Related papers: Analytic Harmonic Approach to the N-body problem
We study a system of $A$ identical interacting bosons trapped by an external field by solving ab initio the many-body Schroedinger equation. A complete solution by using, for example, the traditional hyperspherical harmonics (HH) basis…
The variational approach, used by Feynman in the study of the polaron problem, is generalized to treat a system of N non-relativistic particles interacting with scalar and vector mesons. After integrating out the meson fields in the path…
A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation for $N_0$ condensed bosons in an isotropic harmonic trap with oscillator length $d_0$ and interacting…
The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of $N$ particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically…
We explore the zero-temperature behavior of an assembly of bosons interacting through a zero-range, attractive potential. Because the two-body interaction admits a bound state, the many-body model is best described by a Hamiltonian that…
We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent…
We study two-body correlations for $N$ identical bosons by use of the hyperspherical adiabatic expansion method. We use the zero-range interaction and derive a transcendental equation determining the key ingredient of the hyperradial…
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…
For a gas of N bosons interacting through a two-body Morse potential a variational bound of the free energy of a confined system is obtained. The calculation method is based on the Feynman-Kac functional projected on the symmetric…
We present a method based on hyperspherical harmonics to solve the nuclear many-body problem. It is an extension of accurate methods used for studying few-body systems to many bodies and is based on the assumption that nucleons in nuclei…
We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in…
We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body…
A method has been developed for obtaining equivalent linear two-body equations (ELTBE) for the system of many ($N$) bosons using the variational principle. The method has been applied to the one-dimensional N-body problem with pair-wise…
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this…
For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…
The zero temperature phase diagram of binary boson-fermion mixtures in two-colour superlattices is investigated. The eigenvalue problem associated with the Bose-Fermi-Hubbard Hamiltonian is solved using an exact numerical diagonalization…
We present a pair-wise force law in a system of N particles that produces analytic solutions for arbitrary number of particles, masses, and initial conditions. Each pair of particles interacts via a force that is proportional to the product…