Wave Chaos Experiments with and without Time Reversal Symmetry: GUE and GOE Statistics

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Abstract
It has been predicted that in the semiclassical regime the level statistics of a classically chaotic system correspond to that of the Gaussian unitary ensemble (GUE) of random matrices when time reversal symmetry is broken. This Letter presents the first experimental test of this prediction. The system employed is a microwave cavity containing a thin ferrite strip adjacent to one of the walls. When a sufficiently large magnetic field is applied to the ferrite (thus breaking the time reversal symmetry) good agreement with GUE statistics is obtained. The transition from Gaussian orthogonal ensemble (GOE) (which applies in the absence of the applied field) to GUE is also investigated.