Dipartimento di Scienza Applicata e Tecnologia and u.d.r. CNISM, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.
Phys Rev E. 2017 Jun;95(6-1):062142. doi: 10.1103/PhysRevE.95.062142. Epub 2017 Jun 30.
A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explicit description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.
当两种相互作用的物质在双势阱中被捕获时，形成的玻色气体在相互作用足够强时会表现出宏观局域化效应。排斥相互作用将物质在空间上分离到不同的势阱中，而吸引力相互作用则将两种物质限制在同一个势阱中。我们通过利用半经典方法来研究从弱相互作用到强相互作用的转变，其中玻色子的群体用连续变量来表示。我们找到了一种用模型参数来描述低能本征态和谱的显式描述，其中包括过渡点附近的情况。为了测试连续变量方法的有效性，我们将其预测结果与数值计算得到的精确结果进行了比较。数值计算证实了这种方法在空间局域化时存在的谱坍塌现象。
