Analytic solutions of topologically disjoint systems

Abstract

We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All other interactions are approximated by harmonic oscillator potentials. The problem is first reduced to an analytically solvable $N$-body problem and $N$ independent two-body problems. We calculate analytically spectra, wave functions, and normal modes for both the inverse square and delta-function two-body interactions. In particular, we calculate separation energies between two strings of particles. We find that the string separation energy increases with $N$ and interaction strength.

13 pages, 7 figures, revised and published version

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• Morphology of an interacting three-dimensional trapped Bose-Einstein condensate from many-particle variance anisotropy
• Fragmentation of identical and distinguishable bosons' pairs and natural geminals of a trapped bosonic mixture