Chaotic Scattering Research Articles

Hierarchic Analysis of Chaotic Scattering in Reactive Collisions

Abstract The method of classical trajectories is applied for a double Morse potential modeling indirect reactive collisions of three collinear atoms. The system shows chaotic scattering, which is studied in details through a hierarchic analysis of the singularities of the time delay function. Tools of the thermodynamic formalism are used to extract global quantities characterizing the scattering process.

Inequivalence of weak localization and coherent backscattering.

We define a current-conserving approximation for the local conductivity tensor of a disordered system which includes the effects of weak localization. Using this approximation we show that the weak localization effect in conductance is not obtained simply from the diagram corresponding to the coherent backscattering peak observed in optical experiments. Other diagrams contribute to the effect at the same order and decrease its value. These diagrams appear to have no semiclassical analogues, a fact which may have implications for the semiclassical theory of chaotic systems. The effects of discrete symmetries on weak localization in disordered conductors are evaluated and compared to results from chaotic scatterers.

Convergence of the semiclassical approximation for chaotic scattering.

The series that arises from the semiclassical approximation for scattering amplitudes is studied when the scattering is chaotic. It is argued that the terms of the series decay with an exponent equal to $\frac{1}{2d}$, where $d$ is the capacity dimension of one of the classical scattering functions. The result applies to one-dimensional inelastic and two-dimensional elastic scattering, and it is verified numerically for a one-dimensional model. An estimate of how rapidly the semiclassical series converges is given.

Elliptic Law

Elliptic Law