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The spectral properties of a two-dimensional microwave billiard showingthreefold symmetry have been studied with a new experimental technique. Thismethod is based on the behavior of the eigenmodes under variation of a phaseshift between two input channels, which strongly depends on the symmetries ofthe eigenfunctions. Thereby a complete set of 108 Kramers doublets has beenidentified by a simple and purely experimental method. This set clearly showsGaussian unitary ensemble statistics, although the system is time-reversalinvariant.Comment: RevTex 4, 5 figure

Phase Shift Experiments Identifying Kramers Doublets in a Chaotic Superconducting Microwave Billiard of Threefold Symmetry