Quantum Dynamics for Classical Systems

With Applications of the Number Operator

Inbunden, Engelska, 2012

1 449 kr

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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 modelsIllustrations of the use of creation and annihilation operators for classical problemsExamples of the recent increase in research and literature on the many applications of quantum tools in applied mathematicsClarification 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.

Produktinformation

Utgivningsdatum2012-12-07
Mått163 x 236 x 18 mm
Vikt499 g
FormatInbunden
SpråkEngelska
Antal sidor256
FörlagJohn Wiley & Sons Inc
ISBN9781118370681

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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.

Preface xiAcknowledgments xv1 Why a Quantum Tool in Classical Contexts? 11.1 A First View of (Anti-)Commutation Rules 21.2 Our Point of View 41.3 Do Not Worry About Heisenberg! 61.4 Other Appearances of Quantum Mechanics in Classical Problems 71.5 Organization of the Book 82 Some Preliminaries 112.1 The Bosonic Number Operator 112.2 The Fermionic Number Operator 152.3 Dynamics for a Quantum System 162.4 Heisenberg Uncertainty Principle 262.5 Some Perturbation Schemes in Quantum Mechanics 272.6 Few Words on States 382.7 Getting an Exponential Law from a Hamiltonian 392.8 Green’s Function 44I Systems with Few Actors 473 Love Affairs 493.1 Introduction and Preliminaries 493.2 The First Model 503.3 A Love Triangle 613.4 Damped Love Affairs 713.5 Comparison with Other Strategies 804 Migration and Interaction Between Species 814.1 Introduction and Preliminaries 824.2 A First Model 844.3 A Spatial Model 884.4 The Role of a Reservoir 1004.5 Competition Between Populations 1034.6 Further Comments 1055 Levels of Welfare: the Role of Reservoirs 1095.1 The Model 1105.2 The Small λ Regime 1165.3 Back to S 1215.4 Final Comments 1256 An Interlude: Writing the Hamiltonian 1296.1 Closed Systems 1296.2 Open Systems 1336.3 Generalizations 136II Systems with Many Actors 1397 A First Look at Stock Markets 1417.1 An Introductory Model 1428 All-in-one Models 1518.1 The Genesis of the Model 1518.2 A Two-Traders Model 1628.3 Many Traders 1699 Models with An External Field 1879.1 The Mixed Model 1889.2 A Time-Dependent Point of View 1969.3 Final Considerations 20610 Conclusions 21110.1 Other Possible Number Operators 21110.2 What Else? 217Bibliography 219Index 225