},
volume = {121},
year = {2018},
}
@article{400,
abstract = {We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. In the case of vanishing angular momentum, our results carry over to the three-dimensional case.},
author = {Deuchert, Andreas and Geisinge, Alissa and Hainzl, Christian and Loss, Michael},
journal = {Annales Henri Poincare},
number = {5},
pages = {1507 -- 1527},
publisher = {Springer},
title = {{Persistence of translational symmetry in the BCS model with radial pair interaction}},
doi = {10.1007/s00023-018-0665-7},
volume = {19},
year = {2018},
}
@article{446,
abstract = {We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z > 0 can bind at most Z + C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.},
author = {Frank, Rupert and Phan Thanh, Nam and Van Den Bosch, Hanne},
journal = {Communications on Pure and Applied Mathematics},
number = {3},
pages = {577 -- 614},
publisher = {Wiley-Blackwell},
title = {{The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory}},
doi = {10.1002/cpa.21717},
volume = {71},
year = {2018},
}
@article{455,
abstract = {The derivation of effective evolution equations is central to the study of non-stationary quantum many-body systems, and widely used in contexts such as superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry. We reformulate the Dirac–Frenkel approximation principle in terms of reduced density matrices and apply it to fermionic and bosonic many-body systems. We obtain the Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While we do not prove quantitative error estimates, our formulation does show that the approximation is optimal within the class of quasifree states. Furthermore, we prove well-posedness of the Bogoliubov–de Gennes equations in energy space and discuss conserved quantities},
author = {Benedikter, Niels P and Sok, Jérémy and Solovej, Jan},
journal = {Annales Henri Poincare},
number = {4},
pages = {1167 -- 1214},
publisher = {Birkhäuser},
title = {{The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations}},
doi = {10.1007/s00023-018-0644-z},
volume = {19},
year = {2018},
}
@article{739,
abstract = {We study the norm approximation to the Schrödinger dynamics of N bosons in with an interaction potential of the form . Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large N limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all . The range of β is expected to be optimal for this large class of initial states.},
author = {Nam, Phan and Napiórkowski, Marcin M},
issn = {00217824},
journal = {Journal de Mathématiques Pures et Appliquées},
number = {5},
pages = {662 -- 688},
publisher = {Elsevier},
title = {{A note on the validity of Bogoliubov correction to mean field dynamics}},
doi = {10.1016/j.matpur.2017.05.013},
volume = {108},
year = {2017},
}
@article{741,
abstract = {We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.},
author = {Moser, Thomas and Seiringer, Robert},
issn = {00103616},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {329 -- 355},
publisher = {Springer},
title = {{Stability of a fermionic N+1 particle system with point interactions}},
doi = {10.1007/s00220-017-2980-0},
volume = {356},
year = {2017},
}
@article{484,
abstract = {We consider the dynamics of a large quantum system of N identical bosons in 3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed 0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution in the Nparticle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory.},
author = {Nam, Phan and Napiórkowski, Marcin M},
issn = {10950761},
journal = {Advances in Theoretical and Mathematical Physics},
number = {3},
pages = {683 -- 738},
publisher = {International Press},
title = {{Bogoliubov correction to the mean-field dynamics of interacting bosons}},
doi = {10.4310/ATMP.2017.v21.n3.a4},
volume = {21},
year = {2017},
}