Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves

TL;DR

This paper explores how noncommutative geometry affects the quantum dynamics of a harmonic oscillator subjected to gravitational waves, revealing potential observable signatures in gravitational wave detection experiments.

Contribution

It introduces a quantum model of a harmonic oscillator in noncommutative space influenced by gravitational waves, showing how noncommutativity alters oscillation frequencies and responses.

Findings

Noncommutativity modifies the oscillator's frequency.

Resonance with gravitational waves causes time-dependent oscillations.

Potential noncommutative signatures could be detected as noise in GW experiments.

Abstract

We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GW) in the long wave-length and low-velocity limit. Following the prescription in \cite{ncgw1} we quantize the system. The Hamiltonian of the system is solved by using standard algebraic iterative methods. The solution shows signatures of the coordinate noncommutativity via alterations in the oscillation frequency of the harmonic oscillator system from its commutative counterpart. Moreover, it is found that the response of the harmonic oscillator to periodic GW, when their frequencies match, will oscillate with a time scale imposed by the NC parameter. We expect this noncommutative signature to show up as some noise source in the GW detection experiments since the recent phenomenological upper-bounds set on spatial noncommutative parameter implies a length-scale comparable to the length-variations due to the passage of gravitational waves, detectable in the present day GW detectors.