Wave Propagation in Random Media and Berry Phases

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We investigated the geometrical features of 1D wave propagation, whose dynamics is described by the (2+1)-dimensional Lorentz group. There found many interesting geometrical ingredients such as spinor-like behavior of wave amplitudes, gauge transformations, Bloch-type equations, and Lorentz-group Berry phases. The geometrical descriptions were found to be very useful for intuitive understanding of 1D wave phenomena. The appearance of spinor-like behavior in classical context is very interesting in the sense that the two-valued representation was believed peculiar to the quantum regime. We also propose an optical experiment to verify these effects.