A solvable model for decoupling of interacting clusters

Abstract

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 paper 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.

Clusters in Separated Tubes of Tilted Dipoles

“…With the results found in [28,29,31,30], showing that we could treat the individual layers separately, we inserted the exact repulsion in the in-layer energies, coupled with harmonic attraction between the layers. This treatment failed to agree with earlier SVM calculations in Ref.…”