Volume 125, Number 2, January 2019
|Number of page(s)||7|
|Published online||12 February 2019|
A solvable model for decoupling of interacting clusters
1 Institut für Kernphysik, Technische Universität Darmstadt - 64289 Darmstadt, Germany
2 Department of Physics and Astronomy, Aarhus University - DK-8000 Aarhus C, Denmark
3 Department of Physics, American University - 4400 Massachusetts Ave. NW, Washington, DC 20016, USA
4 Department of Physics and Astronomy, University of Nebraska at Kearney - 2401 11th Avenue Kearney, NE 68849, USA
5 Aarhus Institute of Advanced Studies, Aarhus University - DK-8000 Aarhus C, Denmark
Received: 29 October 2018
Accepted: 10 January 2019
We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This letter derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 02.30.Ik – Integrable systems
© EPLA, 2019
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