Signatures of Noncommutativity in Bar Detectors of Gravitational Waves

Authors

  • S. Gangopadhyay Department of Theoretical Sciences, S.N. Bose National Centre for Basic Sciences
  • S. Bhattacharyya Department of Physics, West Bengal State University
  • A. Saha Department of Physics, West Bengal State University

DOI:

https://doi.org/10.15407/ujpe64.11.1029

Keywords:

gravitational waves, noncommutative (NC), NC quantum field theory, NC quantum mechanics

Abstract

The comparison between the noncommutative length scale √θ and the length variation δL = hL, detected in the GW detectors, indicates that there is a strong possibility to detect the noncommutative structure of space in the GW detector setup. Therefore, we explore how the response of a bar detector gets affected due to the presence of a noncommutative structure of space keeping terms up to the second order in a gravitational wave perturbation (h) in the Hamiltonian. Interestingly, the second-order term in h shows a transition between the ground state and one of the perturbed second excited states that was absent, when the calculation was restricted only to the first order in h.

References

S. Doplicher, K. Fredenhagen, J.E. Roberts. Spacetime quantization induced by classical gravity. Phys. Lett. B 331, 39 (1994). https://doi.org/10.1016/0370-2693(94)90940-7

D. V. Ahluwalia. Quantum measurement, gravitation, and locality. Phys. Lett. B 339, 301 (1994). https://doi.org/10.1016/0370-2693(94)90622-X

M.R. Douglas, N.A. Nekrasov. Noncommutative field theory. Rev. Mod. Phys. 73, 977 (2002). https://doi.org/10.1103/RevModPhys.73.977

N. Seiberg, E. Witten. String theory and noncommutative geometry. JHEP 09, 032 (1999). https://doi.org/10.1088/1126-6708/1999/09/032

V.P. Nair, A.P. Polychronakos. Quantum mechanics on the noncommutative plane and sphere. Phys. Lett. B 505, 267 (2001). https://doi.org/10.1016/S0370-2693(01)00339-2

L. Mezincescu. Star operation in quantum mechanics. [hep-th/0007046].

B. Chakraborty, S. Gangopadhyay, A. Saha. Seiberg-Witten map and Galilean symmetry violation in a noncommutative planar system. Phys. Rev. D 70, 107707 (2004). https://doi.org/10.1103/PhysRevD.70.107707

F.G. Scholtz, B. Chakraborty, S. Gangopadhyay, A.G. Hazra. Dual families of noncommutative quantum systems. Phys. Rev. D 71, 085005 (2005). https://doi.org/10.1103/PhysRevD.71.085005

F.G. Scholtz, B. Chakraborty, S. Gangopadhyay, J. Govaerts. Interactions and non-commutativity in quantum Hall systems. J. Phys. A 38, 9849 (2005). https://doi.org/10.1088/0305-4470/38/45/008

S. Gangopadhyay, F.G. Scholtz. Path-integral action of a particle in the noncommutative plane. Phys. Rev. Lett. 102, 241602 (2009). https://doi.org/10.1103/PhysRevLett.102.241602

S. Bhattacharyya, S. Gangopadhyay, A. Saha. Quantum mechanics of a particle in an accelerated frame and the equivalence principle. Euro. Phys. Lett. 120, 30005 (2017). https://doi.org/10.1209/0295-5075/120/30005

R.J. Szabo. Symmetry, gravity and noncommutativity. Class. Quant. Grav. 23, R199 (2006). https://doi.org/10.1088/0264-9381/23/22/R01

P. Mukherjee, A. Saha. Note on the noncommutative correction to gravity. Phys. Rev. D 74, 027702 (2006). https://doi.org/10.1103/PhysRevD.74.027702

R. Banerjee, S. Gangopadhyay, S.K. Modak. Voros product, noncommutative Schwarzschild black hole and corrected area law. Phys. Lett. B 686, 181 (2010). https://doi.org/10.1016/j.physletb.2010.02.034

I. Mocioiu, M. Pospelov, R. Roiban. Low-energy limits on the antisymmetric tensor field background on the brane and on the non-commutative scale. Phys. Lett. B 489, 390 (2000). https://doi.org/10.1016/S0370-2693(00)00928-X

S.M. Carroll, J.A. Harvey, V.A. Kosteleck?y, C.D. Lane, T. Okamoto. Noncommutative field theory and Lorentz violation. Phys. Rev. Lett. 87, 141601 (2001). https://doi.org/10.1103/PhysRevLett.87.141601

O. Bertolami, J.G. Rosa, C.M.L. de Aragao, P. Castorina, D. Zappala. Noncommutative gravitational quantum well. Phys. Rev. D 72, 025010 (2005). https://doi.org/10.1103/PhysRevD.72.025010

A. Saha. Time-space non-commutativity in gravitational quantum well scenario. Eur. Phys. J. C 51, 199 (2007). https://doi.org/10.1140/epjc/s10052-007-0274-y

P.M. Ho, H.C. Kao. Noncommutative quantum mechanics from noncommutative quantum field theory. Phys. Rev. Lett. 88, 151602 (2002). https://doi.org/10.1103/PhysRevLett.88.151602

T.C. Adorno, D.M. Gitman, A.E. Shabad, D.V. Vassilavich. Noncommutative magnetic moment of charged particles. Phys. Rev. D 84, 085031 (2011). https://doi.org/10.1103/PhysRevD.84.085031

A. Stern. Noncommutative point sources. Phys. Rev. Lett. 100, 061601 (2008). https://doi.org/10.1103/PhysRevLett.100.061601

B.P. Abbott et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

B.P. Abbott et al. GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence. Phys. Rev. Lett. 116, 241103 (2016).

https://advancedligo.mit.edu/.

I. Ciufolini, R.A. Matzner. General Relativity and John Archibald Wheeler (Springer, 2010) [ISBN: 9789048137350] (online). https://doi.org/10.1007/978-90-481-3735-0

P. Astone et al. Long-term operation of the Rome Explorer cryogenic gravitational wave detector. Phys. Rev. D 47, 362 (1993). https://doi.org/10.1103/PhysRevD.47.362

E. Mauceli et al. The Allegro gravitational wave detector: Data acquisition and analysis. Phys. Rev. D 54, 1264 (1996). https://doi.org/10.1103/PhysRevD.54.1264

D.G. Blair et al. High sensitivity gravitational wave antenna with parametric transducer readout. Phys. Rev. Lett. 74, 1908 (1995). https://doi.org/10.1103/PhysRevLett.74.1908

P. Astone et al. The gravitational wave detector NAUTILUS operating at T = 0.1 K. Astropart. Phys. 7, 231 (1997). https://doi.org/10.1016/S0927-6505(97)00023-6

M. Cerdonio et al. The ultracryogenic gravitational-wave detector AURIGA. Class. Quant. Grav. 14, 1491 (1997). https://doi.org/10.1088/0264-9381/14/6/016

A. Abrampvici et al. LIGO: The laser interferometer gravitational-wave observatory. Science 256, 325 (1992). https://doi.org/10.1126/science.256.5055.325

B. Caron et al. The Virgo interferometer. Class. Quant. Grav. 14, 1461 (1997).

H. L?uck et al. The GEO600 project. Class. Quant. Grav. 14, 1471 (1997). https://doi.org/10.1088/0264-9381/14/6/012

M. Ando et al. Stable operation of a 300-m laser interferometer with sufficient sensitivity to detect gravitational-wave events within our galaxy. Phys. Rev. Lett. 86, 3950 (2001).

M. Maggiore. Gravitational Wave. Vol I. Theory and Experiments (Oxford Univ. Press, 2008) [ISBN-13:9780198570745]. https://doi.org/10.1093/acprof:oso/9780198570745.001.0001

A. Saha, S. Gangopadhyay. Noncommutative quantum mechanics of a test particle under linearized gravitational waves. Phys. Lett. B 681, 96 (2009). https://doi.org/10.1016/j.physletb.2009.09.063

A. Saha, S. Gangopadhyay, S. Saha. Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves. Phys. Rev. D 83, 025004 (2011). https://doi.org/10.1103/PhysRevD.83.025004

S. Gangopadhyay, A. Saha, S. Saha. Trace of phase-space noncommutativity in response of a free particle to linearized gravitational waves. Mod. Phys. Lett. A 28, 1350161 (2013). https://doi.org/10.1142/S0217732313501617

S. Gangopadhyay, A. Saha, S. Saha. Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves. Gen. Rel. Grav. 47, 28 (2015). https://doi.org/10.1007/s10714-015-1867-7

A. Saha, S. Gangopadhyay. Resonant detectors of gravitational wave as a possible probe of the noncommutative structure of space. Class. Quant. Grav. 33, 205006 (2016). https://doi.org/10.1088/0264-9381/33/20/205006

A. Saha, S. Gangopadhyay, S. Saha. Quantum mechanical systems interacting with different polarizations of gravitational waves in noncommutative phase space. Phys. Rev. D 97, 044015 (2018). https://doi.org/10.1103/PhysRevD.97.044015

S. Bhattacharyya, S. Gangopadhyay, A. Saha. Footprint of spatial noncommutativity in resonant detectors of gravitational wave. Class. Quant. Grav. 36, 055006 (2019). https://doi.org/10.1088/1361-6382/ab008a

K. Gottfried, T.M. Yan. Quantum Mechanics: Fundamentals (Springer, 2005) [ISBN: 978-0-387-21623-2].

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Published

2019-11-25

How to Cite

Gangopadhyay, S., Bhattacharyya, S., & Saha, A. (2019). Signatures of Noncommutativity in Bar Detectors of Gravitational Waves. Ukrainian Journal of Physics, 64(11), 1029. https://doi.org/10.15407/ujpe64.11.1029

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Section

Fields and elementary particles