Numerical solutions of the Fresnel diffraction integral with various apodizing filter functions are used to indicate that a so-called nondiffracting beam can be produced that maintains a constant spot size and constant axial intensity over a considerable range, approximately 30 m in our example.

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We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic method we obtain a general form for the one, two and three-point connected Green function for this class of ensembles when matrix elements are identically distributed, and then discuss the derivation of higher order functions by the same approach. Using the RG approach we re-derive the one and two-point Green functions and show they are unchanged by choosing certain ensembles with non-identically distributed elements. Throughout, we compare the Green functions we obtain to those from the class of ensembles with unitary invariant distributions and discuss universality in both ensemble classes. PACS number(s): 05.40.+j

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We show how a behavioral form of capital theory can be derived using canonical quantization. In particular, we introduce quantum cognition into capital theory by applying Dirac’s canonical quantization approach to Weitzman’s Hamiltonian formulation of capital theory, the justification for the use of quantum cognition being the incompatibility of questions encountered in the investment decision-making process. We illustrate the utility of this approach by deriving the capital-investment commutator for a canonical dynamic investment problem.