Extension of Bogoliubov theory to quasicondensates
Extension of Bogoliubov theory to quasicondensates
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DOI：
10.1103/physreva.67.053615
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发表时间：
2002-12
影响因子：
2.9
通讯作者：
C. Mora;Y. Castin
中科院分区：
文献类型：
--
作者：
C. Mora;Y. Castin
我们提出了一个著名的Bogoliubov理论的扩展来处理低维退化玻色气体的弱相互作用和低密度波动的限制。我们使用的密度相位表示，并表明，一个精确的定义的相位算子需要一个空间离散化的大小为l的细胞。我们进行了系统的扩展的哈密顿量的两个小参数，相对密度波动内的细胞和细胞的相变。由此产生的宏观观测值可以在没有紫外或红外发散的情况下在一维、二维和三维中计算。此外，当存在真凝聚时，这种方法完全匹配Bogoliubov的方法。我们给出了气体状态方程、基态能量以及场的一阶和二阶关联函数的表达式。显式计算均相系统。
We present an extension of the well-known Bogoliubov theory to treat low-dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretization in cells of size l. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two, and three dimensions with no ultraviolet or infrared divergence. Furthermore, this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, and the first order and second order correlation functions of the field. Explicit calculations are done for homogeneous systems.