An Introduction to Quantum Chaos
by Mason A. Porter
Publisher: arXiv 2001
Number of pages: 57
Nonlinear dynamics ("chaos theory") and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized physics. We give a brief review of the origin and fundamentals of both quantum mechanics and nonlinear dynamics.
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by Curtis T. McMullen - Harvard University
Contents: Ergodic theory; Dynamics on hyperbolic surfaces; Orbit counting, equidistribution and arithmetic; Spectral theory; Mixing of unitary representations of SLnR; Amenability; The Laplacian; All unitary representations of PSL2(R); etc.
by Claudius Gros - arXiv
This textbook covers a wide range of concepts, notions and phenomena of a truly interdisciplinary subject. Complex system theory deals with dynamical systems containing a very large number of variables, showing a plethora of emergent features.
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This article will take up the question of what underlies the quantum formalism, whether it can be derived from simpler mathematical structures, and if so, what physical properties a system must possess in order for the formalism to hold.
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The encyclopedia covers differential equations, numerical analysis, bifurcations, topological dynamics, ergodic theory, hyperbolic dynamics, oscillators, pattern formation, chaos, statistical mechanics, control theory, and applications.