| Description |
1 online resource (xxxv, 344 pages) |
| Contents |
880-01 Composite quantum systems -- Algebra of permutation matrices -- Doubly stochastic matrices in angular momentum theory -- Magic squares -- Alternating sign matrices -- The Heisenberg magnetic ring -- Counting formulas for compositions and partitions -- No single coupling scheme for n>̲ 5 -- Generalization of binary coupling schemes |
|
880-01/(S Contents note continued: 7.3. Strict Gelfand-Tsetlin Patterns for λ = (nn -- 1 ... 21) -- 7.3.1. Symmetries -- 7.4. Sign-Reversal-Shift Invariant Polynomials -- 7.5. The Requirement of Zeros -- 7.6. The Incidence Matrix Formulation -- 8. The Heisenberg Magnetic Ring -- 8.1. Introduction -- 8.2. Matrix Elements of H in the Uncoupled and Coupled Bases -- 8.3. Exact Solution of the Heisenberg Ring Magnet for n = 2,3,4 -- 8.4. The Heisenberg Ring Hamiltonian: Even n -- 8.4.1. Summary of Properties of Recoupling Matrices -- 8.4.2. Maximal Angular Momentum Eigenvalues -- 8.4.3. Shapes and Paths for Coupling Schemes I and II -- 8.4.4. Determination of the Shape Transformations -- 8.4.5. The Transformation Method for n = 4 -- 8.4.6. The General 3(2f -- 1) --- j Coefficients -- 8.4.7. The General 3(2f -- 1) --- j Coefficients Continued -- 8.5. The Heisenberg Ring Hamiltonian: Odd n -- 8.5.1. Matrix Representations of H -- 8.5.2. Matrix Elements of Rj2:j1: The 6f --- j Coefficients |
| Summary |
This monograph is a synthesis of the theory of the pairwise coupling of the angular momenta of arbitrarily many independent systems to the total angular momentum in which the universal role of doubly stochastic matrices and their quantum-mechanical probabilistic interpretation is a major theme. A uniform viewpoint is presented based on the structure of binary trees. This includes a systematic method for the evaluation of all 3n-j coefficients and their relationship to cubic graphs. A number of topical subjects that emerge naturally are also developed, such as the algebra of permutation matrices, the properties of magic squares and an associated generalized Regge form, the Zeilberger counting formula for alternating sign matrices, and the Heisenberg ring problem, viewed as a composite system in which the total angular momentum is conserved. The readership is intended to be advanced graduate students and researchers interested in learning about the relationship between unitary symmetry and combinatorics and challenging unsolved problems. The many examples serve partially as exercises, but this monograph is not a textbook. It is hoped that the topics presented promote further and more rigorous developments that lead to a deeper understanding of the angular momentum properties of complex systems viewed as composite wholes |
| Bibliography |
Includes bibliographical references (pages 327-333) and index |
| Subject |
Symmetry (Physics)
|
|
Combinatorial analysis.
|
|
SCIENCE -- Physics -- Quantum Theory.
|
|
Combinatorial analysis
|
|
Symmetry (Physics)
|
| Form |
Electronic book
|
| ISBN |
9814350729 |
|
9789814350723 |
|
1283433834 |
|
9781283433839 |
|
