Abstract
In the first part of this talk we focus on computational tools of quantum chaos—a classical numerical task of high accuracy computations of eigenvalues and eigenfunctions of Schrödinger and Laplace operators in multidimensional domains. These computations are only tools of the analysis of “chaos” in quantum systems which can be primitively described as the deviation from regular and/or simple statistical behavior. We focus on several practical methods of spectral analysis, needed for high accuracy of eigenvalues and eigenstates calculations. In the second part of the talk we look at a completely different number-theoretic task—a construction of very regular, but still random, finite structures for new generation of computer chips and verification of chip designs.
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Chudnovsky, D.V., Chudnovsky, G.V. (1999). Chaos and Deviation from Uniform Distribution: Eigenfunction Computation; Applied Modular Arithmetic. In: Hejhal, D.A., Friedman, J., Gutzwiller, M.C., Odlyzko, A.M. (eds) Emerging Applications of Number Theory. The IMA Volumes in Mathematics and its Applications, vol 109. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1544-8_4
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