Geodesic
The quantum gravitational wave detector
Matematičeskoe modelirovanie, Tome 11 (1999) no. 8, pp. 32-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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Mathematical model of gravitational wave detector is described by the Hamiltonian of the quantum oscillator perturbed by a periodic potential, and it's evolution is described by the Wigner function $W(p,q, t)$. We prove that there exists a stochastic representation of $W(p,q, t)$ as the mathematical expectation of a functional of the Poisson random jump process in the phase space. The stochastic representation of the Wigner function is used for the Monte- Carlo simulation of the quantum evolution of the measuring device and the output signal of a realistic gravitational wave detector like LIGO gravitometer. The main conclusion is that the quantum of interaction between the gravitational wave and the detector reduces the confidence of measurements. 
@article{MM_1999_11_8_a2,
     author = {A. M. Chebotarev and A. V. Churkin},
     title = {The quantum gravitational wave detector},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {32--44},
     year = {1999},
     volume = {11},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1999_11_8_a2/}
}
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A. M. Chebotarev; A. V. Churkin. The quantum gravitational wave detector. Matematičeskoe modelirovanie, Tome 11 (1999) no. 8, pp. 32-44. http://geodesic.mathdoc.fr/item/MM_1999_11_8_a2/