@article{7611,
abstract = {We consider a system of N bosons in the limit N→∞, interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.},
author = {Rademacher, Simone Anna Elvira},
issn = {0377-9017},
journal = {Letters in Mathematical Physics},
pages = {2143--2174},
publisher = {Springer Nature},
title = {{Central limit theorem for Bose gases interacting through singular potentials}},
doi = {10.1007/s11005-020-01286-w},
volume = {110},
year = {2020},
}
@article{7650,
abstract = {We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross–Pitaevskii limit, where the scattering length a is so small that the interaction energy is of the same order of magnitude as the spectral gap of the Laplacian, and for temperatures that are comparable to the critical temperature of the ideal gas. We show that the difference between the specific free energy of the interacting system and the one of the ideal gas is to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show that the one-particle density matrix of any approximate minimizer of the Gibbs free energy functional is to leading order given by the one of the ideal gas. This in particular proves Bose–Einstein condensation with critical temperature given by the one of the ideal gas to leading order. One key ingredient of our proof is a novel use of the Gibbs variational principle that goes hand in hand with the c-number substitution.},
author = {Deuchert, Andreas and Seiringer, Robert},
issn = {0003-9527},
journal = {Archive for Rational Mechanics and Analysis},
number = {6},
pages = {1217--1271},
publisher = {Springer Nature},
title = {{Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature}},
doi = {10.1007/s00205-020-01489-4},
volume = {236},
year = {2020},
}
@article{7790,
abstract = {We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 .},
author = {Deuchert, Andreas and Mayer, Simon and Seiringer, Robert},
issn = {20505094},
journal = {Forum of Mathematics, Sigma},
publisher = {Cambridge University Press},
title = {{The free energy of the two-dimensional dilute Bose gas. I. Lower bound}},
doi = {10.1017/fms.2020.17},
volume = {8},
year = {2020},
}
@unpublished{7901,
abstract = {We derive rigorously the leading order of the correlation energy of a Fermi
gas in a scaling regime of high density and weak interaction. The result
verifies the prediction of the random-phase approximation. Our proof refines
the method of collective bosonization in three dimensions. We approximately
diagonalize an effective Hamiltonian describing approximately bosonic
collective excitations around the Hartree-Fock state, while showing that
gapless and non-collective excitations have only a negligible effect on the
ground state energy.},
author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert},
booktitle = {arXiv},
title = {{Correlation energy of a weakly interacting Fermi gas}},
year = {2020},
}
@article{6649,
abstract = {While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.
},
author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
pages = {2097–2150},
publisher = {Springer Nature},
title = {{Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime}},
doi = {10.1007/s00220-019-03505-5},
volume = {374},
year = {2020},
}