Extensive and well-written non-technical article on primes and quantum chaos: "A Prime Case of Chaos" by Barry Cipra
N. Patson, "Review of quantum chaology and structural complexity approaches to characterising global behaviour with application to primes" (A more mathematically advanced introduction to these issues.)
S. Nonnenmacher, "Some open questions in "wave chaos"" (preprint 05/2008)
[abstract:] "The subject area referred to as "wave chaos", "quantum chaos" or "quantum chaology" has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability etc. After giving a rough account on "what is quantum chaos?", I intend to list some pending questions, some of them having been raised a long time ago, some others more recent."
T. Kriecherbauer, J. Marklof and A. Soshnikov, "Random matrices and quantum chaos" (brief introductory article, including a description of how this relates to the Riemann Hypothesis)
H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge Univ. Press, 1999)
[publisher's description:] "This book introduces the quantum mechanics of classically chaotic systems, or quantum chaos for short. The author's philosophy has been to keep the discussion simple and to illustrate theory, wherever possible, with experimental or numerical examples. The microwave billiard experiments, initiated by the author and his group, play a major role in this respect. Topics covered include the various types of billiard experiment, random matrix theory, systems with periodic time dependences, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics, where an external parameter takes the role of time, scattering theory distributions and fluctuation, properties of scattering matrix elements, semiclassical quantum mechanics, periodic orbit theory, and the Gutzwiller trace formula. This book will be of great value to anyone working in quantum chaos."
quantum chaos computing group
quantum chaos and the Riemann zeta function
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