论文标题
Bose-Einstein凝结在弯曲的歧管上
Bose-Einstein Condensation on Curved Manifolds
论文作者
论文摘要
在这里，我们在弯曲的歧管上描述了一种弱相互作用的玻璃气体，该弯曲的歧管嵌入了三维欧几里得空间中。 {\ bf 65}，043614（2002）]，我们假设一个足够大的陷阱频率，以便可以将凝结电波函数的正常自由度近似整合。通过这种方式，我们在弯曲歧管的准二维表面上获得有效的冷凝水波函数，其中云的厚度是自谐确定的。对于特定情况时，当歧管是球体时，我们的平衡结果表明了化学电位和云的厚度如何随相互作用强度而增加。
Here we describe a weakly interacting Bose gas on a curved manifold, which is embedded in the three-dimensional Euclidean space.~To this end we start by considering a harmonic trap in the normal direction of the manifold, which confines the three-dimensional Bose gas in the vicinity of its surface.~Following the notion of dimensional reduction as outlined in [L.~Salasnich et al., Phys.~Rev.~A {\bf 65}, 043614 (2002)], we assume a large enough trap frequency so that the normal degree of freedom of the condensate wave function can be approximately integrated out. In this way we obtain an effective condensate wave function on the quasi-two-dimensional surface of the curved manifold, where the thickness of the cloud is determined self-consistently. For the particular case when the manifold is a sphere, our equilibrium results show how the chemical potential and the thickness of the cloud increase with the interaction strength.~Furthermore, we determine within a linear stability analysis the low-lying collective excitations together with their eigenfrequencies, which turn out to reveal an instability for attractive interactions.
