Experimental Studies of Chaos and Localization in Quantum Wave Functions

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Abstract
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with expressions derived fro m a 0-D nonlinear $\sigma $-model of supersymmetry, which coincides with Random Matrix Theory. In contrast, disordered wavefunctions show deviations from this universal behavior due to Anderson localization. A systematic behavior of the distribution function is studied as a function of the localization length, and can be understood in the framework of a 1-D version of the nonlinear $\sigma $-model.Comment: Phys. Rev. Lett. (to appear), used style epsf.st
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