SCIENCE, MUSIC, AND MATHEMATICS: THE DEEPEST CONNE

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Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. From a lifetime's thinking, he offers this extraordinary synthesis exposing the deepest connections between science, music, and mathematics, while avoiding equations and technical jargon. He begins with perception psychology and the dichotomization instinct and then takes us through biological evolution, human language, and acausality illusions all the way to the climate crisis and the weaponization of the social media, and beyond that into the deepest parts of theoretical physics — demonstrating our unconscious mathematical abilities. He also has an important message of hope for the future. Contrary to popular belief, biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is more than a simple competition between selfish genes. Rather, he suggests, in some ways it is more like turbulent fluid flow, a complex process spanning a vast range of timescales. Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has worked on problems as diverse as the Sun's magnetic interior, the Antarctic ozone hole, jet streams in the atmosphere, and the psychophysics of violin sound. He has long been interested in how different branches of science can better communicate with each other and with the public, harnessing aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication. Contents: Foreword by Herbert E Huppert FRS Preface The Unconscious Brain What is Lucidity? What is Understanding? Mindsets, Evolution, and Language Acausality Illusions, and the Way Perception Works What is Science? Music, Mathematics, and the Platonic Postlude: The Amplifier Metaphor for Climate References and Endnotes Index Readership: Undergraduates, graduates, researchers, educators.

The Mathematics of Open Quantum Systems

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This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory. In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs. The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated "double-slit experiment" where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring. Sample Chapter(s) Preface Chapter 1: INTRODUCTION Contents: Acknowledgments Preface Representations of Operator Commutation Relations: Introduction Preliminaries and Basic Definitions The Commutation Relations and Character-Automorphic Functions The Differentiation Operator on Metric Graphs The Magnetic Hamiltonian The Livšic Function s(Ḋ,DΘ)(z) The Weyl-Titchmarsh Function M(Ḋ,DΘ)(z) The Model Dissipative Operators The Characteristic Function S(Ḋ,Ḓ,DΘ)(z) The Transmission Coefficient and the Characteristic Function Uniqueness Results Dissipative Solutions to the CCR Main Results Unitary Dynamics on the Full Graph Continuous Monitoring, Quantum Measurements: Continuous Monitoring of the Quantum Systems The Quantum Zeno versus Anti-zeno Effect Alternative The Quantum Zeno Effect versus Exponential Decay Alternative Preliminaries: Probabilities versus Amplitudes Massless Particles on a Ring Continuous Monitoring with Interference Continuous Monitoring with No Interference The Self-adjoint Dilation General Open Quantum Systems on a Ring Operator Coupling Limit Theorems Appendices: The Characteristic Function for Rank-One Perturbations Prime Symmetric Operators A Functional Model of a Triple The Spectral Analysis of the Model Dissipative Operator Transformation Laws The Invariance Principle The Operator Coupling and the Multiplication Theorem Stable Laws References Index Readership: Graduates and Researchers interested in mathematical physics, operator theory, quantum physics.