ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 17, 18, 55 Tchourkin, A. V., Moscow State University Quantum stochastic model of gravitational wave interferometer detector The quantum model of gravitational wave detector is described by the oscillator perturbed by a periodic potential. The evolution of the system is described by the Wigner function. Theorem. The Wigner function and the position of the perturbed quantum oscillator can be represented by the mathematical expectation of functionals of the Poisson jump process associated to the periodic potential. This stochastic representation [1-2] is used for the Monte-Carlo simulation of the Wigner function and for the Fourier analysis of the dynamics of the measuring device. We evaluate the output signal of a gravitational detector like LIGO project and analyze the influence of the noise.

[1] Chebotarev A. M. et al. Probabilistic representation of solutions of the Cauchy problem for Schrödinger, Pauli and Dirac equations, Russ. Math. Surv. , 1990, 45, N6, p. 3–24.

[2] Chebotarev A. M., Quezada-Batalla R. Stochastic approach to timedependent tunneling, Russ. J. Math. Phys. , 1996, 4, N3, p. 275–286.