Related papers: A note on classical ground state energies
We use exact diagonalization to study an interacting system of $N$ spinless bosons with finite-range Gaussian repulsion, confined in a quasi-two-dimensional harmonic trap with and without an introduced rotation. The diagonalization of the…
We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A…
We consider a harmonically trapped few-Boson system under rotation and investigate the ground state properties beyond the usual ``lowest Landau level'' approximation by using exact diagonalizations in a restricted Hilbert subspace. We find…
As a continuation of \cite{me}, we consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger system with a parameter $a $ and the Coulomb potential $V(x)$ in the $L^2$-critical case, where $a>0$ represents the attractive…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…
We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the…
The understanding of the behaviour of systems of identical composite bosons has progressed significantly in connection with the analysis of the entanglement between constituents and the development of coboson theory. The basis of these…
We study the collapse of a many-body system which is used to model two-component Bose-Einstein condensates with attractive intra-species interactions and either attractive or repulsive inter-species interactions. Such a system consists a…
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…
Complications arising from the non-compact nature of the phase space of N-body systems prevent any asymptotic characterization of chaotic behaviour (since no equilibrium final states can exist). This leads us to revisit some of the old…
We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual…
We show that classical states can emerge as pure ground state solutions of a quantum many-body system. We use a simple Hubbard model in 1D with strong short-range interactions and a second nearest neighbor hopping with N particles arranged…
The polariton system is studied by a concise approach using a simple model. A new ground state with negative energy is obtained and found to exhibit the symmetry breaking.
We show that the ground state energy of the translationally invariant Nelson model, describing a particle coupled to a relativistic field of massless bosons, is an analytic function of the coupling constant and the total momentum. We derive…
A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to…
We investigate the ground state properties of a family of $N$-body systems in 1-dimension, trapped in a polynomial potential and having long range 2-body interaction in addition to the inverse square potential studied in the…
A space-periodic ground state is shown to exist for lattices of point ions in $\R^3$ coupled to the Schr\"odinger and scalar fields. The coupling requires the renormalization of the selfaction because of the singularity of the Coulomb…
The characterization of ground states among all quantum states is an important problem in quantum many-body physics. For example, the celebrated entanglement area law for gapped Hamiltonians has allowed for efficient simulation of 1d and…
We investigate the existence and the properties of normalized ground states of a nonlinear Schr\"odinger equation on a quantum hybrid formed by two planes connected at a point. The nonlinearities are of power type and $L^2$-subcritical,…
We consider Hamiltonian with $N$ point interactions in $\R^d, d=2,3,$ all with the same coupling constant, placed at vertices of an equilateral polygon $\PP_N$. It is shown that the ground state energy is locally maximized by a regular…