Armstrong, J. R.^{2}; Volosniev, A. G.^{3}; Fedorov, D. V.^{4}; Jensen, A. S.^{4}; Zinner, Nikolaj Thomas^{4}

Affiliations:

^{1} Department of Physics and Astronomy, Science and Technology, Aarhus University^{2} unknown^{3} Department of Physics and Astronomy, Faculty of Science, Aarhus University, Aarhus University^{4} Department of Physics and Astronomy, Science and Technology, Aarhus University

DOI:

10.1088/1751-8113/48/8/085301

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.

Type:

Journal article

Language:

English

Published in:

Journal of Physics A: Mathematical and Theoretical, 2015, Vol 48, Issue 8