{"product_id":"quantum-dynamics-for-classical-systems-9781118370681","title":"Quantum Dynamics for Classical Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\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 toolsthe number operator in particularcan 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 \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\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\u003e2.3.1 Schr¨odinger Representation 17\u003c\/p\u003e \u003cp\u003e2.3.2 Heisenberg Representation 20\u003c\/p\u003e \u003cp\u003e2.3.3 Interaction Representation 21\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\u003e2.5.1 A Time-Dependent Point of View 28\u003c\/p\u003e \u003cp\u003e2.5.2 Feynman Graphs 31\u003c\/p\u003e \u003cp\u003e2.5.3 Dyson’s Perturbation Theory 33\u003c\/p\u003e \u003cp\u003e2.5.4 The Stochastic Limit 35\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\u003e2.7.1 Non-Self-Adjoint Hamiltonians for Damping 42\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\u003e3.2.1 Numerical Results for M \u0026gt;1 54\u003c\/p\u003e \u003cp\u003e3.3 A Love Triangle 61\u003c\/p\u003e \u003cp\u003e3.3.1 Another Generalization 66\u003c\/p\u003e \u003cp\u003e3.4 Damped Love Affairs 71\u003c\/p\u003e \u003cp\u003e3.4.1 Some Plots 76\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\u003e4.3.1 A Simple Case: Equal Coefficients 90\u003c\/p\u003e \u003cp\u003e4.3.2 Back to the General Case: Migration 95\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\u003e5.2.1 The Sub-Closed System 117\u003c\/p\u003e \u003cp\u003e5.2.2 And Now, the Reservoirs! 119\u003c\/p\u003e \u003cp\u003e5.3 Back to S 121\u003c\/p\u003e \u003cp\u003e5.3.1 What If M = 2? 123\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\u003e8 ALL-IN-ONE MODELS 151\u003c\/p\u003e \u003cp\u003e8.1 The Genesis of the Model 151\u003c\/p\u003e \u003cp\u003e8.1.1 The Effective Hamiltonian 155\u003c\/p\u003e \u003cp\u003e8.2 A Two-Traders Model 162\u003c\/p\u003e \u003cp\u003e8.2.1 An Interlude: the Definition of cPˆ 163\u003c\/p\u003e \u003cp\u003e8.2.2 Back to the Model 164\u003c\/p\u003e \u003cp\u003e8.3 Many Traders 169\u003c\/p\u003e \u003cp\u003e8.3.1 The Stochastic Limit of the Model 172\u003c\/p\u003e \u003cp\u003e8.3.2 The FPL Approximation 177\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\u003e9.1.1 Interpretation of the Parameters 194\u003c\/p\u003e \u003cp\u003e9.2 A Time-Dependent Point of View 196\u003c\/p\u003e \u003cp\u003e9.2.1 First-Order Corrections 200\u003c\/p\u003e \u003cp\u003e9.2.2 Second-Order Corrections 203\u003c\/p\u003e \u003cp\u003e9.2.3 Feynman Graphs 204\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\u003e10.1.1 Pauli Matrices 212\u003c\/p\u003e \u003cp\u003e10.1.2 Pseudobosons 213\u003c\/p\u003e \u003cp\u003e10.1.3 Nonlinear Pseudobosons 213\u003c\/p\u003e \u003cp\u003e10.1.4 Algebra for an M + 1 Level System 215\u003c\/p\u003e \u003cp\u003e10.2 What Else? 217\u003c\/p\u003e \u003cp\u003eBIBLIOGRAPHY 219\u003c\/p\u003e \u003cp\u003eINDEX 225\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":51359348195671,"sku":"9781118370681","price":73.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118370681.jpg?v=1754124392","url":"https:\/\/bookcurl.com\/products\/quantum-dynamics-for-classical-systems-9781118370681","provider":"Book Curl","version":"1.0","type":"link"}