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Informationen zum Autor FABIO BAGARELLO, PhD, is Professor in the Department of Electrical Engineering and Telecommunications, Chemical Technology, Automatic, and Mathematical Models at the University of Palermo in Italy. He is the author of over 100 journal articles and has presented lectures at several international conferences on quantum probability, functional analysis, operator algebras, wavelets, and non-hermitian quantum mechanics. Klappentext Introduces number operators with a focus on the relationship between quantum mechanics and social scienceMathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools--the number operator in particular--can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results.The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include:* Applications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models* Illustrations of the use of creation and annihilation operators for classical problems* Examples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics* Clarification on numerous misunderstandings and misnomers while shedding light on new approaches in the fieldQuantum Dynamics for Classical Systems is an ideal reference for researchers, professionals, and academics in applied mathematics, economics, physics, biology, and sociology. The book is also excellent for courses in dynamical systems, quantum mechanics, and mathematical models. Zusammenfassung With a focus on the relationship between quantum mechanics and social science, this book introduces the main ideas of number operators while avoiding excessive technicalities that aren't necessary in understanding the various mathematical applications. Inhaltsverzeichnis PREFACE xi ACKNOWLEDGMENTS xv 1 WHY A QUANTUM TOOL IN CLASSICAL CONTEXTS? 1 1.1 A First View of (Anti-)Commutation Rules 2 1.2 Our Point of View 4 1.3 Do Not Worry About Heisenberg! 6 1.4 Other Appearances of Quantum Mechanics in Classical Problems 7 1.5 Organization of the Book 8 2 SOME PRELIMINARIES 11 2.1 The Bosonic Number Operator 11 2.2 The Fermionic Number Operator 15 2.3 Dynamics for a Quantum System 16 2.3.1 Schr¿odinger Representation 17 2.3.2 Heisenberg Representation 20 2.3.3 Interaction Representation 21 2.4 Heisenberg Uncertainty Principle 26 2.5 Some Perturbation Schemes in Quantum Mechanics 27 2.5.1 A Time-Dependent Point of View 28 2.5.2 Feynman Graphs 31 2.5.3 Dyson's Perturbation Theory 33 2.5.4 The Stochastic Limit 35 2.6 Few Words on States 38 2.7 Getting an Exponential Law from a Hamiltonian 39 2.7.1 Non-Self-Adjoint Hamiltonians for Damping 42 2.8 Green's Function 44 I SYSTEMS WITH FEW ACTORS 47 3 LOVE AFFAIRS 49 3.1 Introduction and Preliminaries 49 3.2 The First Model 50 >1 54 3.3 A Love Triangle 61 3.3.1 Another Generalization 66 3.4 Damped Love Affairs 71 3.4.1 Some Plots 76 3.5 Comparison with Other Strategie...
