We present an exact solution for an asymmetric exclusion process on a ring with three classes of particles and vacancies. Using a matrix product Ansatz, we find explicit expressions for the weights of the configurations in the stationary state. The solution involves tensor products of quadratic algebras.

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International audienceWe study two-beam interaction in photorefractive sillenite crystals in reflection geometry and derive analytic expressions for the signal gain and its polarization direction in the presence of a strong pump beam. The crystal is cut normal to one of the crystallographic axes, and no external electric field is applied. Crystal absorption and its natural optical activity are taken into account. The coupling effects are strongly dependent on the polarization directions of the interacting beams. We determine the optimal polarization directions and optimal crystal thickness that give maximum signal gain. Experimental results are in excellent agreement with theoretical calculations

Self-generation of spatial subharmonics when two coherent, almost collinear, pump beams propagate in a nonlinear photorefractive crystal of Bi12 SiO20, is reported. The intensity of the self-generated light beam at the half-angle between the two pumps is as high as 40% of the pump beam intensity. This phenomenon is probably a spatial analog of the temporal subharmonics obtained in a cavity containing a nonlinear medium. Application of the subharmonic of half-spatial frequency to collinear Bragg diffraction of a near infrared beam is demonstrated.