二元玻色气体超声速流中的驻波
Stationary waves in a supersonic flow of a two-component Bose gas
摘要：
本文研究了双组分玻色-爱因斯坦凝聚体通过障碍物时出现的定常波型。我们考虑两个超流分量速度不等的一般情况。朗道判据应用于两组分系统，确定了速度空间中可能发生超流的某个区域。驻波出现在这个区域之外，但是在附加的条件下，组分的相对速度不超过某个临界值。随着相对速度的增加，激励谱变为复值，驻波模式被打破。在速度相等的情况下，可以出现两组驻波，对应于较低和较高的Bogolyubov模式。如果一个组分流动而另一个组分静止，那么只会出现一组波。如果速度近似相等，且速度之间的夹角接近π/2，则可能出现两组甚至三组干涉波。在后两种情况下，驻波对应于较低的模式，并且分量的密度异相振荡。计算了驻波中各分量的振幅比。这个量取决于相对速度，对于不同的波组是不同的，并且沿着波峰变化。对于两个或三个波干涉的情况，获得密度图像。
英文摘要：
A stationary wave pattern occurring in a flow of a two-component Bose-Einstein condensate past an obstacle is studied. We consider the general case of unequal velocities of two superfluid components. The Landau criterium applied to the two-component system determines a certain region in the velocity space in which superfluidity may take place. Stationary waves arise out of this region, but under the additional condition that the relative velocity of the components does not exceed some critical value. Under increase of the relative velocity the spectrum of the excitations becomes complex valued and the stationary wave pattern is broken. In case of equal velocities two sets of stationary waves that correspond to the lower and the upper Bogolyubov mode can arise. If one component flows and the other is at rest only one set of waves may emerge. Two or even three interfere sets of waves may arise if the velocities approximately of equal value and the angle between the velocities is close to pi/2. In two latter cases the stationary waves correspond to the lower mode and the densities of the components oscillate out-of-phase. The ratio of amplitudes of the components in the stationary waves is computed. This quantity depends on the relative velocity, is different for different sets of waves, and varies along the crests of the waves. For the cases where two or three waves interfere the density images are obtained.
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