Lyapunov exponent for a gas of soft scatterers

Abstract

For a fast particle moving within a two-dimensional array of soft scatterers - centers of weak and short-range potential - the dependence of the Lyapunov exponent on the system parameters is studied. The use of the linearized equations for variations of the propagation angles and impact parameters of consequent collisions reduces the problem to that of calculation of the Lyapunov exponent of an ensemble of strongly correlated random matrices with given statistics of matrix elements. In the simplest approximation this Lyapunov exponent is proportional to the interaction strength and inversely proportional to the square root of the interaction range. The model satisfactorily describes the intensity of chaos in a system of two weakly interacting particles moving in a two-dimensional regular confining potential.