Applications of unitary symmetry and combinatorics /:
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 un...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2011.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xxxv, 344 pages) |
| Bibliographie: | Includes bibliographical references (pages 327-333) and index. |
| ISBN: | 9814350729 9789814350723 1283433834 9781283433839 |
Internformat
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| 245 | 1 | 0 | |a Applications of unitary symmetry and combinatorics / |c James D. Louck. |
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| 504 | |a Includes bibliographical references (pages 327-333) and index. | ||
| 505 | 0 | |6 880-01 |a 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. | |
| 520 | |a 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. | ||
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| 650 | 6 | |a Analyse combinatoire. | |
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| 880 | 0 | |6 505-00/(S |a Machine generated contents note: 1.Composite Quantum Systems -- 1.1. Introduction -- 1.2. Angular Momentum State Vectors of a Composite System -- 1.2.1. Group Actions in a Composite System -- 1.3. Standard Form of the Kronecker Direct Sum -- 1.3.1. Reduction of Kronecker Products -- 1.4. Recoupling Matrices -- 1.5. Preliminary Results on Doubly Stochastic Matrices and Permutation Matrices -- 1.6. Relationship between Doubly Stochastic Matrices and Density Matrices in Angular Momentum Theory -- 2. Algebra of Permutation Matrices -- 2.1. Introduction -- 2.2. Basis Sets of Permutation Matrices -- 2.2.1. Summary -- 3. Coordinates of A in Basis PΣn(e, p) -- 3.1. Notations -- 3.2. The A-Expansion Rule in the Basis PΣn(e, p) -- 3.3. Dual Matrices in the Basis Set Σn(e, p) -- 3.3.1. Dual Matrices for Σ3(e, p) -- 3.3.2. Dual Matrices for Σ4(e, p) -- 3.4. The General Dual Matrices in the Basis Σn(e, p) -- 3.4.1. Relation between the A-Expansion and Dual Matrices. | |
| 880 | 0 | |6 505-01/(S |a 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. | |
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Datensatz im Suchindex
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| _version_ | 1816881783649599488 |
| adam_text | |
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| author | Louck, James D. |
| author_facet | Louck, James D. |
| author_role | |
| author_sort | Louck, James D. |
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| callnumber-subject | QC - Physics |
| collection | ZDB-4-EBA |
| contents | 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. |
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| dewey-ones | 530 - Physics |
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| discipline | Physik |
| format | Electronic eBook |
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Louck.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">Hackensack, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2011.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xxxv, 344 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 327-333) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="6">880-01</subfield><subfield code="a">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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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. 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| id | ZDB-4-EBA-ocn773799229 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:12Z |
| institution | BVB |
| isbn | 9814350729 9789814350723 1283433834 9781283433839 |
| language | English |
| oclc_num | 773799229 |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Louck, James D. Applications of unitary symmetry and combinatorics / James D. Louck. Singapore ; Hackensack, NJ : World Scientific, ©2011. 1 online resource (xxxv, 344 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 327-333) and index. 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. 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. Symmetry (Physics) http://id.loc.gov/authorities/subjects/sh85131443 Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Combinatorial analysis. Symmetry (Physics) Symétrie (Physique) Analyse combinatoire. SCIENCE Physics Quantum Theory. bisacsh Combinatorial analysis fast Symmetry (Physics) fast has work: Applications of unitary symmetry and combinatorics (Text) https://id.oclc.org/worldcat/entity/E39PCGJTYxdjmYtF6CCTMD96jC https://id.oclc.org/worldcat/ontology/hasWork Print version: 9789814350716 9814350710 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426336 Volltext 505-00/(S Machine generated contents note: 1.Composite Quantum Systems -- 1.1. Introduction -- 1.2. Angular Momentum State Vectors of a Composite System -- 1.2.1. Group Actions in a Composite System -- 1.3. Standard Form of the Kronecker Direct Sum -- 1.3.1. Reduction of Kronecker Products -- 1.4. Recoupling Matrices -- 1.5. Preliminary Results on Doubly Stochastic Matrices and Permutation Matrices -- 1.6. Relationship between Doubly Stochastic Matrices and Density Matrices in Angular Momentum Theory -- 2. Algebra of Permutation Matrices -- 2.1. Introduction -- 2.2. Basis Sets of Permutation Matrices -- 2.2.1. Summary -- 3. Coordinates of A in Basis PΣn(e, p) -- 3.1. Notations -- 3.2. The A-Expansion Rule in the Basis PΣn(e, p) -- 3.3. Dual Matrices in the Basis Set Σn(e, p) -- 3.3.1. Dual Matrices for Σ3(e, p) -- 3.3.2. Dual Matrices for Σ4(e, p) -- 3.4. The General Dual Matrices in the Basis Σn(e, p) -- 3.4.1. Relation between the A-Expansion and Dual Matrices. 505-01/(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. |
| spellingShingle | Louck, James D. Applications of unitary symmetry and combinatorics / 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. Symmetry (Physics) http://id.loc.gov/authorities/subjects/sh85131443 Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Combinatorial analysis. Symmetry (Physics) Symétrie (Physique) Analyse combinatoire. SCIENCE Physics Quantum Theory. bisacsh Combinatorial analysis fast Symmetry (Physics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85131443 http://id.loc.gov/authorities/subjects/sh85028802 |
| title | Applications of unitary symmetry and combinatorics / |
| title_auth | Applications of unitary symmetry and combinatorics / |
| title_exact_search | Applications of unitary symmetry and combinatorics / |
| title_full | Applications of unitary symmetry and combinatorics / James D. Louck. |
| title_fullStr | Applications of unitary symmetry and combinatorics / James D. Louck. |
| title_full_unstemmed | Applications of unitary symmetry and combinatorics / James D. Louck. |
| title_short | Applications of unitary symmetry and combinatorics / |
| title_sort | applications of unitary symmetry and combinatorics |
| topic | Symmetry (Physics) http://id.loc.gov/authorities/subjects/sh85131443 Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Combinatorial analysis. Symmetry (Physics) Symétrie (Physique) Analyse combinatoire. SCIENCE Physics Quantum Theory. bisacsh Combinatorial analysis fast Symmetry (Physics) fast |
| topic_facet | Symmetry (Physics) Combinatorial analysis. Symétrie (Physique) Analyse combinatoire. SCIENCE Physics Quantum Theory. Combinatorial analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426336 |
| work_keys_str_mv | AT louckjamesd applicationsofunitarysymmetryandcombinatorics |