Comparison between microscopic methods for finite-temperature Bose gases
Comparison between microscopic methods for finite-temperature Bose gases
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DOI：
10.1103/physreva.83.043619
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发表时间：
2011-04-21
影响因子：
2.9
通讯作者：
Henkel, C.
中科院分区：
文献类型：
--
作者：
Cockburn, S. P.;Negretti, A.;Henkel, C.
我们分析了有限温度下弱相互作用的准一维玻色气体的平衡性质，并比较了不同的理论方法。我们特别关注两个随机理论：一个数量守恒的Bogoliubov（NCB）方法和随机Gross-Pitaevskii方程（SGPE），已被广泛用于数值模拟。平衡性质，如密度分布，相关函数，和冷凝物的统计相比，预测的基础上，一些替代理论。我们发现，由于热相位波动，以及相应的冷凝物耗尽，NCB方法在相对较低的温度下失去其有效性。这可以归因于Bogoliubov光谱的变化，因为冷凝物变得热耗尽，以及超出微扰理论的大波动。虽然这两个随机理论建立在不同的热力学系综（NCB，正则; SGPE，巨正则）上，但它们在大的玻色-爱因斯坦凝聚（BEC）（足够强的粒子相互作用）中产生了正确的凝聚统计。对于较小的系统，SGPE的结果容易出现非常大的数值波动，这是众所周知的巨正则理想玻色气体。基于上述理论的比较，修改后的波波夫方法，我们提出了一个简单的程序，近似提取Penrose-Onsager冷凝物的一阶和二阶相关函数，这是计算方便和潜在的使用实验。这也澄清了在低维系统的波波夫理论中凝聚态和准凝聚态之间的联系。
We analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a number-conserving Bogoliubov (NCB) approach and a stochastic Gross-Pitaevskii equation (SGPE) that have been extensively used in numerical simulations. Equilibrium properties like density profiles, correlation functions, and the condensate statistics are compared to predictions based upon a number of alternative theories. We find that due to thermal phase fluctuations, and the corresponding condensate depletion, the NCB approach loses its validity at relatively low temperatures. This can be attributed to the change in the Bogoliubov spectrum, as the condensate gets thermally depleted, and to large fluctuations beyond perturbation theory. Although the two stochastic theories are built on different thermodynamic ensembles (NCB, canonical; SGPE, grand-canonical), they yield the correct condensate statistics in a large Bose-Einstein condensate (BEC) (strong enough particle interactions). For smaller systems, the SGPE results are prone to anomalously large number fluctuations, well known for the grand-canonical, ideal Bose gas. Based on the comparison of the above theories to the modified Popov approach, we propose a simple procedure for approximately extracting the Penrose-Onsager condensate from first-and second-order correlation functions that is both computationally convenient and of potential use to experimentalists. This also clarifies the link between condensate and quasicondensate in the Popov theory of low-dimensional systems.