Abstract
Ray splitting is a universal phenomenon that occurs with appreciable amplitude in all wave systems when the properties of the system change on a scale smaller than the wave length. We study the quantum implications of ray splitting theoretically and experimentally with the help of ray-splitting billiards in one and two dimensions. We show that Gutzwiller's trace formula works even in the context of ray-splitting systems provided reflection and transmission of waves at ray-splitting boundaries is properly included.
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At the time of writing only numerical evidence for the exactness of (12) was available. The computations were performed by Y. Dabaghian, R. V. Jensen, and R. Blümel. Now an analytical proof for the exactness of (12) is available (see Note Added in Proof ).
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Y. Dabaghian, R. V. Jensen, and R. Blümel, submitted to Phys. Rev. E (September 2000).
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Blümel, R., Koch, P.M. & Sirko, L. Ray-Splitting Billiards. Foundations of Physics 31, 269–281 (2001). https://doi.org/10.1023/A:1017590503566
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DOI: https://doi.org/10.1023/A:1017590503566