Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians PDF Download

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:Aspects of Geometric and Operator Theories:Manifolds and Dynamical SystemsOperators and Their Direct IntegralsOrthodox and Generalized Quantum Mechanics:Orthodox Quantum MechanicsPhysical Theory in Hilbert SpaceGeneralized Quantum MechanicsPoint Interactions, Macroscopic Quantum Systems and Superselection Rules:Point InteractionsMacroscopic Quantum SystemsAsymptotic Disjointness, Asymptotic Separability, Quantum Mechanics on Path Space and Superselection Rules:Separability and DecoherenceQuantum 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 systemsIntroduction of a quantization-by-part scheme to treat point interactionsSystematic and explicit treatment of quantum circuits in terms of point interactionsDistinctive selection of materials rarely discussed elsewhere, including a large number of examples and contemporary topicsDiscussions on the interplay of mathematics and physicsKeywords:Quantum Mechanics;Quantization;Macroscopic Quantum Systems;Superconducting Circuits;Point Contact InteractionsReviews:“Numerous sections of the book can be studied (and are really worth studying) like a textbook and without the necessity of going through the rest of the volume … certainly, everyone who works through the book will be rewarded by an enhanced comprehension of orthodox quantum theory … there are many solid reasons for recommending this book to the whole community of physicists and mathematicians — from graduate students to researchers — interested in a fresh description of the microscopic and macroscopic quantum worlds.”Mathematical Reviews