Analytic solutions of topologically disjoint systems

J. R. Armstrong; A. G. Volosniev; D. V. Fedorov; A. S. Jensen; Nikolaj Thomas Zinner

doi:10.1088/1751-8113/48/8/085301

Analytic solutions of topologically disjoint systems

J. R. Armstrong, A. G. Volosniev, D. V. Fedorov, A. S. Jensen, Nikolaj Thomas Zinner

Department of Physics and Astronomy

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

26 Citations (Scopus)

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.

Translated title of the contribution	Analytic solutions of topologically disjoint systems
Original language	English
Article number	085301
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	48
Issue	8
ISSN	1751-8113
DOIs	https://doi.org/10.1088/1751-8113/48/8/085301
Publication status	Published - 28 Jan 2015

Keywords

quant-ph

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10.1088/1751-8113/48/8/085301

http://iopscience.iop.org/1751-8121/48/8/085301/

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Cite this

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AU - Fedorov, D. V.

AU - Jensen, A. S.

AU - Zinner, Nikolaj Thomas

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AB - 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.

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