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-Re
About the Author:
Prof. Ion I. Geru got the PhD degree in 1967. In 1986, he became professor of theoretical physics, State University of Moldova. In 1996-1997, he was head of the Department of General Physics. In the years 2005-2008, he was director of the National Center for Analytical Methods and Metrology of the Academy of Sciences of Moldova. In 2008-2013, he was head of the Laboratory "Magnetic Resonance and Laser Spectroscopy", Center of Chemical Physics and Nanocomposites, Institute of Chemistry of the Academy of Sciences of Moldova. Currently, he is Chief Researcher at the same Institute.
In the years 2004-2007, Prof. Geru was a part-time visiting professor at the Florida State University. Since 2000, he is a Corresponding Member of the Academy of Sciences of Moldova. In 1998-2017, he was member of the AMPERE Committee. Since 1984, he is the Vice-President of the Moldovan Physical Society. He has more than 330 publications and 4 books, including I. Geru, D. Suter, Resonance Effects of Excitons and Electrons: Basics and Applications, Springer-Verlag, 2013.
