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Semiclassical Construction of Random Wave Functions for Confined Systems

We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions as Gaussian random fields. Thereby we generalize Berry's isotropic random wave model by incorporating confinement effects through classical paths reflected at the boundaries. Our approach allows to explicitly calculate highly non-trivial statistics, such as intensity distributions, in terms of usually few short orbits, depending on the energy window considered. We compare with numerical quantum results for the Africa billiard and derive non-isotropic random wave models for other prominent confinement geometries.