ua nt - p h / 02 02 15 0 v 2 1 5 O ct 2 00 2 Hidden symmetries in deformed microwave resonators
نویسنده
چکیده
Lauber et al [1] experimentally studied the pattern of Berry phases that emerges when a microwave cavity is cyclically deformed around a rectangular shape. Standing electromagnetic waves in the cavity can be mapped and the “wave functions” followed through the cyclic deformation to measure the Berry phase. Apart from the Berry phases, which were primarily of interest in ref [1], those authors also noticed a curious symmetry: the standing wave patterns at different deformations are related. Subsequent theoretical work [2,3] has clarified the pattern of Berry phases seen in the experiment. However, the “hidden symmetry” has not been explained so far. The purpose of this brief report is to provide an understanding of the “hidden symmetry” and thus a complete and correct interpretation of the experiment described in [1]. Consider a rectangular cavity (see Fig.1) with sides (a, b) having n degenerate modes: the scalar Laplacian −∇2 has n degenerate eigenfunctions. If the cavity is deformed, the degeneracy will in general be broken. Let us suppose that the deformation consists (as in the experiment of ref. [1]) of moving the corner around its undeformed position so that the rectangle is deformed to a quadrilateral.
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