@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{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},
}
@phdthesis{52,
abstract = {In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques- tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the point-interacting model. By restricting the N + 1 system to a box we define a finite density model with point in- teractions. In the context of this system we will discuss the energy change when introducing a point-interacting impurity into a system of non-interacting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the non-interacting system.},
author = {Moser, Thomas},
pages = {115},
publisher = {IST Austria},
title = {{Point interactions in systems of fermions}},
doi = {10.15479/AT:ISTA:th_1043},
year = {2018},
}