From micro to macro quantum systems : a unified formalism with superselection rules and its applications / K. Kong Wan.

Format:

Book

Author/Creator:

Wan, K. Kong.

Language:

English

Subjects (All):

Quantum theory.

Nuclear physics.

Physical Description:

1 online resource (xix, 688 p. ) ill.

Edition:

1st ed.

Place of Publication:

London : Imperial College Press, c2006.

Language Note:

English

Summary:

"Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations. This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schrödinger's cat states in superconducting systems, and a path space formulation of quantum mechanics. This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators."

Contents:

I. Aspects of geometric and operator theories. 1. Manifolds and dynamical systems. 1.1. Topological spaces and topological equivalence. 1.2. Euclidean spaces. 1.3. Differential operators, vectors and fields. 1.4. Cotangent vectors and differential forms. 1.5. Differentiable manifolds. 1.6. Classical dynamical systems. 2. Operators and their direct integrals. 2.1. Hilbert spaces. 2.2. Operators: basic definitions. 2.3. Types of operators and their reductions. 2.4. Unitary operators and unitary transforms. 2.5. Extensions of symmetric operators. 2.6. Probability and expectation values. 2.7. Spectral measures and probability. 2.8. Selfadjointness and spectral decomposition. 2.9. Generalized spectral measures and probability. 2.10. Spectral functions of symmetric operators. 2.11. Probability and operators. 2.12. Local operators in coordinate space. 2.13. Direct integrals of Hilbert spaces. 2.14. Direct integrals of operators. 2.15. Direct integrals of tensor products

II. Orthodox and generalized quantum mechanics. 3. Orthodox quantum mechanics. 3.1. Introduction. 3.2. Orthodox quantum statics. 3.3. Quantization in IE[symbol]. 3.4. Orthodox quantum dynamics. 3.5. Quantum state preparation. 3.6. Quantum measurement. 4. Physical theory in Hilbert space. 4.1. Introduction. 4.2. Unified statics in direct integral space. 4.3. States and superposition principle. 4.4. Unified dynamics in direct integral space. 4.5 Classical systems of finite order. 4.6. Mixed quantum systems. 4.7. Coupling of systems of different types. 4.8. Concluding remarks. 5. Generalized quantum mechanics. 5.1. Introduction. 5.2. Maximal symmetric operators and observables. 5.3. Approximate and related observables. 5.4. Implications on quantization. 5.5. Time operators and uncertainty relation. 5.6. Local values in coordinate and in phase spaces. 5.7. Appendix on maximal probability families. 5.8. Appendix on time operators. 5.9. Concluding remarks

III. Point interactions, macroscopic quantum systems and superselection rules. 6. Point interactions. 6.1. Introduction. 6.2. Extensions of symmetric operators. 6.3. Extensions of direct sum operators. 6.4. Quantization by parts and point interactions. 6.5. Classification of point interactions in IE. 6.6. Remarks on quantization by parts. 6.7. Charged particles in circular motion. 6.8. Point interactions in a circle. 6.9. Classification of point interactions in C. 6.10. Current and stationary states in a circle. 7. Macroscopic quantum systems. 7.1. Single-particle representation. 7.2. Macroscopic wave function hypothesis. 7.3. Uniformly thick superconducting rings. 7.4. Superconducting rings with a junction. 7.5. Feynman's derivation of Josephson's equation. 7.6. Superconducting wire with a junction. 7.7 Y-shape circuits. 7.8. Continuous Y-Shape circuit. 7.9. Superconducting quantum interference devices. 7.10. Non-equilibrium mixed quantum system. 7.11. BCS theory and superselection rules. 7.12. Conceptual analyses. 7.13. Orthodox quantum systems. 7.14. Prospects and other approaches

IV. Asymptotic disjointness, asymptotic separability, quantum mechanics on path space and superselection rules. 8. Separability and decoherence. 8.1. Introduction. 8.2. Scattering systems and de Broglie paradox. 8.3. Schr�odinger's cat states. 8.4. Superconducting Schr�odinger's cat states. 8.5. Asymptotically separable quantum theory. 8.6. Entanglement and decoherence. 8.7. Chronological disordering. 9. Quantum mechanics on path space. 9.1. Introduction. 9.2. Physical space and path space. 9.3. Functions on path space. 9.4. Quantum mechanics on path space. 9.5. Josephson effect and superselection rules. 9.6. Concluding remarks.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

9786611867195

9781281867193

1281867195

9781860949081

1860949088

OCLC:

748530863