Lecture Notes in Physics

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 Schrodinger 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.