From Micro To Macro Quantum Systems

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, Schrodinger'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: Aspects of Geometric and Operator Theories: Manifolds and Dynamical Systems; Operators and Their Direct Integrals; Orthodox and Generalized Quantum Mechanics: Orthodox Quantum Mechanics; Physical Theory in Hilbert Space; Generalized Quantum Mechanics; Point Interactions, Macroscopic Quantum Systems and Superselection Rules: Point Interactions; Macroscopic Quantum Systems; Asymptotic Disjointness, Asymptotic Separability, Quantum Mechanics on Path Space and Superselection Rules: Separability and Decoherence; Quantum Mechanics on Path Space. Readership: Theoretical and mathematical physicists, applied and pure mathematicians, physicists and philosophers of science (with an interest in quantum theory). Key Features Rigorous formulation of a unified theory in a form directly applicable to physical systems Introduction of a quantization-by-part scheme to treat point interactions Systematic and explicit treatment of quantum circuits in terms of point interactions Distinctive selection of materials rarely discussed elsewhere, including a large number of examples and contemporary topics Discussions on the interplay of mathematics and physics.