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Motivated by recent experiments on Bose-Einstein condensed atoms which rotatein annular/toroidal traps we study the effect of the finiteness of the atomnumber $N$ on the states of lowest energy for a fixed expectation value of theangular momentum, under periodic boundary conditions. To attack this problem,we develop a general strategy, considering a linear superposition of theeigenstates of the many-body Hamiltonian, with amplitudes that we extract fromthe mean field approximation. This many-body state breaks the symmetry of theHamiltonian, it has the same energy to leading order in $N$ as the mean-fieldstate and the corresponding eigenstate of the Hamiltonian, however it has alower energy to subleading order in $N$ and thus it is energetically favorable.

physical review. a/physical review, a

Rotating Bose-Einstein condensates with a finite number of atoms  confined in a ring potential: Spontaneous symmetry breaking, beyond the  mean-field approximation