Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a diverse range of macroscopic systems both within and outside of physics. This book describes how complex systems from a variety of fields can be modelled using quantum mechanical principles; from biology and ecology, to sociology and decision-making. The mathematical basis of these models is covered in detail, furnishing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new interdisciplinary research frontiers. It will be an essential resource for students and researchers in applied mathematics or theoretical physics who are interested in applying quantum mechanics to dynamical systems in the social, biological or ecological sciences.
Author(s): Fabio Bagarello
Publisher: Cambridge University Press
Year: 2019
Language: English
Pages: 316
Tags: Quantum Theory
Contents......Page 8
Preface......Page 12
Acknowledgments......Page 14
1 Why a Quantum Tool in Classical Contexts? (Part II)......Page 16
1.1 Organization of the Book......Page 18
Part I The General Framework......Page 20
2.1 The Bosonic Number Operator......Page 22
2.2 The Fermionic Number Operator......Page 26
2.3 Other Possibilities......Page 27
2.4 Dynamics for a Quantum System......Page 36
2.5 Heisenberg Uncertainty Principle......Page 43
2.6 A few Words on States......Page 46
2.7 More on Dynamics......Page 48
2.8 The (H, ρ)-Induced Dynamics......Page 58
2.9 A Two-Mode System......Page 66
Part II Applications......Page 72
3.1 Introduction......Page 74
3.2 A First Model......Page 75
3.3 Extending the Model, Part 1: More Interactions......Page 102
3.4 Extending the Model, Part 2: Adding a Rule ρ......Page 112
3.5 Nonlinearities......Page 120
3.6 Conclusions......Page 127
4.1 Introduction......Page 128
4.2 The Model......Page 129
4.3 Numerical Results......Page 135
4.4 Conclusions......Page 154
5.1 Introduction......Page 156
5.2 The Model......Page 157
5.3 Numerical Simulations......Page 162
5.4 Conclusions......Page 182
6 Closed Ecosystems......Page 183
6.1 A Linear Model with a Single Garbage......Page 184
6.2 A Linear Model with Two Garbages......Page 187
6.3 A Nonlinear Model with Two Garbages......Page 194
6.4 A Phenomenological Damping......Page 200
6.5 Conclusions......Page 208
7.1 Introduction......Page 209
7.2 Tumor Cell Proliferation......Page 210
7.3 Numerical Results......Page 214
7.4 Conclusions......Page 220
8.1 Introduction......Page 221
8.2 The Quantum Game of Life......Page 224
8.3 Some Results......Page 228
8.4 Conclusions......Page 231
9.1 Introduction......Page 232
9.2 Introducing the Model......Page 234
9.3 Results......Page 244
9.4 Conclusions......Page 248
10.1 Introduction......Page 249
10.2 Before the Trading Begins......Page 250
10.3 After the Trading Has Begun......Page 256
10.4 Conclusions......Page 263
11.1 Introduction......Page 265
11.2 The Environment and Its Hamiltonian......Page 266
11.3 Asymptotic Values: Absence of Interferences......Page 274
11.4 Finite Time Behavior: The Role of Interference......Page 277
11.5 Conclusions......Page 281
12.1 Introduction......Page 282
12.2 The Mathematical Framework......Page 283
12.3 An Application to Decision-Making and Order Effect......Page 298
12.4 Conclusions......Page 300
13 This Is Not the End......Page 302
13.1 What Next?......Page 303
References......Page 305
Index......Page 312
