A Solvable Model for Decoupling of Interacting Clusters
arXiv:1810.10281 · doi:10.1209/0295-5075/125/20003
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.
arXiv commentVersion accepted for publication in EPL
References in corpus (21)
- Nonequilibrium dynamics of closed interacting quantum systems
- The physics of dipolar bosonic quantum gases
- Cold atoms in cavity-generated dynamical optical potentials
- Fermi gases in one dimension: From Bethe Ansatz to experiments
- Entanglement Properties of the Harmonic Chain
- Fundamental Aspects of Quantum Brownian Motion
- Strongly interacting confined quantum systems in one dimension
- Quantum Simulations with Cold Trapped Ions
- Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
- Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
- Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
- Analytic Harmonic Approach to the N-body problem
- Achieving translational symmetry in trapped cold ion rings
- Bound states of Dipolar Bosons in One-dimensional Systems
- Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension
- Analytic solutions of topologically disjoint systems
- Layers of Cold Dipolar Molecules in the Harmonic Approximation
- Two Cold Atoms in a Time-Dependent Harmonic Trap in One Dimension
- Bound Chains of Tilted Dipoles in Layered Systems
- Sympathetic Wigner function tomography of a dark trapped ion
- Entanglement Pre-thermalization in an Interaction Quench between Two Harmonic Oscillators