Scar functions in the Bunimovich Stadium billiard

Abstract

In the context of the semiclassical theory of short periodic orbits, scar functions play a crucial role. These wavefunctions live in the neighbourhood of the trajectories, resembling the hyperbolic structure of the phase space in their immediate vicinity. This property makes them extremely suitable for investigating chaotic eigenfunctions. On the other hand, for all practical purposes reductions to Poincare sections become essential. Here we give a detailed explanation of resonances and scar functions construction in the Bunimovich stadium billiard and the corresponding reduction to the boundary. Moreover, we develop a method that takes into account the departure of the unstable and stable manifolds from the linear regime. This new feature extends the validity of the expressions.

21 pages, 10 figures

References in corpus (1)

• Localization properties of groups of eigenstates in chaotic systems

Cited by in corpus (10)

• Survival Probability for the Stadium Billiard
• Quantum chaotic resonances from short periodic orbits
• Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport
• The short periodic orbit method for excited chaotic eigenfunctions
• Quantifying intermittency in the open drivebelt billiard
• Semi-classical Scar functions in phase space
• Universal wave functions structure in mixed systems
• The classical skeleton of open quantum chaotic maps
• Semiclassical matrix elements for a chaotic propagator in the Scar functions basis
• The simplest 2D quantum walk detects chaoticity