2014/11/07 by Robert G. Niemeyer, Niemeyer, Robert G.
Computer Science · Mathematics · Physics and Astronomy · #37C27 #37D40 #37D50 #37E35 #37F40 #58J99 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 28A80 #Quantum chaos and dynamical systems #Secondary: 28A75
paper · pdf · doi:10.48550/arxiv.1411.1825
openalex publication_date 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A formal definition of a (mathematical) polygonal Andreev billiard and a construction of an equivalence relation that captures the dynamics described in physical toy model of Andreev reflection are given. The continuous flow and discrete flow on the respective phase spaces. It is then shown that the continuous flow preserves the absolute value of the volume element dx\wedge dy\wedge dθ and the billiard (collision) map preserves the measure cos ϕdr dϕ, respectively. One can then characterize the dynamics of a rational polygonal Andreev billiard table. Finally, a discussions of the effect of a fractal perturbation of the toy model of a rectangular nanowire lying upon a superconducting medium is given.