Time-Reversal Symmetry

1. Time Reversal in Classical and Relativistic Physics 1.1 The Time Conception and Time Translation Invariance 1.2 Cinematically Admissible Transformations and Time Reversal 1.3 Time-Reversal Symmetry in Dynamical Systems 1.4 Painlevé's Theorem 1.5 Time-Reversal Symmetry in Classical Electrodynamics 1.6 Time-Reversal Symmetry in Relativistic Electrodynamics 1.7 Dynamical Reversibility and Statistical Irreversibility of the Time 1.8 Reversibility of Fluctuations in Closed Systems as Consequence of Onsager Relationships 1.9 Poincaré Recurrence Theorem 2. Time Reversal in Quantum Mechanics and Theory of Quantized Fields 2.1  The Basic Concepts of Quantum Mechanics 2.2   Antilinear and Antiunitary Operators 2.3   Wigner's Time-Reversal Operator  2.4   Time-Reversal Operator for High Spin Systems 2.5   Time-Reversal Operator for Symmetry Point Groups 2.6   Wigner's Criterion of Energy Levels Degeneracy due to Time-Reversal Symmetry 2.7   Herring's Criterion of Energy Bands Degeneracy due to Time-Reversal Symmetry 2.8   Co-representations of Symmetry Groups 2.9 Geometrical Interpretation of the Time Reversal and Kramers Theorem 2.10 Nonconventional Time-Reversal Symmetry 2.11 Selection Rules due to Time-Reversal Symmetry 2.12 Time-Reversal and Detailed Balance Principle 2.13 Dynamic Matrix and Time-Reversal Operator 2.14 Time-Reversal Symmetry in Theory of Quantized Fields 2.15 The CPT Theorem 3. Magnetic Symmetry Point Groups 3.1 Magnetic Two-Color Point Symmetry Groups of non-Kramers Systems 3.2 Invariant Spin Arrangement and Admissible Magnetic Point Groups of non-Kramers Systems 3.3 Magnetic Four-Color Point Symmetry Groups of Kramers Systems 4. Anomalous Behavior of Trihomonuclear Kramers Clusters Due to Their Four-Color     Symmetry 4.1 Structural Asymmetry of Trihomonuclear Kramers Clusters as Consequence of Time-Reversal       Symmetry 4.2 Trinuclear Chromium(III) and Iron(III) Carboxylate Clusters 4.3 Trinuclear Copper(II) Clusters 4.4 Trinuclear Vanadium(IV) and Cobalt(II) Clusters  4.5 Concluding Remarks     5. Time Reversal Symmetry of Quantum Systems with Quasi-Energy Spectrum 5.1 Non-Stationary States of Quantum Systems under Time-Reversal Operator 5.2 Time-Reversal Invariance of Schrödinger Equation for the Green Function 5.3 Quasi-Energy Spectrum and Brillouin Zone in Quasi-Energy Space 5.4 Time-Reversal Symmetry in the Case of Commuting Time Translation and Time-Reversal Operators 5.5 Quasi-Energy Doublets due to non-Commuting Time Translation and Time-Reversal Operators 6. Transformation of Antiferromagnetic Type of Exchange Interactions into Ferromagnetic     One in Dimer Clusters 6.1 Magnetic Dimer Clusters in Coordination Compounds       6.1.1 Copper(II) Dimers       6.1.2 Dimer clusters of Other 3d Elements       6.1.3 Dimer Clusters of 4f-Elements 6.2 Combined Time-Reversal Transformation  6.3 Spin Levels Inversion in Cu (II) - Cu (II) Dimers due to Combined Time-Reversal Symmetry 6.43 Spin Levels Inversion in 3d-3d and 4f-4f Dimer Clusters due to Combined Time-Reversal       Symmetry 6.5 Experimental Evidence of Spin Levels Inversion in Dimer Magnetic Clusters due to Combined          Time-Reversal Symmetry    7. Is there an Analogy between Jahn-Teller Effect and the Instability of Spin Population in Kramers Clusters with Odd Number of Atoms?  7.1 Kahn's Instability of an Equilateral Spin Trimer 1/2 x1/2 x1/2 with Respect to a Weak       Structural Perturbation    7.2 Mutual Compensation of Distorted-Induced Spin Polarization in a Trimer 1/2 x1/2 x1/2        due to Time-Reversal Symmetry                                                                                                 7.3   Mutual Compensation of Distorted-Induced Spin Polarization in a Trimer 5/2 x5/2 x5/2        due to Time-Reversal Symmetry  7.4     Distorted-Induced Spin Populations Instability of Trimer Homonuclear Clusters with        Kramers Degeneracy of Energy Levels Due to Time-Reversal Symmetry Violation 8. Non-Abelian Symmetry Groups Containing the Time-Reversal Operator       8.1 Non-Abelian Group G8(1/2) of 8th Order Related to a Particle with the Spin 1/2       8.2 Extention of the Group G8(1/2) to non-Abelian Groups of 16th Order Related to Kramers Systems          8.3 Non-Abelian Groups of 8th Order Related to non-Kramers Systems Systems       8.4 Non-Abelian Groups of 16th Order Related to non-Kramers Systems Systems       8.5 Pecularities of the Structure of non-Abelian Groups of of 8th and 16th Orders  9. Factorization of the Wigner's Time-Reversal Operator and Reduction of Time-Reversal Symmetry   9.1  Six New Types of Time-Reversal Symmetry Related to Kramers Systems 9.2 Violation of the Kramers Theorem 9.3 Six New Types of Time-Reversal Symmetry Related to non-Kramers Systems 9.4 Commutation and Anticommutation Relations for Time-Reversal Operators 9.5 Unitarity of Spinor Operators in Two-Boson Representation of Angular Momentum and        Time-Reversal Symmetry 9.6 Boson-Antiboson Representation of Angular Momentum and Its Correlation with       Factorization of the Wigner's Time-Reversal Operator 9.7 Restoration of the Wigner Time-Reversal Symmetry: Six Types of Metaparticles and Metaworlds 10. Time-Reversal Symmetry Violation 10.1 Time-Reversal Symmetry Violation in Meson Systems 10.2 Time-Reversal Symmetry Violation in Light and Heavy Nuclei 10.3 Time-Reversal Symmetry Violation in Atoms and Molecules 10.4 Time-Reversal Symmetry Violation in Superconductors 10.5 Time-Reversal Symmetry Violation and Transformation of Zeeman Levels in Energy Bands 10.6 Time-Reversal Symmetry Violation in Hyperfine Interaction 10.7 Time-Reversal Symmetry Violation in Optical Nonlinear Stimulated Radiation and Absorption 10.8 Time-Reversal Symmetry Violation and the Enhancement of Quantum Transport 10.9 Time-Reversal Symmetry Violation and the Unidirectionality of the Time 11. Conclusions Appendices Glossary References Index ... Mehr