Novel classical ground state of a many body system in arbitrary dimensions

Abstract

The classical ground state of a D- dimensional many body system with two and three body interactions is studied as a function of the strength of the three body interaction. We prove exactly that beyond a critical strength of the three body interaction, the classical ground state of the system is one in which all the particles are on a line. The positions of the particles in this string configuration are uniquely determined by the zeros of the Hermite polynomials.

4 pages, RevTeX, no figure; version to appear in Physical Review Letters

References in corpus (6)

• Analytic results for $N$ particles with $1/r^2$ interaction in two dimensions and an external magnetic field
• A Quantum Many-body Problem in Two Dimensions: Ground State
• Supersymmetric Model of a 2D Long-Range Bose Liquid
• Classical Many-particle Clusters in Two Dimensions
• Classical Dynamics of Anyons and the Quantum Spectrum
• Microscopic analytical theory of a correlated, two-dimensional N-electron gas in a magnetic field

Cited by in corpus (7)

• Conformal mechanics in Newton-Hooke spacetime
• Remark on quantum mechanics with N=2 Schrodinger supersymmetry
• Extended superconformal symmetry and Calogero-Marchioro model
• Generalized Calogero model in arbitrary dimensions
• Explosion-implosion duality in the Bose-Einstein condensation
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• 2D Calogero Model in the Collective-Field Approach