论文标题
几何形状如何影响量子气体？
How does geometry affect quantum gases?
论文作者
论文摘要
在这项工作中，我们研究了限制在各种形状空间的量子气体的热力学功能，即球体，圆柱体和椭圆形。我们从最简单的情况开始，即在规范合奏框架内处理的无旋气气。在下一步中，我们考虑使用Grand Canonical Ensemble描述的使用\ TextIt {非相互作用}气体（费米和玻色子）。对于这种情况，计算是数值执行的。我们还观察到，我们的结果可能应用于\ textit {Bose-Einstein Condensate}和\ textit {氦二聚体}。此外，玻色粒部门独立于几何形状，获得熵和内部能量，而内部能量大于费米子情况。最后，我们还设计了一个模型，允许我们在\ textit {互动}量子气体的情况下分析计算，然后将其应用于立方体盒。
In this work, we study the thermodynamic functions of quantum gases confined to spaces of various shapes, namely, a sphere, a cylinder, and an ellipsoid. We start with the simplest situation, namely, a spinless gas treated within the canonical ensemble framework. As a next step, we consider \textit{noninteracting} gases (fermions and bosons) with the usage of the grand canonical ensemble description. For this case, the calculations are performed numerically. We also observe that our results may possibly be applied to \textit{Bose-Einstein condensate} and to \textit{helium dimer}. Moreover, the bosonic sector, independently of the geometry, acquires entropy and internal energy greater than for the fermionic case. Finally, we also devise a model allowing us to perform analytically the calculations in the case of \textit{interacting} quantum gases, and, afterwards, we apply it to a cubical box.
