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

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

2005-07-07

arxiv.org/abs/cond-mat/0507186v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, no figures

Scientific paper

10.1088/0305-4470/38/49/023

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 $\sigma $-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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