{"product_id":"quantum-dynamics-for-classical-systems-isbn-9781118370681","title":"Quantum Dynamics for Classical Systems","description":"\u003cp\u003e\u003cb\u003eIntroduces number operators with a focus on the relationship between quantum mechanics and social science\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. \u003ci\u003eQuantum Dynamics for Classical Systems\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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 \u003ci\u003eQuantum Dynamics for Classical Systems\u003c\/i\u003e include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eApplications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models\u003c\/li\u003e \u003cli\u003eIllustrations of the use of creation and annihilation operators for classical problems\u003c\/li\u003e \u003cli\u003eExamples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics\u003c\/li\u003e \u003cli\u003eClarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eQuantum Dynamics for Classical Systems\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Why a Quantum Tool in Classical Contexts? 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 A First View of (Anti-)Commutation Rules 2\u003c\/p\u003e \u003cp\u003e1.2 Our Point of View 4\u003c\/p\u003e \u003cp\u003e1.3 Do Not Worry About Heisenberg! 6\u003c\/p\u003e \u003cp\u003e1.4 Other Appearances of Quantum Mechanics in Classical Problems 7\u003c\/p\u003e \u003cp\u003e1.5 Organization of the Book 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Some Preliminaries 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Bosonic Number Operator 11\u003c\/p\u003e \u003cp\u003e2.2 The Fermionic Number Operator 15\u003c\/p\u003e \u003cp\u003e2.3 Dynamics for a Quantum System 16\u003c\/p\u003e \u003cp\u003e2.4 Heisenberg Uncertainty Principle 26\u003c\/p\u003e \u003cp\u003e2.5 Some Perturbation Schemes in Quantum Mechanics 27\u003c\/p\u003e \u003cp\u003e2.6 Few Words on States 38\u003c\/p\u003e \u003cp\u003e2.7 Getting an Exponential Law from a Hamiltonian 39\u003c\/p\u003e \u003cp\u003e2.8 Green’s Function 44\u003c\/p\u003e \u003cp\u003e\u003cb\u003eI Systems with Few Actors 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Love Affairs 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction and Preliminaries 49\u003c\/p\u003e \u003cp\u003e3.2 The First Model 50\u003c\/p\u003e \u003cp\u003e3.3 A Love Triangle 61\u003c\/p\u003e \u003cp\u003e3.4 Damped Love Affairs 71\u003c\/p\u003e \u003cp\u003e3.5 Comparison with Other Strategies 80\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Migration and Interaction Between Species 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction and Preliminaries 82\u003c\/p\u003e \u003cp\u003e4.2 A First Model 84\u003c\/p\u003e \u003cp\u003e4.3 A Spatial Model 88\u003c\/p\u003e \u003cp\u003e4.4 The Role of a Reservoir 100\u003c\/p\u003e \u003cp\u003e4.5 Competition Between Populations 103\u003c\/p\u003e \u003cp\u003e4.6 Further Comments 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Levels of Welfare: the Role of Reservoirs 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Model 110\u003c\/p\u003e \u003cp\u003e5.2 The Small λ Regime 116\u003c\/p\u003e \u003cp\u003e5.3 Back to S 121\u003c\/p\u003e \u003cp\u003e5.4 Final Comments 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 An Interlude: Writing the Hamiltonian 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Closed Systems 129\u003c\/p\u003e \u003cp\u003e6.2 Open Systems 133\u003c\/p\u003e \u003cp\u003e6.3 Generalizations 136\u003c\/p\u003e \u003cp\u003e\u003cb\u003eII Systems with Many Actors 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 A First Look at Stock Markets 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 An Introductory Model 142\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 All-in-one Models 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Genesis of the Model 151\u003c\/p\u003e \u003cp\u003e8.2 A Two-Traders Model 162\u003c\/p\u003e \u003cp\u003e8.3 Many Traders 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Models with An External Field 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Mixed Model 188\u003c\/p\u003e \u003cp\u003e9.2 A Time-Dependent Point of View 196\u003c\/p\u003e \u003cp\u003e9.3 Final Considerations 206\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Conclusions 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Other Possible Number Operators 211\u003c\/p\u003e \u003cp\u003e10.2 What Else? 217\u003c\/p\u003e \u003cp\u003eBibliography 219\u003c\/p\u003e \u003cp\u003eIndex 225\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eFABIO BAGARELLO, PhD,\u003c\/b\u003e 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.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eIntroduces number operators with a focus on the relationship between quantum mechanics and social science\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. \u003ci\u003eQuantum Dynamics for Classical Systems\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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 \u003ci\u003eQuantum Dynamics for Classical Systems\u003c\/i\u003e include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eApplications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models\u003c\/li\u003e \u003cli\u003eIllustrations of the use of creation and annihilation operators for classical problems\u003c\/li\u003e \u003cli\u003eExamples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics\u003c\/li\u003e \u003cli\u003eClarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eQuantum Dynamics for Classical Systems\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989898019045,"sku":"NP9781118370681","price":105.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118370681.jpg?v=1761785838","url":"https:\/\/k12savings.com\/es\/products\/quantum-dynamics-for-classical-systems-isbn-9781118370681","provider":"K12savings","version":"1.0","type":"link"}