Path Integral Action for a Resonant Detector of Gravitational Waves in the Generalized Uncertainty Principle Framework

Sen, Soham; Bhattacharyya, Sukanta; Gangopadhyay, Sunandan

doi:10.3390/universe8090450

Cited by 6 publications

(8 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The importance of looking for the Berry phase in the quantum harmonic oscillator-gravitational wave system is evident. Finding a non-trivial detectable Berry phase can prove to be important in the detection of gravitational waves in resonant bar detector systems [5,[7][8][9]. The most important insight that we obtain via this analysis is that the Lewis phase, which can be considered to be the total phase of the system, has no contribution from the gravitational wave in its dynamic part after applying the adiabatic approximation.…”

Section: Introductionmentioning

confidence: 84%

“…In this section, we shall calculate the geometric phase from the boundary term in equation (9). We start by rewriting the term (equation ( 9)) as…”

Section: Geometric Phase From the Boundary Termmentioning

confidence: 99%

“…Thereafter, there has been a monumental effort to increase the sensitivity of these detectors. The possibility of increasing their sensitivity to higher levels has also led to the idea of probing quantum gravity effects in these setups [3][4][5][6][7][8][9][10]. The basic model in the resonant bar detector setup can be interpreted as a quantum mechanical forced gravitational wave harmonic oscillator system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

Sen,

Dutta,

Gangopadhyay

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In this work, we compute the Lewis and Berry phases for a gravitational wave interacting with a two dimensional quantum harmonic oscillator in the transverse-traceless gauge. We have considered a gravitational wave consisting of the plus polarization term only. Considering the cross polarization term to be absent makes the Hamiltonian separable in terms of the first and the second spatial coordinates. We then compute the Lewis phase by assuming a suitable form of the Lewis invariant considering only quadratic order contributions from both position and momentum variables. Next, we obtain two Lewis invariants corresponding to each separable part of the full Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase. Then making an adiabatic approximation enables us to isolate the Berry phase for the full system. After this we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency. Finally, we consider a gravitational wave with cross polarization only interacting with an isotropic two dimensional harmonic oscillator. For this we obtain the Lewis phase and the total Berry phase of the system, which is found to be dependent upon the cross polarization part of the gravitational wave.

show abstract

Section: Introductionmentioning

confidence: 84%

“…In this section, we shall calculate the geometric phase from the boundary term in equation (9). We start by rewriting the term (equation ( 9)) as…”

Section: Geometric Phase From the Boundary Termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

Sen,

Dutta,

Gangopadhyay

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…( 34) by substituting m 0 with the Planck mass m p . Equation (34) resembles the uncertainty product as given in [8] for one dimension. This can also be interpreted as a derivation of the well-known generalized uncertainty principle form.…”

Section: Vacuum Statementioning

confidence: 99%

Uncertainty principle from the noise of gravitons

Sen,

Gangopadhyay

2024

Eur. Phys. J. C

Self Cite

View full text Add to dashboard Cite

The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in Phys. Rev. D 107, 066024 (2023). There the authors have calculated the quantum gravity modified Newton’s law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum.

show abstract

“…Therefore, it is possible to simply write down the resonant detectors of gravitational waves as a gravitational wave-harmonic oscillator interaction model. The possibility of detecting these Planck length relics in the gravitational wave detection technique motivates us to a rigorous investigation of the quantum mechanical responses of the gravitational wave detectors in noncommutativity and GUP framework [40][41][42][43][44][45][46][47]. Recently, in [32], we have seen that the measurements of resonant frequencies of a mechanical oscillator bear the signature of GUP.…”

Section: Introductionmentioning

confidence: 99%

Generalized Uncertainty Principle in Bar Detectors of Gravitational Waves

Bhattacharyya

Gangopadhyay

Saha

2022

Springer Proceedings in Physics

View full text Add to dashboard Cite

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 [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.

show abstract

Path Integral Action for a Resonant Detector of Gravitational Waves in the Generalized Uncertainty Principle Framework

Cited by 6 publications

References 52 publications

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

Uncertainty principle from the noise of gravitons

Generalized Uncertainty Principle in Bar Detectors of Gravitational Waves

Contact Info

Product

Resources

About