Shumovsky, A. S.Tanatar, Bilal2016-02-082016-02-0819931050-2947http://hdl.handle.net/11693/26076A model describing three boson fields with the decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. The problem of exact eigenvalues and eigenstates is reduced to the calculation of zeros of new orthogonal polynomials defined in terms of difference and differential equations. The instability of the spectrum of eigenvalues is established. The quantum-statistical properties are investigated for various initial conditions. The possibility of using the correlation Raman spectroscopy to measure the quantum-statistical properties of the vibration mode is discussed. © 1993 The American Physical Society.EnglishArticle10.1103/PhysRevA.48.4735