@article{80,
abstract = {We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.},
author = {Deuchert, Andreas and Seiringer, Robert and Yngvason, Jakob},
journal = {Communications in Mathematical Physics},
number = {2},
pages = {723--776},
publisher = {Springer},
title = {{Bose–Einstein condensation in a dilute, trapped gas at positive temperature}},
doi = {10.1007/s00220-018-3239-0},
volume = {368},
year = {2019},
}
@article{6840,
abstract = {We discuss thermodynamic properties of harmonically trapped
imperfect quantum gases. The spatial inhomogeneity of these systems imposes
a redefinition of the mean-field interparticle potential energy as compared
to the homogeneous case. In our approach, it takes the form a
2N2 ωd, where
N is the number of particles, ω—the harmonic trap frequency, d—system’s
dimensionality, and a is a parameter characterizing the interparticle interaction.
We provide arguments that this model corresponds to the limiting case of
a long-ranged interparticle potential of vanishingly small amplitude. This
conclusion is drawn from a computation similar to the well-known Kac scaling
procedure, which is presented here in a form adapted to the case of an isotropic
harmonic trap. We show that within the model, the imperfect gas of trapped
repulsive bosons undergoes the Bose–Einstein condensation provided d > 1.
The main result of our analysis is that in d = 1 the gas of attractive imperfect
fermions with a = −aF < 0 is thermodynamically equivalent to the gas of
repulsive bosons with a = aB > 0 provided the parameters aF and aB fulfill
the relation aB + aF = . This result supplements similar recent conclusion
about thermodynamic equivalence of two-dimensional (2D) uniform imperfect
repulsive Bose and attractive Fermi gases.},
author = {Mysliwy, Krzysztof and Napiórkowski, Marek},
issn = {1742-5468},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
number = {6},
publisher = {IOP Publishing},
title = {{Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps}},
doi = {10.1088/1742-5468/ab190d},
volume = {2019},
year = {2019},
}
@article{7235,
abstract = {We consider the Fröhlich model of a polaron, and show that its effective mass diverges in thestrong coupling limit.},
author = {Lieb, Elliott H. and Seiringer, Robert},
issn = {0022-4715},
journal = {Journal of Statistical Physics},
publisher = {Springer},
title = {{Divergence of the effective mass of a polaron in the strong coupling limit}},
doi = {10.1007/s10955-019-02322-3},
year = {2019},
}
@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},
publisher = {Springer},
title = {{Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime}},
doi = {10.1007/s00220-019-03505-5},
year = {2019},
}
@article{6788,
abstract = {We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.},
author = {Leopold, Nikolai K and Petrat, Sören P},
issn = {1424-0661},
journal = {Annales Henri Poincare},
number = {10},
pages = {3471–3508},
publisher = {Springer Nature},
title = {{Mean-field dynamics for the Nelson model with fermions}},
doi = {10.1007/s00023-019-00828-w},
volume = {20},
year = {2019},
}
@article{7015,
abstract = {We modify the "floating crystal" trial state for the classical homogeneous electron gas (also known as jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground-state energy of jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in density functional theory. Finally, in the third system each electron interacts with a periodic image of itself; that is, periodic boundary conditions are imposed on the interaction potential.},
author = {Lewin, Mathieu and Lieb, Elliott H. and Seiringer, Robert},
issn = {2469-9950},
journal = {Physical Review B},
number = {3},
publisher = {APS},
title = {{Floating Wigner crystal with no boundary charge fluctuations}},
doi = {10.1103/physrevb.100.035127},
volume = {100},
year = {2019},
}
@article{7100,
abstract = {We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.},
author = {Jeblick, Maximilian and Leopold, Nikolai K and Pickl, Peter},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {1--69},
publisher = {Springer Nature},
title = {{Derivation of the time dependent Gross–Pitaevskii equation in two dimensions}},
doi = {10.1007/s00220-019-03599-x},
volume = {372},
year = {2019},
}
@article{5856,
abstract = {We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the change in energy compared to the system in the absence of the impurity is bounded in terms of the gas density and the scattering length of the interaction, independently of N. Our bound holds as long as the ratio of the mass of the impurity to the one of the gas particles is larger than a critical value m∗ ∗≈ 0.36 , which is the same regime for which we recently showed stability of the system.},
author = {Moser, Thomas and Seiringer, Robert},
issn = {14240637},
journal = {Annales Henri Poincare},
number = {4},
pages = {1325–1365},
publisher = {Springer},
title = {{Energy contribution of a point-interacting impurity in a Fermi gas}},
doi = {10.1007/s00023-018-00757-0},
volume = {20},
year = {2019},
}
@article{6906,
abstract = {We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential.},
author = {Boccato, Chiara and Brennecke, Christian and Cenatiempo, Serena and Schlein, Benjamin},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
publisher = {Springer},
title = {{Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime}},
doi = {10.1007/s00220-019-03555-9},
year = {2019},
}
@article{7226,
author = {Jaksic, Vojkan and Seiringer, Robert},
issn = {00222488},
journal = {Journal of Mathematical Physics},
number = {12},
publisher = {AIP},
title = {{Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018}},
doi = {10.1063/1.5138135},
volume = {60},
year = {2019},
}