Foundations of Nonlinear Quantum Physics

Haipeng Peng

Marek Czachor

J. R. Croca, João L. Cordovil

P. D. Drummond, Mark S. Hillery

Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamics is assumed, but no prior knowledge of nonlinear optics is required.

Wm. C. McHarris

A number of the paradoxes encountered in the Copenhagen interpretation of quantum mechanics have apparent resolutions through parallels based in nonlinear dynamics and chaos theory. An overview of these is presented, with Bell’s theorem treated in somewhat greater detail. In these conferences (both “Quantum Theory: Reconsiderations of Foundations” and “Foundations of Probability and Physics”) Bell’s theorem has already been attacked by a number of authors in a number of ways, but here I demonstrate that the so‐called “classical” (or hidden variables) side of the derivation of Bell‐type inequalities is flawed because it is usually based on standard, non‐correlated statistics. When correlated statistics (including nonextensive thermodynamics) is considered, the classical upper limit on correlations is raised, overlapping with quantum predictions using entangled states. Thus, many of the Bell‐type experiments are rendered moot in ruling out “local reality.” Nonlinear dynamics/chaos could well provide a bridge between the determinism of Einstein and the probability of the Bohr school. Possible nonlinear underpinnings for quantum mechanics could also have implications lowering the plausibility of quantum computing.