@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{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{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},
publisher = {Springer},
title = {{Energy contribution of a point-interacting impurity in a Fermi gas}},
doi = {10.1007/s00023-018-00757-0},
year = {2019},
}
@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},
publisher = {Springer},
title = {{Bose–Einstein condensation in a dilute, trapped gas at positive temperature}},
doi = {10.1007/s00220-018-3239-0},
year = {2018},
}
@article{295,
abstract = {We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter (Formula presented.). The lower bounds extend to Lieb–Thirring inequalities for all anyons except bosons.},
author = {Lundholm, Douglas and Seiringer, Robert},
journal = {Letters in Mathematical Physics},
number = {11},
pages = {2523--2541},
publisher = {Springer},
title = {{Fermionic behavior of ideal anyons}},
doi = {10.1007/s11005-018-1091-y},
volume = {108},
year = {2018},
}
@article{180,
abstract = {In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density. We prove that the UEG arises in Density Functional Theory in the limit of a slowly varying density, minimizing the indirect Coulomb energy. We also construct the quantum UEG and compare it to the classical UEG at low density.},
author = {Lewi, Mathieu and Lieb, Élliott and Seiringer, Robert},
journal = {Journal de l'Ecole Polytechnique - Mathematiques},
pages = {79 -- 116},
publisher = {Ecole Polytechnique},
title = {{Statistical mechanics of the uniform electron gas}},
doi = {10.5802/jep.64},
volume = {5},
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},
journal = {Mathematical Physics Analysis and Geometry},
number = {19},
publisher = {Springer},
title = {{Stability of the 2+2 fermionic system with point interactions}},
doi = {10.1007/s11040-018-9275-3},
volume = {21},
year = {2018},
}
@article{1198,
abstract = {We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.},
author = {Moser, Thomas and Seiringer, Robert},
issn = {03779017},
journal = {Letters in Mathematical Physics},
number = {3},
pages = { 533 -- 552},
publisher = {Springer},
title = {{Triviality of a model of particles with point interactions in the thermodynamic limit}},
doi = {10.1007/s11005-016-0915-x},
volume = {107},
year = {2017},
}
@article{1120,
abstract = {The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 83 years ago. Here we reveal the self-localization transition for the rotational analogue of the polaron -- the angulon quasiparticle. We show that, unlike for the polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of the symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. The predicted effects can potentially be addressed in experiments on cold molecules trapped in superfluid helium droplets and ultracold quantum gases, as well as on electronic excitations in solids and Bose-Einstein condensates. },
author = {Li, Xiang and Seiringer, Robert and Lemeshko, Mikhail},
issn = {24699926},
journal = {Physical Review A},
number = {3},
publisher = {American Physical Society},
title = {{Angular self-localization of impurities rotating in a bosonic bath}},
doi = {10.1103/PhysRevA.95.033608},
volume = {95},
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{1143,
abstract = {We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive nonlinear Schrödinger functional whose quartic term is proportional to the scattering length of the interparticle interaction potential. We propose a new derivation of this limit problem, with a method that bypasses some of the technical difficulties that previous derivations had to face. The new method is based on a combination of Dyson\'s lemma, the quantum de Finetti theorem and a second moment estimate for ground states of the effective Dyson Hamiltonian. It applies equally well to the case where magnetic fields or rotation are present.},
author = {Nam, Phan and Rougerie, Nicolas and Seiringer, Robert},
journal = {Analysis and PDE},
number = {2},
pages = {459 -- 485},
publisher = {Mathematical Sciences Publishers},
title = {{Ground states of large bosonic systems: The gross Pitaevskii limit revisited}},
doi = {10.2140/apde.2016.9.459},
volume = {9},
year = {2016},
}
@article{1422,
abstract = {We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg–Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.},
author = {Frank, Rupert and Hainzl, Christian and Schlein, Benjamin and Seiringer, Robert},
journal = {Letters in Mathematical Physics},
number = {7},
pages = {913 -- 923},
publisher = {Springer},
title = {{Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations}},
doi = {10.1007/s11005-016-0847-5},
volume = {106},
year = {2016},
}
@inproceedings{1428,
abstract = {We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential.},
author = {Könenberg, Martin and Moser, Thomas and Seiringer, Robert and Yngvason, Jakob},
booktitle = {Journal of Physics: Conference Series},
location = {Shanghai, China},
number = {1},
publisher = {IOP Publishing Ltd.},
title = {{Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential}},
doi = {10.1088/1742-6596/691/1/012016},
volume = {691},
year = {2016},
}
@article{1478,
abstract = {We consider the Tonks-Girardeau gas subject to a random external potential. If the disorder is such that the underlying one-particle Hamiltonian displays localization (which is known to be generically the case), we show that there is exponential decay of correlations in the many-body eigenstates. Moreover, there is no Bose-Einstein condensation and no superfluidity, even at zero temperature.},
author = {Seiringer, Robert and Warzel, Simone},
journal = {New Journal of Physics},
number = {3},
publisher = {IOP Publishing Ltd.},
title = {{Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas}},
doi = {10.1088/1367-2630/18/3/035002},
volume = {18},
year = {2016},
}
@article{1620,
abstract = {We consider the Bardeen–Cooper–Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg–Landau equation.},
author = {Frank, Rupert and Hainzl, Christian and Seiringer, Robert and Solovej, Jan},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {189 -- 216},
publisher = {Springer},
title = {{The external field dependence of the BCS critical temperature}},
doi = {10.1007/s00220-015-2526-2},
volume = {342},
year = {2016},
}
@article{1486,
abstract = {We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J. P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg-Landau model can be derived from the BCS theory in a suitable parameter regime.},
author = {Hainzl, Christian and Seiringer, Robert},
journal = {Journal of Mathematical Physics},
number = {2},
publisher = {American Institute of Physics},
title = {{The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties}},
doi = {10.1063/1.4941723},
volume = {57},
year = {2016},
}
@article{1291,
abstract = {We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than dÂ +Â 1, with d the space dimension, this happens for all values of J smaller than a critical value Jc(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for pÂ >Â 2d and J in a left neighborhood of Jc(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (dÂ =Â 2) or slabs (dÂ =Â 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.},
author = {Giuliani, Alessandro and Seiringer, Robert},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {983 -- 1007},
publisher = {Springer},
title = {{Periodic striped ground states in Ising models with competing interactions}},
doi = {10.1007/s00220-016-2665-0},
volume = {347},
year = {2016},
}
@article{1259,
abstract = {We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional.},
author = {Bräunlich, Gerhard and Hainzl, Christian and Seiringer, Robert},
journal = {Mathematical Physics, Analysis and Geometry},
number = {2},
publisher = {Springer},
title = {{Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit}},
doi = {10.1007/s11040-016-9209-x},
volume = {19},
year = {2016},
}
@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},
}