Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2005-04-26
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
5 pages, 1 figure
Scientific paper
10.1103/PhysRevB.72.193311
A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary, and optical cavities with random surface refractive index. The specific example we study is a circular (integrable) billiard with no internal impurities weakly coupled to the exterior by a large number of leads with one channel open in each lead. We construct a supersymmetric nonlinear $\sigma$-model by averaging over the random coupling strengths between bound states and channels. The resulting theory can be used to evaluate the statistical properties of any physically measurable quantity in a billiard. As an illustration, we present results for the local density of states.
Murthy Ganpathy
Rozhkov Igor
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