论文标题
偶极玻色 - 因子凝结物中量子波动的量子水动力学理论
Quantum hydrodynamic theory of quantum fluctuations in dipolar Bose-Einstein condensate
论文作者
论文摘要
Bose-Einstein冷凝物（BEC）的传统量子水动力学受到连续性和Euler方程的限制。它对应于众所周知的Gross-Pitaevskii方程。但是，量子BOHM电位是动量通量的一部分，它具有非平凡的部分，可以在量子波动下演变。为了涵盖这种现象，从流体动力学方法方面，我们需要得出动量通量的方程，而第三等级张量。在所有方程式中，我们都会考虑相互作用半径在一阶中的短程相互作用（SRI）的主要贡献。衍生的流体动力学由四个流体动力方程组成。第三刻进化方程包含导致量子波动的相互作用。它包括新的相互作用常数。总比塔维斯基的相互作用常数是电势的组成部分，但第二相互作用常数是电势的第二个衍生物的组成部分。如果我们有偶极性BEC，我们会处理远程相互作用。它的贡献与偶极 - 偶极相互作用（DDI）的潜力成正比。 Euler方程包含电势的导数。第三等级张量演化方程包含电势的第三个导数。量子波动导致第二波解的存在。此外，量子波动引入了BEC的不稳定性。如果DDI具有吸引力，但较小，则以第一个相互作用常数呈现的排斥性SRI，则具有长波长的不稳定性。对于排斥的DDI，这是更复杂的图片。有一个小区域具有长波长不稳定性，可转变为存在两个波的稳定性间隔。还有短波长的不稳定。对于DDI强度与Gross-Pitaevskii Sri相当的DDI强度是可以发现的。
Traditional quantum hydrodynamics of Bose-Einstein condensates (BECs) is restricted by the continuity and Euler equations. It corresponds to the well-known Gross-Pitaevskii equation. However, the quantum Bohm potential, which is a part of the momentum flux, has a nontrivial part with can evolve under the quantum fluctuations. To cover this phenomenon in terms of hydrodynamic methods we need to derive equations for the momentum flux, and the third rank tensor. In all equations we consider the main contribution of the short-range interaction (SRI) in the first order by the interaction radius. Derived hydrodynamics consists of four hydrodynamic equations. The third moment evolution equation contains interaction leading to the quantum fluctuations. It includes new interaction constant. The Gross-Pitaevskii interaction constant is the integral of potential, but the second interaction constant is the integral of second derivative of potential. If we have dipolar BECs we deal with a long-range interaction. Its contribution is proportional to the potential of dipole-dipole interaction (DDI). The Euler equation contains the derivative of the potential. The third rank tensor evolution equation contains the third derivative of the potential. The quantum fluctuations lead to existence of the second wave solution. Moreover, the quantum fluctuations introduce the instability of BECs. If the DDI is attractive, but being smaller then the repulsive SRI presented by the first interaction constant, there is the long-wavelength instability. For the repulsive DDI these is more complex picture. There is the small area with the long-wavelength instability which transits into stability interval, where two waves exist. There is the short-wavelength instability as well. These results are found for the DDI strength comparable with the Gross-Pitaevskii SRI.
