论文标题
在托马斯 - 弗米近似中的雪茄形对数bose-enstein冷凝物中的声学振荡
Acoustic oscillations in cigar-shaped logarithmic Bose-Einstein condensate in the Thomas-Fermi approximation
论文作者
论文摘要
我们考虑使用Thomas-Fermi和线性近似值，使用对数波方程与对数波方程与对数波方程描述的雪茄形玻璃纤维凝结物中密度波动的动力学特性。结果表明，在强烈各向异性陷阱中，沿凝结肿块的长轴沿着长轴的繁殖繁殖基本上是一维的，而在线性状态下可以忽略捕获势。根据非线性耦合的迹象，波动要么采取翻译对称的脉冲和站立波的形式，要么以不同的幅度变为振荡。我们还使用弹性理论的概念研究了轴向谐波陷阱中的冷凝物。线性粒子密度和能量的行为也不同，具体取决于非线性耦合的值。如果是负的，则密度随着肿块的半径而单调生长，而能量是密度的单调函数。对于正耦合，密度是从上方绑定的，而能量则根据密度而单调生长，直到达到其全局最大值为止。
We consider the dynamical properties of density fluctuations in the cigar-shaped Bose-Einstein condensate described by the logarithmic wave equation with a constant nonlinear coupling by using the Thomas-Fermi and linear approximations. It is shown that the propagation of small density fluctuations along the long axis of a condensed lump in a strongly anisotropic trap is essentially one-dimensional, while the trapping potential can be disregarded in the linear regime. Depending on the sign of nonlinear coupling, the fluctuations either take the form of translationally symmetric pulses and standing waves, or become oscillations with varying amplitudes. We also study the condensate in an axial harmonic trap, by using elasticity theory's notions. Linear particle density and energy also behave differently depending on the nonlinear coupling's value. If it is negative, the density monotonously grows along with lump's radius, while energy is a monotonous function of density. For the positive coupling, the density is bound from above, whereas energy grows monotonously as a function of density until it reaches its global maximum.
