The soft stadium's classical dynamics

Abstract

Billiards are physical models employed to probe experiments that measure the conductivity of quantum dots. In this context, the stadium billiard have been adopted as an standard model for realizations. We study the effect of softening in a classical mechanics context, pursuing a more realistic model. This classical approach is a first step towards the truly quantum or semiclassical case. We define the soft stadium as a monomial potential with an exponent α ∈ as a parameter, such that for α = 1 the system is integrable and the α → ∞ limit converges to the hard billiard. Then, and for computational simplicity, we set up the construction of the classical Poincare map in such a way that it only depends on the partial separability of the system which holds for all α's. We present numerical results describing the classical transition from the integrable regime towards the chaotic regime.