一维环中的玻色-爱因斯坦凝聚体
Bose-Einstein condensate confined in a 1D ring stirred with a rotating delta link
摘要：
本文考虑了一维环中具有排斥作用的玻色-爱因斯坦凝聚体，环中的狄拉克三角洲以恒定速度旋转。从非线性耦合、δ速度和δ强度的角度分析了δ同动标架中定态解的谱，这些参数可以取正值和负值。它被组织成一组能级，在参数空间中符合多燕尾结构，包括亮孤子，灰色和黑暗的孤子序列，和涡旋。给出了波函数和化学势的Jacobi椭圆函数的解析表达式。我们计算的临界速度，并进行Bogoliubov分析的基态和前几个激发能级，建立可能的绝热过渡之间的固定和稳定的解决方案。提出了一组绝热循环，其中通过设置和取消设置旋转δ，从基态获得任意量子化角动量的灰孤子和涡旋。
英文摘要：
We consider a Bose-Einstein condensate with repulsive interactions confined in a 1D ring where a Dirac delta is rotating at constant speed. The spectrum of stationary solutions in the delta comoving frame is analyzed in terms of the nonlinear coupling, delta velocity, and delta strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting in bright solitons, gray and dark solitonic trains, and vortices. Analytical expressions in terms Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray solitons and vortices of arbitrary quantized angular momenta are obtained from the ground state by setting and unsetting a rotating delta.
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