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Ballistic dynamics of a convex smooth-wall billiard with finite escape rate along the boundary

Igor Rozhkov·Ganpathy Murthy
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Abstract

We focus on the problem of an impurity-free billiard with a random position-dependent boundary coupling to the environment. The response functions of such an open system can be obtained non-perturbatively from a supersymmetric generating functional. The derivation of this functional is based on averaging over the escape rates and results in a non-linear ballistic $σ$-model, characterized by system-specific parameters. Particular emphasis is placed on the {}``whispering gallery modes'' as the origin of surface diffusion modes in the limit of large dimensionless conductance.

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Igor Rozhkov, Ganpathy Murthy. 2005-09-23. Ballistic dynamics of a convex smooth-wall billiard with finite escape rate along the boundary. https://doi.org/10.1088/0305-4470%2F38%2F49%2F023

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