# Oscillation bands of condensates on a ring: Beyond the mean field theory

## TL;DR

This paper investigates the oscillation bands of condensates on a ring by diagonalizing the Hamiltonian of a bosonic system, revealing excitation modes, clustering phenomena, and the relation between vortex and low-lying states beyond mean field theory.

## Contribution

It introduces a detailed analysis of excitation modes, clustering, and state classification in a bosonic ring system beyond traditional mean field approaches.

## Key findings

- Identification of basic oscillation modes involving pair excitations
- Discovery of Bose-clustering and cluster structures in the system
- Establishment of a relation between vortex states and low-lying excitations

## Abstract

The Hamiltonian of a N-boson system confined on a ring with zero spin and repulsive interaction is diagonalized. The excitation of a pair of p-wave-particles rotating reversely appears to be a basic mode. The fluctuation of many of these excited pairs provides a mechanism of oscillation, the states can be thereby classified into oscillation bands. The particle correlation is studied intuitively via the two-body densities. Bose-clustering originating from the symmetrization of wave functions is found, which leads to the appearance of 1-, 2-, and 3-cluster structures. The motion is divided into being collective and relative, this leads to the establishment of a relation between the very high vortex states and the low-lying states.