Related papers: Exact Quantum Solutions of Extraordinary N-body Pr…
The use of exactly-solvable Richardson-Gaudin (R-G) models to describe the physics of systems with strong pair correlations is reviewed. We begin with a brief discussion of Richardson's early work, which demonstrated the exact solvability…
Trigonometric Rosen-Morse potential is suggested as the quark-antiquark interaction potential for studying the thermodynamic properties and the masses of heavy and heavy-light mesons. For this purpose, N-radial Schrodinger equation is…
We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finite-range attractive heavy-light interaction…
Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic…
The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing…
Achieving precise control of ultracold atomic gases requires a detailed understanding of atom loss mechanisms. Motivated by the anomalous three-body decay in a three-component Fermi gas reported in Ref. [1], this work investigates…
We consider the four-boson and 3+1 fermionic problems with a model Hamiltonian which encapsulates the mechanism of the Feshbach resonance involving the coherent coupling of two atoms in the open channel and a molecule in the closed channel.…
Progress toward the solution of the strongly correlated electron problem has been stymied by the exponential complexity of the wave function. Previous work established an exact two-body exponential product expansion for the ground-state…
$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…
We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component…
We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $…
Complete spectrum of exact interdimensional degeneracies for a quantum $N$-body system in $D$-dimensions is presented by the method of generalized spherical harmonic polynomials. In an $N$-body system all the states with angular momentum…
We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go…
Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly…
Some novel TWO-body effects analogous to the well-known THREE-body Efimov effect are predicted. In the systems considered, particle A is constrained on a TRUNCATED or BENT one-dimensional line or two-dimensional plane, or on one side of a…
The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is solution of the n-body Coulomb Schr\"odinger equation in (a large…
We investigate degenerate quantum gases in one dimension trapped in a harmonic potential that is split in the centre by a pointlike potential. Since the single particle eigenfunctions of such a system are known for all strengths of the…
We employ generalized Euler coordinates for the $n$ body system in $d \geq n-1$ dimensional space, which consists of the centre-of-mass vector, relative (mutual), mass-independent distances $r_{ij}$ and angles as remaining coordinates. We…
The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent…