标题： 旋转的有限原子数在环势中束缚的玻色-爱因斯坦凝聚体：自发对称性破缺，超越平均场近似 显示英文标题

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

摘要： 受最近关于在环形/环状陷阱中旋转的玻色-爱因斯坦凝聚原子实验的启发，我们研究了原子数量$N$的有限性对最低能量态的影响，在角动量期望值固定的情况下，且在周期性边界条件下。 为了解决这个问题，我们开发了一种通用策略，考虑多体哈密顿量本征态的线性叠加，其振幅我们从平均场近似中提取。 这种多体状态破坏了哈密顿量的对称性，它在$N$的主导阶上与平均场状态和相应的哈密顿量本征态具有相同的能量，然而它在$N$的次主导阶上具有更低的能量，因此在能量上是有利的。 显示英文摘要

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