Demirkaya Betül, Dereli Tekin, Güven Kaan
Department of Physics, Koç University, 34450 Sarıyer, İstanbul, Turkey.
Heliyon. 2019 Sep 30;5(9):e02497. doi: 10.1016/j.heliyon.2019.e02497. eCollection 2019 Sep.
This paper investigates the acoustic superradiance of the density and phase fluctuations from the single vortex state of a Bose-Einstein condensate, by employing full time-domain and asymptotic frequency domain numerical calculations. The draining bathtub model of an incompressible barotropic fluid is adopted to describe the vortex. The propagation of the axisymmetric density and phase fluctuations in the condensate are governed by the massless scalar Klein-Gordon wave equation, which establishes the rotating black-hole analogy. Hence, the amplified scattering of these fluctuations from the vortex comprise the superradiance effect. A particular coordinate transformation is applied to reveal the event horizon and the ergosphere termwise in the metric and the respective asymptotic spectral solutions. A comparative analysis of the time domain and asymptotic frequency domain results are given for a range of rotational speed of the vortex and the frequency of the impinging fluctuations. The agreement at low rotational speeds of the vortex is shown to be very good, which starts to deteriorate at higher rotational speeds due to increasing constraint violations of the time-domain calculations. We further demonstrate an asymptotic upper bound for the superradiance as a function of vortex rotational speed, provided that the vortex remains stable.
本文通过采用全时域和渐近频域数值计算方法，研究了玻色 - 爱因斯坦凝聚体单涡旋态密度和相位涨落的声学超辐射现象。采用不可压缩正压流体的排水浴缸模型来描述涡旋。凝聚体中轴对称密度和相位涨落的传播由无质量标量克莱因 - 戈登波动方程控制，该方程建立了旋转黑洞类比。因此，这些涨落在涡旋处的放大散射构成了超辐射效应。应用一种特殊的坐标变换来逐项揭示度规中的事件视界和能层以及各自的渐近谱解。针对一系列涡旋旋转速度和入射涨落频率，给出了时域和渐近频域结果的对比分析。结果表明，在涡旋低旋转速度下两者吻合得非常好，但在较高旋转速度下由于时域计算中约束违反情况增加，吻合度开始变差。我们进一步证明了在涡旋保持稳定的情况下，超辐射作为涡旋旋转速度函数的渐近上限。
