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E-grāmata: Time-Reversal Symmetry: Seven Time-Reversal Operators for Spin Containing Systems

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  • Formāts: EPUB+DRM
  • Sērija : Springer Tracts in Modern Physics 281
  • Izdošanas datums: 31-Dec-2018
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030012106
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Time-Reversal Symmetry: Seven Time-Reversal Operators for Spin Containing SystemsPalielināt
  • Formāts: EPUB+DRM
  • Sērija : Springer Tracts in Modern Physics 281
  • Izdošanas datums: 31-Dec-2018
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030012106
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This book introduces new developments in the field of Time-Reversal Symmetry presenting, for the first time, the Wigner time-reversal operator in the form of a product of two- or three time-reversal operators of lower symmetry. The action of these operators leads to the sign change of only one or two angular momentum components, not of all of them. It demonstrates that there are six modes of time-reversal symmetry breaking that do not lead to the complete disappearance of the symmetry but to its lowering. The full restoration of the time-reversal symmetry in the six cases mentioned is possible by introducing six types of metaparticles. The book also confirms the presence of six additional time-reversal operators using a group-theoretical method. The problem is only where to seek these metaparticles. 





The book discusses time-reversal symmetry in classical mechanics, classical and relativistic electrodynamics, quantum mechanics and theory of quantized fields, including dynamical reversibility and statistical irreversibility of the time, Wigners and Herrings criteria, Kramers theorem, selection rules due to time-reversal symmetry, Onsagers relations, Poincaré recurrence theorem, and CPT theorem. It particularly focuses attention on time-reversal symmetry violation. It is proposed a new method of testing the time-reversal symmetry, which is confirmed experimentally by EPR spectroscopy data. 





It shows that the traditional black-white point groups of magnetic symmetry are not applicable to magnetic systems with Kramers degeneration of energy levels and that magnetic groups of four-color symmetry are adequate for them. Further, it addresses the predicted structural distortions in Kramers three-homonuclear magnetic clusters due to time-reversal symmetry that have been identified experimentally. 





Lastly, it proposes a method of synthesis of two-nuclear coordination compounds with predictable magnetic properties, based on the application of the time-reversal transformation that was confirmed experimentally.

Recenzijas

The present book is a wonderful explanation of this subject. The book begins with basic facts but mostly is devoted to the modern theory. It is to mention that experimental confirmation are also discussed in details. (Dmitry Artamonov, zbMath 1412.81005, 2019)

1 Time Reversal in Classical and Relativistic Physics
1(32)
1.1 The Time Conception and Time Translation Invariance
1(5)
1.2 Kinematically Admissible Transformations and Time Reversal
6(3)
1.3 Time-Reversal Symmetry in Dynamical Systems
9(3)
1.4 Painleve Theorem
12(3)
1.5 Time-Reversal Symmetry in Classical Electrodynamics
15(3)
1.6 Time-Reversal Symmetry in Relativistic Electrodynamics
18(6)
1.7 Dynamical Reversibility and Statistical Irreversibility of Time
24(3)
1.8 Reversibility of Fluctuations in the Closed Systems and Onsager's Relationships
27(3)
1.9 Poincare Recurrence Theorem
30(3)
2 Time Reversal in Quantum Mechanics and Quantized Field Theory
33(94)
2.1 The Basic Concepts of Quantum Mechanics
33(5)
2.2 Antilinear and Antiunitary Operators
38(2)
2.3 Wigner Time-Reversal Operator
40(14)
2.4 Time-Reversal Operator in High Spin Systems
54(3)
2.5 Time-Reversal Operator in Symmetry Point Groups
57(1)
2.6 Wigner Criteria of Energy Levels Degeneracy Due to Time-Reversal Symmetry
58(5)
2.7 Herring Criteria for Energy Bands Degeneracy Due to Time-Reversal Symmetry
63(7)
2.8 Corepresentations of a Symmetry Group
70(3)
2.9 Time Reversal and Kramers Theorem Geometrical Interpretation
73(3)
2.10 Non-conventional Time-Reversal Symmetry
76(3)
2.11 Selection Rules Due to Time-Reversal Symmetry
79(2)
2.12 Time Reversal and Detailed Balance Principle
81(9)
2.13 Dynamic Matrix and Time-Reversal Operator
90(16)
2.14 Time-Reversal Symmetry in Quantized Field Theory
106(7)
2.15 The CPT Theorem
113(14)
3 Magnetic Symmetry Point Groups
127(16)
3.1 Magnetic Two-Color Point Symmetry Groups for Non-Kramers Systems
127(8)
3.2 Invariant Spin Arrangement and Admissible Magnetic Point Groups for Non-Kramers Systems
135(2)
3.3 Magnetic Four-Color Point Groups of Kramers Systems
137(6)
4 Kramers Trimer Clusters and Time-Reversal Symmetry
143(12)
4.1 The Structural Asymmetry of Trihomonuclear Kramers Clusters as a Consequence of Time-Reversal Symmetry
143(2)
4.2 Trinuclear Chromium(III) and Iron(III) Carboxylate Clusters
145(3)
4.3 Trinuclear Copper(II) Clusters
148(3)
4.4 Trinuclear Vanadium(IV) and Cobalt(II) Clusters
151(2)
4.5 Concluding Remarks
153(2)
5 Time-Reversal Symmetry of Quantum Systems with Quasi-energy Spectrum
155(18)
5.1 Non-stationary States of Quantum System Under Time-Reversal Operator
156(4)
5.2 Time-Reversal Invariance of Schrodinger Equation for Green Function
160(2)
5.3 Quasi-energy Spectrum and Brillouin Zone in Quasi-energy Space
162(3)
5.4 Time-Reversal Symmetry at Commuting Time-Reversal and Quasi-energy Operators
165(4)
5.5 Quasi-energy Doublets Due to Non-commuting Time-Reversal and Time-Translation Operators
169(4)
6 Transformation of Antiferromagnetic Type of Exchange Interaction into Ferromagnetic One in Dimer Clusters
173(38)
6.1 Magnetic Dimer Clusters in Coordination Compounds
174(21)
6.1.1 Copper (II) Dimers
182(3)
6.1.2 Dimer Clusters of Other 3d-Elements
185(3)
6.1.3 Dimer Clusters of 4f-Elements
188(7)
6.2 Combined Time-Reversal Transformation
195(3)
6.3 Spin Levels Inversion in Cu(II)-Cu(II) Dimers Caused by Combined Time-Reversal
198(2)
6.4 Changing the Position of Spin Levels in 3d - 3d and 4f - 4f Dimer Clusters Caused by Combined Time Reversal
200(4)
6.5 Experimental Evidence of Spin Levels Inversion in Dimer Magnetic Clusters Caused by Combined Time Reversal
204(7)
7 Is There an Analogy Between Jahn-Teller Effect and an Instability of Spin Populations in Kramers Clusters with Odd Number of Atoms?
211(18)
7.1 Kahn's Instability of an Equilateral Spin Trimer 1/2 ⊗ 1/2 ⊗ 1/2 Due to a Weak Perturbation
212(2)
7.2 Mutual Compensation of Distorted-Induced Spin Polarization in a Trimer 1/2 ⊗ 1/2 ⊗ 1/2 Due to Time-Reversal Symmetry
214(4)
7.3 Mutual Compensation of Distorted-Induced Spin Polarization in a Trimer 5/2 ⊗ 5/2 ⊗ 5/2 Due to Time-Reversal Symmetry
218(4)
7.4 Distortion-Induced Spin Population Instability of Trimer Homonuclear Kramers Clusters Caused by Time-Reversal Symmetry Violation
222(7)
8 Non-Abelian and Abelian Symmetry Groups Containing Time-Reversal Operators
229(28)
8.1 Non-Abelian Group of Eighth Order Related to Spin-1/2 Particle
230(9)
8.2 Extension of the Group Gg (1/2) to Non-Abelian Groups of Sixteenth Order Related to Kramers Systems
239(5)
8.3 Abelian Groups of Eighth and Sixteenth Orders Related to Non-Kramers Systems
244(7)
8.4 Peculiarities of the Structure of Eighth- and Sixteenth-Order Non-Abelian Groups
251(6)
9 Factorization of Wigner Time-Reversal Operator and Reduction of Time-Reversal Symmetry
257(26)
9.1 Six New Types of Time-Reversal Symmetry Related to Kramers Systems
258(2)
9.2 Violation of Kramers Theorem
260(1)
9.3 Six New Types of Time-Reversal Symmetry Related to Non-Kramers Systems
261(2)
9.4 Commutation and Anticommutation Relations for Time-Reversal Operators
263(1)
9.5 Unitarity of Spinor Operators in Two-Boson Representation of Angular Momentum and Time-Reversal Symmetry
264(7)
9.6 Boson-Antiboson Representation of Angular Momentum and Its Correlation with Factorization of Wigner Time-Reversal Operator
271(5)
9.7 About Restoration of Broken Wigner Time-Reversal Symmetry
276(7)
10 Time-Reversal Symmetry Violation
283(40)
10.1 Time-Reversal Symmetry Violation in Meson Systems
284(2)
10.2 Time-Reversal Symmetry Violation in Atomic Nuclei
286(2)
10.3 Time-Reversal Symmetry Violation in Atoms and Molecules
288(6)
10.4 Time-Reversal Symmetry Violation in Superconductors
294(10)
10.5 Time-Reversal Symmetry Violation and Enhancement of Quantum Transport
304(5)
10.6 Time-Reversal Symmetry Violation and Unidirectionality of Time
309(5)
10.7 Virtual Time-Reversal Method and Its Application to EPR Spectroscopy
314(9)
Appendix A 323(4)
Appendix B 327(2)
Appendix C 329(2)
Appendix D 331(2)
Appendix E 333(2)
References 335(16)
Index 351
Prof. Ion I. Geru got the PhD degree in 1967. In 1986, he became professor of theoretical physics, State University of Moldova. In 19961997, he was head of the Department of General Physics. In the years 20052008, 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 20042007, 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.
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