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arXiv 2005.09454gr-qchep-th
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引力波共振探测器中的广义不确定原理

Generalized uncertainty principle in resonant detectors of gravitational waves

Sukanta Bhattacharyya, Sunandan Gangopadhyay, Anirban Saha

摘要:

随着先进的LIGO探测器对引力波的直接探测,打开了通向量子引力唯象学的新“窗口”。目前,这些检测器实现了检测长度变化的灵敏度($δL$)、$\mathcal{O} \approx 10^{-17}-10^{-21}$米。最近,在广义不确定原理的影响下,给出了无量纲参数$β_0$的一个更严格的上界,它对应于中间长度尺度$l_{im}= \sqrt{β_0} l_{pl} \sim 10^{-23} m$ .因此,广义不确定原理的味道可以通过观察这种共振探测器中声子模式的振动响应在不久的将来实现。因此,本文在广义不确定原理框架下,计算了入射引力波在这些探测器上引起的共振频率和跃迁率。结果表明,广义不确定原理的影响在引力波-谐振子哈密顿量的时间无关部分和时间相关部分都有明显的体现。我们还对GUP参数进行了上界估计。

英文摘要:

With the direct detection of gravitational waves by advanced LIGO detector, a new "window" to quantum gravity phenomenology has been opened. At present, these detectors achieve the sensitivity to detect the length variation ($δL$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $β_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{β_0} l_{pl} \sim 10^{-23} m$. Hence the flavour of the generalized uncertainty principle can be realised by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. In this paper, therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. It is observed that the effects of the generalized uncertainty principle bears its signature in both the time independent and dependent part of the gravitational wave-harmonic oscillator Hamiltonian. We also make an upper bound estimate of the GUP parameter.

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