Simulation of electron transport through a quantum dot with soft walls

Closed billiards have long served as prototype systems in the field of clas-sical and quantum dynamics [1]. Studying the motion of a particle on a two-dimensional confined surface contributed enormously to an understanding of dynamical phenomena. Since the behaviour of the billiard system strongly depends on the geometry of the limiting boundary, regular and chaotic mo-tion can be investigated by shaping this boundary accordingly. One of the systems that has been studied extensively in the literature is the so-called “Bunimovich ” stadium [2]. In spite of its simple shape this struc-ture can be proven to be a strongly chaotic billiard [3]. The contrast to its regular counterpart (i.e. the circle) has received considerable attention in the past. In addition to a thorough investigation of numerous classical features, bil-liards were subject to a quantum mechanical study. Many interesting results on the statistics of energy levels [4], and the density distribution of the wave-function (“scars”) [5, 6] have been obtained