Spectral-correlation characteristics of the Brownian motion of inertial particles

An analytical-numerical approach is used for studying the correlation function and spectrum of one-dimensional Brownian motion of real (inertial) particles in the symmetric monomodal potential profile. The method of analysis is based on cumulantless expansions of the moment functions. The obtained results can also be interpreted as the spectral-correlation characteristics of a nonlinear oscillator affected by intense wideband noise. The dependence of the spectral-correlation characteristics of the Brownian motion on the noise intensity, nonlinear rigidity, and viscosity of the medium is obtained. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 1, pp. 82–89, January 2008.