论文标题
原子玻色子凝结物的流体动力学超出平均场近似值：微型审查
Hydrodynamics of the atomic Bose-Einstein condensate beyond the mean-field approximation: a mini-review
论文作者
论文摘要
几种流体动力学模型从一个角度一起讨论了均值场近似之外的原子 - 玻色子冷凝水。所有这些模型均来自微观量子描述。该推导是在L. kuz'menkov建议的许多粒子量子流体动力学方法中进行的。为平均场式策略展示并讨论了派生，揭示了总比塔维斯基方程作为最简单的例证。它以相互作用半径为一阶。讨论了相互作用半径以三阶获得的流体动力欧拉方程的概括。它包括由浓度平方的第三空间衍生物提出的各向同性短距离相互作用的贡献。 Euler方程还包括与二阶球形函数成正比的短程相互作用的各向异性部分的贡献。量子波动的系统描述是根据许多粒子量子流体动力学方法来扩展从夫妻连续性和欧拉方程到四个方程组的一组流体动力方程，其中还包括压力演化方程和第三级压力级别的进化方程。压力演化方程不包含相互作用半径在第一阶的相互作用贡献。量子波动的来源是在第三级张量演化方程中引起的相互作用，该方程是由相互作用半径在一阶获得的。
Several hydrodynamic models the atomic Bose-Einstein condensate beyond the mean-field approximation are discussed together from one point of view. All these models are derived from microscopic quantum description. The derivation is made within the many-particle quantum hydrodynamics method suggested by L. Kuz'menkov. The derivation is demonstrated and discussed for the mean-field regime revealing the Gross-Pitaevskii equation as the simplest illustration. It appears in the first order by the interaction radius. Generalization of the hydrodynamic Euler equation obtained in the third order by the interaction radius are discussed. It includes the contribution of the isotropic short-range interaction presented by the third space derivative of the square of concentration. The Euler equation also includes the contribution of the anisotropic part of the short-range interaction proportional to the second order spherical function. Systematic account of the quantum fluctuations in terms of the many-particle quantum hydrodynamics method requires the extension of the set of hydrodynamic equations from the couple continuity and Euler equations to the set of four equations which also includes the pressure evolution equation and the evolution equation for the third rank analog of pressure. The pressure evolution equation contains no interaction contribution in the first order by the interaction radius. The source of the quantum fluctuations is in the interaction caused term in the third rank tensor evolution equation which is obtained in the first order by the interaction radius.
