Related papers: Ground-state-energy universality of noninteracting…
We study the ground-state energy of one-dimensional, non-interacting fermions subject to an external potential in the thermodynamic limit. To this end, we fix some (Fermi) energy $\nu>0$, confine fermions with total energy below $\nu$…
We derive analytically the full distribution of the ground-state energy of $K$ non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of $N$ i.i.d.~random energy levels with distribution…
We study the ground state energy of a gas of $N$ fermions confined to a unit box in $d$ dimensions. The particles interact through a 2-body potential with strength scaled in an $N$-dependent way as $N^{-\alpha}v$, where $\alpha\in \mathbb…
The dimensionless universal coefficient $\xi$ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson Problem is taken as a…
We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the…
The ground state properties of $N$ spinless free fermions in a $d$-dimensional confining potential are studied. We find that any $n$-point correlation function has a simple determinantal structure that allows us to compute several…
Motivated by our earlier work, we show in this paper rigorously that the ground state energy and degeneracy of an infinitely extended system of interacting electrons in the background of a homogeneous magnetic field and two separated…
We consider a system of $N$ spinless fermions, interacting with each other via a power-law interaction $\epsilon/r^n$, and trapped in an external harmonic potential $V(r) = r^2/2$, in $d=1,2,3$ dimensions. For any $0 < n < d+2$, we obtain…
We study the ground-state of a Fermi gas with short range attrative interactions in one or two dimensions. N fermions are placed in a confining potential, and interact with each other through a negative potential, whose range is larger than…
We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection,…
We consider a large atom with nuclear charge $Z$ described by non-relativistic quantum mechanics with classical or quantized electromagnetic field. We prove that the absolute ground state energy, allowing for minimizing over all possible…
Recent developments in the physics of low density trapped gases make it worthwhile to verify old, well known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently…
A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…
Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in…
Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an…
We investigate universal properties of one-dimensional multi-component systems comprised of fermions, bosons, or an arbitrary mixture, with contact interactions and subjected to an external potential. The masses and the coupling strengths…
We consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger systems with the Coulomb potential $V(x)$ in the $L^2$-subcritical case. By studying the associated constraint variational problem, we prove the existence of…
We give an upper bound on the modulus of the ground-state overlap of two non-interacting fermionic quantum systems with $N$ particles in a large but finite volume $L^d$ of $d$-dimensional Euclidean space. The underlying one-particle…
We consider the many-body ground state of polarized fermions interacting via zero-range $\mathfrak{p}$-wave forces in a one-dimensional geometry. We rigorously prove that in the limit of infinite attractions spectral properties of any-order…
We consider a pairwise interacting quantum 3-body system in 3-dimensional space with finite masses and the interaction term $V_{12} + \lambda(V_{13} + V_{23})$, where all pair potentials are assumed to be nonpositive. The pair interaction…