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

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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.