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Quantum techniques in stochastic mechanics

Author: John C Baez; Jacob D Biamonte
Publisher: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets -- important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Baez, John C., 1961-
Quantum techniques in stochastic mechanics.
New Jersey : World Scientific, [2018]
(DLC) 2017038767
(OCoLC)1010585430
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: John C Baez; Jacob D Biamonte
ISBN: 9789813226951 9813226951 9789813226968 981322696X
OCLC Number: 1027138118
Description: 1 online resource
Contents: Intro; Contents; Preface; 1 Stochastic Petri Nets; 1.1. The Rate Equation; 1.2. References; 1.3. Answers; 2 The Rate Equation; 2.1. Rate Equations: The General Recipe; 2.2. The Formation of Water (1); 2.3. The Formation of Water (2); 2.4. The Dissociation of Water (1); 2.5. The Dissociation of Water (2); 2.6. The SI Model; 2.7. The SIR Model; 2.8. The SIRS Model; 2.9. The General Recipe Revisited; 2.10. Answers; 3 The Master Equation; 3.1. The Master Equation; 3.2. Answers; 4 Probabilities vs Amplitudes; 4.1. A Poisson Process; 4.2. Probability Theory vs Quantum Theory. 4.3. Stochastic vs Unitary Operators; 4.4. Infinitesimal Stochastic vs Self-adjoint Operators; 4.5. The Moral; 5 Annihilation and Creation Operators; 5.1. Rabbits and Quantum Mechanics; 5.2. Catching Rabbits; 5.3. Dying Rabbits; 5.4. Breeding Rabbits; 5.5. Dueling Rabbits; 5.6. Brawling Rabbits; 5.7. The General Rule; 5.8. Kissing Rabbits; 5.9. References; 5.10. Answers; 6 An Example from Population Biology; 6.1. Amoeba Fission and Competition; 6.2. The Rate Equation; 6.3. The Master Equation; 6.4. An Equilibrium State; 6.5. Answers; 7 Feynman Diagrams; 7.1. Stochastic Petri Nets Revisited. 7.2. The Rate Equation; 7.3. The Master Equation; 7.4. Feynman Diagrams; 8 The Anderson-Craciun-Kurtz Theorem; 8.1. The Rate Equation; 8.2. Complex Balance; 8.3. The Master Equation; 8.4. Coherent States; 8.5. Proof of the Anderson-Craciun-Kurtz Theorem; 8.6. An Example; 8.7. Answers; 9 An Example of the Anderson-Craciun-Kurtz Theorem; 9.1. A Reversible Reaction; 9.2. Equilibrium Solutions of the Rate Equation; 9.3. Complex Balanced Equilibria; 9.4. Conserved Quantities; 10 A Stochastic Version of Noether's Theorem; 10.1. Markov Processes; 10.2. Noether's Theorem. 10.3. Markov Chains; 10.4. Answers; 11 Quantum Mechanics vs Stochastic Mechanics; 11.1. States; 11.2. Observables; 11.3. Symmetries; 11.4. Time Evolution in Quantum Mechanics; 11.5. Time Evolution in Stochastic Mechanics; 11.6. The Hille-Yosida Theorem; 11.7. Answers; 12 Noether's Theorem: Quantum vs Stochastic; 12.1. Two Versions of Noether's Theorem; 12.2. Proof of the Quantum Version; 12.3. Comparison; 13 Chemistry and the Desargues Graph; 13.1. The Ethyl Cation; 13.2. The Desargues Graph; 13.3. The Ethyl Cation, Revisited; 13.4. Trigonal Bipyramidal Molecules. 13.5. Drawing the Desargues Graph; 13.6. Desargues' Theorem; 13.7. Answers; 14 Graph Laplacians; 14.1. A Random Walk on the Desargues Graph; 14.2. Graph Laplacians; 14.3. The Laplacian of the Desargues Graph; 15 Dirichlet Operators and Electrical Circuits; 15.1. Dirichlet Operators and Electrical Circuits; 15.2. Circuits Made of Resistors; 15.3. The Big Picture; 16 Perron-Frobenius Theory; 16.1. At the Intersection of Two Theories; 16.2. Stochastic Mechanics vs Quantum Mechanics; 16.3. From Graphs to Matrices; 16.4. Perron's Theorem; 16.5. From Matrices to Graphs. 16.6. The Perron-Frobenius Theorem.
Responsibility: by John Baez (UC Riverside & Centre for Quantum Technologies, Singapore), Jacob D. Biamonte (Skolkovo Institute of Science and Technology, Russia).

Abstract:

"We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets -- important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets."--

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