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# The Physics of Phase Space: Nonlinear Dynamics and Chaos, Geometric Quantization,and Wigner Function

## EditorYoung S. Kim, Woodford W. Zachary

### Paperback | August 23, 2014

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The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study of the Wigner distribution. This volume gives the first complete survey of the progress made by both mathematicians and physicists. It will serve as an excellent reference for further research.

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Title:The Physics of Phase Space: Nonlinear Dynamics and Chaos, Geometric Quantization,and Wigner FunctionFormat:PaperbackPublished:August 23, 2014Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3662136538

ISBN - 13:9783662136539

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Table of Contents

Entropy and volume as measures of orbit complexity.- A chaotic 1-D gas: Some implications.- Singular approximation of chaotic slow-fast dynamical systems.- Dimension calculations in a minimal embedding space: Low-dimensional attractors for human electroencephalograms.- Chaotic space-times.- On relaxation chaos : An example from celestial mechanics.- Computation of invariant tori and acceleration of the K.A.M. algorithm.- Fractal basin boundaries.- Quasi-periodic Schrödinger equations and strange nonchaotic attractors of pendula and Josephson junctions.- Long-time correlation in classical Hamiltonian systems with two degrees of freedom.- Dimension density - an intensive measure of chaos, in spatially extended turbulent systems.- Properties of the maximal attractor for the Landau-Lifschitz equations.- A comparison of the fractal dimensions of cloud radiance graphs for two infrared color bands.- The genealogy of periodic trajectories.- Perturbation theory and the single sextupole.- Stochastic instability in a system with two degrees of freedom.- Nonlinear stability in anisotropic magnetohydrodynamics.- On resonant Hamiltonians with n frequencies.- Singular perturbation and almost periodic solutions of nonlinear dynamic systems.- Diffusion in a turbulent phase space.- Increase in phase space accessible to particles when their attractive interactions are short-ranged.- Experimental measurements of phase space.- Simulation of arbitrary ensembles by extended dynamics: A unified scheme.- Self-organized structures in the forced Burgers' turbulence.- Critical points, critical exponents, and stability-instability transitions in Hamiltonian systems.- Maximum likelihood method for evaluating correlation dimension.- Microwave ionization of highly excited hydrogen atoms: Experiment and theory.- Highly excited hydrogen in microwaves: Measurements on the externally driven bound electron at the classical threshold for chaos.- Transition strength fluctuations and the onset of chaos.- Application of phase space to quantum statics and classical adiabatics.- Evolution and exact eigenstates of a resonance quantum system.- Quantum KAM theorem.- Atoms in strong fields: Candidates for laboratory studies of quantum chaos.- Quantum analysis of states near a separatrix.- Adiabatic invariants, resonances, and multidimensional semiclassical quantization.- Intrinsic nonadiabaticities on the Farey tree.- Chaotic ionization of highly excited hydrogen atoms.- The role of KAM-tori for the dynamics of nonlinear quantum systems.- Quantum chaos, is there any?.- The general properties of the distribution function and remarks on its weakness.- Wigner distribution function approach to the calculation of quantum effects in condensed matter physics.- Signal processing using bilinear and nonlinear time-frequency-joint-representations.- Interference in phase space.- A quantum mechanical moment problem.- Tomographic procedure for constructing phase space representations.- Wigner distribution on SU(2).- Phase space calculations of composite particle production.- The geometry of Wigner's function.- Distribution functions in elementary particle physics.- Single and multiparticle Wigner distributions in inhomogeneous Fermi systems.- Squeezed states and their Wigner functions.- Application of the Wigner function in the theory of atomic and molecular electronic structure.- Wigner phase-space approach in the molecular collision theory - search for Wigner trajectories.- Optical Eigenmodes and the Wigner distribution.- Time frequency representation of broad band signals.- Quasi-probability distributions for arbitrary operators.- Operator relations, the eigenvalue problem, and representability for quantum phase space distributions.- Quantum phase space dynamics of hard rod systems.- An introduction to Tomita representations in physics.- A semiclassical scheme for the description of the static properties of nuclei at finite temperatures.- Wigner-Kirkwood expansion and many body quantum corrections calculations.- A general approximation scheme for quantum many-body dynamics.- Coherent states and the global, uniform approximation of wave equation solutions.- Quantum wave-functions from classical phase-space manifolds: An introduction to Maslov's semiclassical theory.- Semiclassical analysis of coupled channel system with non-local interaction.- A functional density matrix for quantum electrodynamics and its classical limit.- Structural connections between the WKB and Wigner-Kirkwood semiclassical approximations.- Simple connected graph expansions of propagators.- Theorem on the Schwinger representations of Lie groups and its application to the coherent states and the vibron model.- Multiple-path expansion in quantum mechanics and quantum field theory.- Strange semiclassical phenomena for the equation ?2? t 2 ?+ A(? x 2 +? y 2 )?+B ? z 2 manifolds from the conformal group.- Reduction of degenerate lagrangians and the symplectic reduction theorem.- Formal quantization of quadratic momentum observables.- The use of ghost variables in the description of constrained systems.- Geometric quantization of particles in quark model.- Cohomology and locally-Hamiltonian dynamical systems.- The third quantization of phase space and bilocal lattice fields.- Pauli-forbidden region in the phase space of the inter-nucleus relative motion.- Quantum corrections to time-dependent mean-field method.- The remarkable phase space of the radiating electron.- The quantization of symmetric spaces and its applications.- A closed form for the intrinsic symbol of the resolvent parametrix of an elliptic operator.- Quantum mechanics in coherent algebras on phase space.- Maximal-acceleration invariant phase space.- Octonionic hadronic supersymmetry and linearly rising Regge trajectories.- Rotations and gauge transformations.- Heisenberg algebras in the theory of special functions.- Experimental and philosophical foundations of the formalism of stochastic quantum mechanics.- Explicit multidimensional solitary wave solutions to nonlinear evolution equations.- Entropy, frequency mixing, and particle creation.- The entropy of Hawking radiation.- Thermodynamical reduction of the anisotropy of time by introducing irreversibility on microscopical scale.- Steepest entropy ascent in Quantum Thermodynamics.