具有吸引1/r相互作用气体的玻色-爱因斯坦凝聚中异常点的发现
Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction
摘要：
具有吸引1/r相互作用的气体的玻色-爱因斯坦凝聚的扩展Gross-Pitaevskii方程有第二个解，它与基态一起产生于切向分岔。在分叉点，两个状态合并，即，能量和波函数相同。我们调查的分歧点的背景下，例外点，已知的线性非厄米哈密顿的现象。我们指出，平均场能量，化学势，和波函数表现出同样的行为作为一个例外点的线性，非对称系统。解析连续的Gross-Pitaevskii方程的分析揭示了复杂的波在负散射长度低于切分叉。这些解被解释为由吸收势引起的凝结物的衰变。
英文摘要：
The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with attractive 1/r-interaction has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. We investigate the bifurcation point in the context of exceptional points, a phenomenon known for linear non-Hermitian Hamiltonians. We point out that the mean field energy, the chemical potential, and the wave functions show the same behavior as an exceptional point in a linear, non-symmetric system. The analysis of the analytically continued Gross-Pitaevskii equation reveals complex waves at negative scattering lengths below the tangent bifurcation. These solutions are interpreted as a decay of the condensate caused by an absorbing potential.
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