00 1 Delay Equation for Charged Brown Particle

In previous work (physics/0004026) was shown, with the help of numerical calculations, that the effective Brown temperature for charged particle is lower than that for particle without charge. Here we derive this result without numerical calculations, integrating the delay equation analytically, as for zero, so for nonzero viscosity. To describe motion of charged Brown particle in so called " extended quasi-stationary approximation " [1] in [2] was used the Sommerfeld model [3] of charged rigid sphere. The equation of straightline motion of such Brown particle in dimensionless form reads [2]: ˙ y(x) = f (x) + γ · [y(x − δ) − y(x)] (1) here y(x)-is dimensionless velocity of the particle; x-is dimensionless " time " ; f (x)-is some external (stochastic) force; δ-is " time " delay; γ-is coefficient: γ · δ is proportional to the ratio of particle's electromagnetic mass to the mechanical mass: γ · δ = (2/3)(Q 2 /a)/(mc 2) (2a-is the size of Sommerfeld particle of charge Q and mass m); the viscosity Γ of the surrounding medium is zero. In [2] was shown, with the help of numerical calculations, that the effective Brown temperature for charged particle is lower than that for particle without charge. Here we derive this result without numerical calculations, integrating the delay equation (1) analytically.