Related papers: A note on classical ground state energies
We study the quantum mechanical many-body problem of $N \geq 1$ non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and $K \geq 0$ static nuclei. We model the dynamics of the electrons…
The existence of a ground state of the Nelson Hamiltonian with a perturbation is considered. The self-adjointness of the Hamiltonian and the existence of a ground state are proven for arbitrary values of coupling constants.
Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional…
The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy…
The ground-state energy of a three-dimensional polaron gas in a magnetic field is investigated. An upper bound for the ground-state energy is derived within a variational approach which is based on a many-body generalization of the…
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
The ground state and its structure for a rotating, harmonically trapped N-Boson system with a weak repulsive contact interaction are studied as the angular momentum L increases up to 3N. We show that the ground state is generally a…
We present a study of the two dimensional circular quantum dot model Hamiltonian using a range of quantum chemical ab initio methods. Ground and excited state energies are computed on different levels of perturbation theories including the…
A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal…
We continue the study of the two-component charged Bose gas initiated by Dyson in 1967. He showed that the ground state energy for $N$ particles is at least as negative as $-CN^{7/5}$ for large $N$ and this power law was verified by a lower…
We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy…
We study the use of von Neumann entropy constraints for obtaining lower bounds on the ground energy of quantum many-body systems. Known methods for obtaining certificates on the ground energy typically use consistency of local observables…
We study the consequences of the $f(R/\Box)$ gravity models for the Solar system and the large scale structure of the universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the…
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…
Gravity is the weakest of all four known forces in the universe. Quantum states of an elementary particle due to such a weak field is certainly very shallow and would therefore be an experimental challenge to detect. Recently an…
We consider a finite number $N$ of interacting bosonic atoms at zero temperature confined in a one-dimensional double-well trap and study this system by using the two-site Bose-Hubbard (BH) Hamiltonian. For systems with $N=2$ and $N=3$, and…
Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity…
In this paper estimates on the ground state energy of Fr\"ohlich $N$-polarons in electromagnetic fields in the strong coupling limit, $\alpha\to\infty$, are derived. It is shown that the ground state energy is given by $\alpha^2$ multiplied…
We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $\nu = 5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable…
We study the ground states for the Schr\"odinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every value of the mass; moreover they are positive, radially…