Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework

Abstract

In this work, we consider a resonant bar detector of gravitational wave in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis [http://dx.doi.org/10.1088/1361-6382/abac45, Class. Quantum Grav. 37 (2020) 195006]. We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis.

19 pages LATEX. Comments are welcome

References in corpus (12)

• Universality of Quantum Gravity Corrections
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• 30 years in: Quo vadis generalized uncertainty principle?
• Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
• Baryon Asymmetry from the Generalized Uncertainty Principle
• Primordial Big Bang Nucleosynthesis and Generalized Uncertainty Principle
• Generalized uncertainty principle in resonant detectors of gravitational waves
• Probing the generalized uncertainty principle through quantum noises in optomechanical systems
• Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity
• Path integral action in the generalized uncertainty principle framework
• Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework
• Uncertainty principle from the noise of gravitons

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