Analytic solutions of topologically disjoint systems

J. R. Armstrong, A. G. Volosniev, D. V. Fedorov, A. S. Jensen, N. T. Zinner

Research output: Contribution to journalArticle

10 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 deltafunction 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.

Original languageEnglish (US)
Article number085301
JournalJournal of Physics A: Mathematical and Theoretical
Volume48
Issue number8
DOIs
StatePublished - Feb 27 2015

Fingerprint

Analytic Solution
Disjoint
Wave functions
Interaction
strings
Strings
interactions
two body problem
Calculate
N-body Problem
many body problem
Normal Modes
Energy
Harmonic Oscillator
Wave Function
harmonic oscillators
wave functions
energy
Arbitrary

Keywords

  • exactly solvable models
  • few-body systems
  • harmonic expansion

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Analytic solutions of topologically disjoint systems. / Armstrong, J. R.; Volosniev, A. G.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 48, No. 8, 085301, 27.02.2015.

Research output: Contribution to journalArticle

Armstrong, J. R. ; Volosniev, A. G. ; Fedorov, D. V. ; Jensen, A. S. ; Zinner, N. T. / Analytic solutions of topologically disjoint systems. In: Journal of Physics A: Mathematical and Theoretical. 2015 ; Vol. 48, No. 8.
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