| Titre : |
Quantum Mechanics : From classical analytical mechanics to quantum mechanics, simulation, foundations and engineering |
| Type de document : |
texte imprimé |
| Auteurs : |
Mark Julian Everitt, Auteur ; Kieran Niels Bjergstrom, Auteur ; Stephen Neil Alexander Duffus, Auteur |
| Mention d'édition : |
1éd. |
| Editeur : |
USA : John Wiley et Sons |
| Année de publication : |
2024 |
| Importance : |
402p. |
| Présentation : |
Couverture externe,tableaux,figures |
| Format : |
25X17cm |
| ISBN/ISSN/EAN : |
978-1-119-82987-4 |
| Note générale : |
Mark Julian Everitt is the Director of Studies for Physics at Loughborough University, UK, where he has led a comprehensive revision of the physics degrees, increasing the level of challenge, guided by principles of authenticity and industry requirements. The first seven chapters of the book are derived from his second-year introductory core Quantum Physics module in these new degrees. His research includes the engineering of quantum circuits and devices for quantum technologies, feedback, measurement and control of quantum systems, and pioneering the field of quantum systems engineering as a distinct discipline.
Kieran Niels Bjergstrom began his career as a theoretical physicist researching the realistic modelling of open quantum systems, the reliability of quantum devices, and early notions of Quantum Systems Engineering (QSE) ― which was the topic of his PhD. He has worked in academia, industry and business developing QSE principles, tools and methodologies for maturing commercially relevant quantum technologies. He is director of a technology and strategy consultancy advising on areas of innovation including the strategic impact of quantum technologies, methods and policies for realising quantum technology’s commercial potential, and applied QSE.
Stephen Neil Alexander Duffus is a university teacher within the Physics Department at Loughborough University. He has an established reputation of communicating complex ideas in an engaging and accessible fashion. During his PhD, his main area of research was in open quantum systems. |
| Langues : |
Anglais moyen (ca.1100-1500) (enm) Langues originales : Anglais moyen (ca.1100-1500) (enm) |
| Catégories : |
2 Science
|
| Mots-clés : |
SCIENCE,physique,machanics |
| Index. décimale : |
530 Physique |
| Résumé : |
Quantum mechanics is a fundamental and conceptually challenging area of physics. It is usually assumed that students are unfamiliar with Lagrangian and Hamiltonian formulations of classical mechanics and the role played by probability. As a result, quantum physics is typically introduced using heuristic arguments, obscuring synergies with classical mechanics.
This book takes an alternative approach by leveraging classical analytical mechanics to facilitate a natural transition to quantum physics. By doing so, a solid foundation for understanding quantum phenomena is provided.
Key features of this textbook include: Mathematics and Classical Analytical Mechanics: The necessary mathematical background and classical analytical mechanics are introduced gradually, allowing readers to focus on one conceptual challenge at a time. Deductive Approach: Quantum mechanics is presented on the firm foundation of classical analytical mechanics, ensuring a logical progression of concepts. Pedagogical Features: This book includes helpful notes, worked examples, problems, computational challenges, and problem-solving approaches to enhance understanding. Comprehensive Coverage: Including advanced topics such as open quantum systems, phase-space methods, and computational methods for quantum physics including good programming practice and code design. Much of the code needed to reproduce figures throughout this book is included. Consideration of Foundations: The measurement problem and correspondence principle are addressed, including an open and critical discussion of their interpretation and consequences. Introduction to Quantum Systems Engineering: This is the first book to introduce Quantum Systems Engineering approaches for applied quantum technologies development.
This textbook is suitable for undergraduate students in physics and graduate students in mathematics, chemistry, engineering, and materials science.
|
| Note de contenu : |
Cover
Title Page
Copyright
Contents
Acronyms
About the Authors
Preface
Acknowledgements
About the Companion Website
Introduction
Chapter 1 Mathematical Preliminaries
1.1 Introduction
1.2 Generalising Vectors
1.2.1 Vector Spaces
1.2.2 Inner Product
1.2.3 Dirac Notation
1.2.4 Basis and Dimension
1.3 Linear Operators
1.3.1 Definition and Some Key Properties of Linear Operators
1.3.2 Expectation Value of Random Variables
1.3.3 Inverse of Operators
1.3.4 Hermitian Adjoint Operators
1.3.5 Unitary Operators
1.3.6 Commutators
1.3.7 Eigenvectors and Eigenvalues
1.3.8 Eigenvectors of Commuting Operators
1.3.9 Functions of Operators
1.3.10 Differentiation of Operators
1.3.11 Baker Campbell Hausdorff, Zassenhaus Formulae, and Hadamard Lemma
1.3.12 Operators and Basis State – Resolutions of Identity
1.3.12.1 Outer Product and Projection
1.3.12.2 Resolutions of Identity
1.4 Representing Kets as Vectors, and Operators as Matrices and Traces
1.4.1 Trace
1.4.2 Basis, Representation, and Inner Products
1.4.3 Observables
1.4.4 Labelling Vectors – Complete Sets of Commuting Observables – CSCO
1.5 Tensor Product
1.5.1 Setting the Scene: The Cartesian Product
1.5.2 The Tensor Product
1.6 The Heisenberg Uncertainty Relation
1.7 Concluding Remarks
Chapter 2 Notes on Classical Mechanics
2.1 Introduction
2.2 A Brief Revision of Classical Mechanics
2.2.1 Lagrangian Mechanics
2.2.2 Hamiltonian Mechanics
2.3 On Probability in Classical Mechanics
2.3.1 The Liouville Equation
2.3.2 Expectation Values
2.4 Damping
2.5 Koopman–von Neumann (KvN) Classical Mechanics
2.6 Some Big Problems with Classical Physics
2.6.1 Atoms and Polarisers
2.6.2 The Stern–Gerlach Experiment
2.6.3 The Correspondence Principle – What It Is and What It Is Not
Chapter 3 The Schrödinger View/Picture
3.1 Introduction
3.2 Motivating the Schrödinger Equation
3.2.1 Ehrenfest's Theorem, Poisson Brackets, and Commutation Relations
3.2.2 The Main Proposition
3.2.2.1 Summarising an Issue with the Above Argument
3.3 Measurement
3.3.1 Introducing Measurement
3.3.2 On the Possible Connection Between the State Vector and Probabilities
3.3.3 The Time‐independent Schrödinger Equation
3.3.4 Measurement Outcomes
3.4 Representation of Quantum Systems
3.4.1 The Position and Momentum Representation
3.4.1.1 The One‐dimensional Case
3.4.1.2 Three Dimensions
3.4.2 Spin
3.4.3 Spin and Position – The Spinor
3.5 Closing Remarks and the Axioms of Quantum Mechanics
Chapter 4 Other Formulations of Quantum Mechanics
4.1 Introduction
4.2 The Heisenberg Picture
4.2.1 Background
4.2.2 Motivating the Heisenberg Equation of Motion
4.2.3 A Specific Example: the One‐dimensional Harmonic Oscillator
4.2.4 The State,
Representation, and Dynamics
4.2.5 Axioms of Quantum Mechanics Revisited
4.2.6 The Evolution Operator
4.2.7 Connection to the Schrödinger Picture, and Revisiting Issues with Ehrenfest's Theorem
4.3 Wigner's Phase‐space Quantum Mechanics
4.3.1 Background
4.3.2 Motivating the Phase‐space Equation of Motion
4.3.3 Quantising Phase Space
4.3.4 Joining the Dots
4.3.5 The Heisenberg Uncertainty Relation
4.3.6 Generalising Wigner Functions to Spins
4.3.7 Axioms of Quantum Mechanics Revisited
4.4 The Path Integral Formulation of Quantum Mechanics
4.5 Closing Remarks
Chapter 5 Vectors and Angular Momentum
5.1 Introduction
5.2 On Curvilinear Coordinates (Using Spherical Coordinates as an Example)
5.2.1 The Coordinate Representation: A Statement of the Problem
5.2.2 Canonical Quantisation in Spherical Coordinates
5.2.3 Spherical Coordinates, Vectors, and Momenta
5.3 The Theory of Orbital and General Angular Momentum
5.3.1 From Classical to Quantum Angular Momentum
5.3.2 General Properties of Angular Momentum
5.3.3 Eigenvalues and Eigenvectors of Angular Momentum
5.3.4 Worked Examples of Matrix Construction
5.3.5 Orbital Angular Momentum Basis
5.4 Addition of Angular Momentum
5.4.1 The General Theory
5.4.2 Two‐particle Systems
5.4.3 Example: Addition of Spins
Chapter 6 Some Analytic and Semi‐analytic Methods
6.1 Introduction
6.2 Problems of the Form Ĥ0+Ŵ
6.2.1 The Interaction Picture
6.2.2 Time‐independent Perturbation Theory
6.2.3 Time‐dependent Perturbation Theory
6.3 The Variational Method
6.4 Instantaneous Energy Eigenbasis
6.5 Moving Basis
6.6 Time periodic Systems and Floquet Theory
6.7 Two‐level Systems
6.7.1 Non‐degenerate Uncoupled System
6.7.2 Non‐degenerate Coupled System
6.7.3 Degenerate Coupled System
Chapter 7 Applications and Examples
7.1 Introduction
7.2 Position Representation Examples of Particles and Potentials
7.2.1 The Free Particle
7.2.2 Infinitely Deep Potential Well
7.2.3 The Finite Potential Barrier
7.2.4 Finite Potential Well
7.3 The Harmonic Oscillator
7.3.1 A Scheme for Creating Ladder Operators
7.3.2 Ladder Operators and Some Eigenvalue Properties of the QHO
7.3.3 A Walk‐through of Repeatedly Applying a^† to 0
7.3.4 The General Form of the Action of a^ and a^† on n
7.3.5 Matrix Representation
7.3.6 The Position Representation of Wave‐functions
7.3.7 Coherent States
7.3.7.1 Introduction
7.3.7.2 Coherent States in the Number Basis
7.3.7.3 Coherent States as Displaced Vacuum States
7.3.7.4 The Position Representation
7.4 The Hydrogen Atom
7.4.1 Introduction
7.4.2 Quantum Analysis
7.4.2.1 Choosing a Representation
7.4.3 Fine Structure of Hydrogen: Spin–Orbit Coupling
7.5 The Dihydrogen Ion
7.6 The Jaynes–Cummings Model
7.6.1 The Hamiltonian
7.6.2 The Eigenstates and Eigenvalues
7.6.3 Dynamics of the Atomic Inversion
7.7 The Stern–Gerlach Experiment
Chapter 8 Computational Simulation of Quantum Systems
8.1 Introduction
8.2 General Points for Consideration
8.2.1 On Code Clarity and Performance
8.2.1.1 On Comments
8.2.1.2 Clear Code
8.2.2 Should I Use Third‐party Libraries?
8.2.3 Choice of Language
8.3 Some Overarching Coding Principles
8.3.1 Have Clear Objectives
8.3.2 Trust Your Code
8.3.3 Plan for the Future
8.3.4 Test, Test, Test
8.3.5 Object‐oriented Design
8.3.6 Be a SOLID Scientific Programmer
8.3.6.1 The Single‐responsibility Principle
8.3.6.2 The Open‐closed Principle
8.3.6.3 The Liskov Substitution Principle
8.3.6.4 The Interface Segregation Principle
8.3.6.5 The Dependency Inversion Principle
8.3.7 Be a Clean Coder
8.3.8 Continue to Master Your Craft
8.4 A Small Generic Quantum Library
8.4.1 Some Swift Basics
8.4.1.1 Comments
8.4.1.2 Primitive Types and Their Declaration
8.4.2 Complex Numbers and the ‘Generic’ Decision
8.4.2.1 Introducing Structure and Classes
8.4.2.2 A First Look at Generics
8.4.2.3 Functions
8.4.2.4 Operator Overloading
8.4.2.5 Introducing Protocols and Extensions
8.4.2.6 An Aside on the Power of Extensions
8.4.3 Adding Quantum Structure to the Code
8.4.3.1 Spaces
8.4.3.2 Vectors
8.4.3.3 Operators
8.4.4 Quantum Functionality
8.4.5 Dynamics
8.4.6 Plotting the Output
8.5 Concluding Remarks
8.6 Appendix I – Some Useful Calculated Quantities
8.6.1 Exponentials of the Annihilation and Creation Operators
8.6.2 The Pauli Vector: Euler Formula and Other Functions
8.6.3 Cosine of the Position Operator
8.7 Appendix II – Wigner Function Code
Chapter 9 Open Quantum Systems
9.1 Introduction
9.1.1 Context
9.1.2 Background
9.1.3 System Plus Bath Models
9.2 Classical Brownian Motion
9.2.1 Brownian Motion from Hamiltonian Mechanics
9.3 Master Equations
9.3.1 The Redfield Master Equations
9.3.2 The Caldeira–Leggett Model
9.3.2.1 Spectral Density
9.3.3 Master Equations of Lindblad Form
9.3.4 Low‐temperature Regime
9.3.5 Lindblads: Strengths and Weaknesses
9.3.6 Effective Hamiltonians
9.4 Master Equation Approximations and Their Implications
9.4.1 The Baker Campbell Hausdorff Approximations
9.4.2 The Born Approximation
9.4.3 Choice of Spectral Density
9.4.4 High Cut‐off Limit
9.5 A Master Equation Derivation Example
9.5.1 Inductive Coupling
9.5.2 Introducing Capacitive Coupling
9.5.3 Where Does the Model Break Down?
9.6 Unravelling the Master Equation
Chapter 10 Foundations: Measurement and the Quantum‐to‐Classical Transition
10.1 Introduction
10.2 The Measurement Problem
10.3 Refining the Idea of Measurement
10.4 My First Foray into Model‐based Measurement
10.5 Two Other Measurement Devices and Their Classical Limit
10.6 The Quantum‐to‐Classical Transition
10.7 A Model‐based Approach to Quantum Measurement
10.8 Questions for the Reader to Ponder
Chapter 11 Quantum Systems Engineering
11.1 Introduction
11.2 What Is Systems Engineering?
11.2.1 An Overview
11.2.2 Notes on Complexity and Interconnectedness
11.2.3 Industry Standard Systems Engineering
11.3 Quantum Systems Engineering
11.3.1 Motivation
11.3.2 Modelling and Simulation Challenges
11.3.2.1 What Is in a Model?
11.3.2.2 Design for Modelability
11.3.2.3 Hierarchical Modelling
11.3.2.4 An Aside on Standards
11.3.2.5 Extensibility
11.3.2.6 State of Play
11.3.3 Reliability Engineering
11.3.4 System‐of‐interest Boundaries
11.3.5 Requirements Analysis
11.3.6 Test and Verification
11.3.7 Device Characterisation
11.3.8 Model‐based Systems Engineering
11.4 Concluding Remarks
Bibliography
Index |
Quantum Mechanics : From classical analytical mechanics to quantum mechanics, simulation, foundations and engineering [texte imprimé] / Mark Julian Everitt, Auteur ; Kieran Niels Bjergstrom, Auteur ; Stephen Neil Alexander Duffus, Auteur . - 1éd. . - [S.l.] : USA : John Wiley et Sons, 2024 . - 402p. : Couverture externe,tableaux,figures ; 25X17cm. ISBN : 978-1-119-82987-4 Mark Julian Everitt is the Director of Studies for Physics at Loughborough University, UK, where he has led a comprehensive revision of the physics degrees, increasing the level of challenge, guided by principles of authenticity and industry requirements. The first seven chapters of the book are derived from his second-year introductory core Quantum Physics module in these new degrees. His research includes the engineering of quantum circuits and devices for quantum technologies, feedback, measurement and control of quantum systems, and pioneering the field of quantum systems engineering as a distinct discipline.
Kieran Niels Bjergstrom began his career as a theoretical physicist researching the realistic modelling of open quantum systems, the reliability of quantum devices, and early notions of Quantum Systems Engineering (QSE) ― which was the topic of his PhD. He has worked in academia, industry and business developing QSE principles, tools and methodologies for maturing commercially relevant quantum technologies. He is director of a technology and strategy consultancy advising on areas of innovation including the strategic impact of quantum technologies, methods and policies for realising quantum technology’s commercial potential, and applied QSE.
Stephen Neil Alexander Duffus is a university teacher within the Physics Department at Loughborough University. He has an established reputation of communicating complex ideas in an engaging and accessible fashion. During his PhD, his main area of research was in open quantum systems. Langues : Anglais moyen (ca.1100-1500) ( enm) Langues originales : Anglais moyen (ca.1100-1500) ( enm)
| Catégories : |
2 Science
|
| Mots-clés : |
SCIENCE,physique,machanics |
| Index. décimale : |
530 Physique |
| Résumé : |
Quantum mechanics is a fundamental and conceptually challenging area of physics. It is usually assumed that students are unfamiliar with Lagrangian and Hamiltonian formulations of classical mechanics and the role played by probability. As a result, quantum physics is typically introduced using heuristic arguments, obscuring synergies with classical mechanics.
This book takes an alternative approach by leveraging classical analytical mechanics to facilitate a natural transition to quantum physics. By doing so, a solid foundation for understanding quantum phenomena is provided.
Key features of this textbook include: Mathematics and Classical Analytical Mechanics: The necessary mathematical background and classical analytical mechanics are introduced gradually, allowing readers to focus on one conceptual challenge at a time. Deductive Approach: Quantum mechanics is presented on the firm foundation of classical analytical mechanics, ensuring a logical progression of concepts. Pedagogical Features: This book includes helpful notes, worked examples, problems, computational challenges, and problem-solving approaches to enhance understanding. Comprehensive Coverage: Including advanced topics such as open quantum systems, phase-space methods, and computational methods for quantum physics including good programming practice and code design. Much of the code needed to reproduce figures throughout this book is included. Consideration of Foundations: The measurement problem and correspondence principle are addressed, including an open and critical discussion of their interpretation and consequences. Introduction to Quantum Systems Engineering: This is the first book to introduce Quantum Systems Engineering approaches for applied quantum technologies development.
This textbook is suitable for undergraduate students in physics and graduate students in mathematics, chemistry, engineering, and materials science.
|
| Note de contenu : |
Cover
Title Page
Copyright
Contents
Acronyms
About the Authors
Preface
Acknowledgements
About the Companion Website
Introduction
Chapter 1 Mathematical Preliminaries
1.1 Introduction
1.2 Generalising Vectors
1.2.1 Vector Spaces
1.2.2 Inner Product
1.2.3 Dirac Notation
1.2.4 Basis and Dimension
1.3 Linear Operators
1.3.1 Definition and Some Key Properties of Linear Operators
1.3.2 Expectation Value of Random Variables
1.3.3 Inverse of Operators
1.3.4 Hermitian Adjoint Operators
1.3.5 Unitary Operators
1.3.6 Commutators
1.3.7 Eigenvectors and Eigenvalues
1.3.8 Eigenvectors of Commuting Operators
1.3.9 Functions of Operators
1.3.10 Differentiation of Operators
1.3.11 Baker Campbell Hausdorff, Zassenhaus Formulae, and Hadamard Lemma
1.3.12 Operators and Basis State – Resolutions of Identity
1.3.12.1 Outer Product and Projection
1.3.12.2 Resolutions of Identity
1.4 Representing Kets as Vectors, and Operators as Matrices and Traces
1.4.1 Trace
1.4.2 Basis, Representation, and Inner Products
1.4.3 Observables
1.4.4 Labelling Vectors – Complete Sets of Commuting Observables – CSCO
1.5 Tensor Product
1.5.1 Setting the Scene: The Cartesian Product
1.5.2 The Tensor Product
1.6 The Heisenberg Uncertainty Relation
1.7 Concluding Remarks
Chapter 2 Notes on Classical Mechanics
2.1 Introduction
2.2 A Brief Revision of Classical Mechanics
2.2.1 Lagrangian Mechanics
2.2.2 Hamiltonian Mechanics
2.3 On Probability in Classical Mechanics
2.3.1 The Liouville Equation
2.3.2 Expectation Values
2.4 Damping
2.5 Koopman–von Neumann (KvN) Classical Mechanics
2.6 Some Big Problems with Classical Physics
2.6.1 Atoms and Polarisers
2.6.2 The Stern–Gerlach Experiment
2.6.3 The Correspondence Principle – What It Is and What It Is Not
Chapter 3 The Schrödinger View/Picture
3.1 Introduction
3.2 Motivating the Schrödinger Equation
3.2.1 Ehrenfest's Theorem, Poisson Brackets, and Commutation Relations
3.2.2 The Main Proposition
3.2.2.1 Summarising an Issue with the Above Argument
3.3 Measurement
3.3.1 Introducing Measurement
3.3.2 On the Possible Connection Between the State Vector and Probabilities
3.3.3 The Time‐independent Schrödinger Equation
3.3.4 Measurement Outcomes
3.4 Representation of Quantum Systems
3.4.1 The Position and Momentum Representation
3.4.1.1 The One‐dimensional Case
3.4.1.2 Three Dimensions
3.4.2 Spin
3.4.3 Spin and Position – The Spinor
3.5 Closing Remarks and the Axioms of Quantum Mechanics
Chapter 4 Other Formulations of Quantum Mechanics
4.1 Introduction
4.2 The Heisenberg Picture
4.2.1 Background
4.2.2 Motivating the Heisenberg Equation of Motion
4.2.3 A Specific Example: the One‐dimensional Harmonic Oscillator
4.2.4 The State,
Representation, and Dynamics
4.2.5 Axioms of Quantum Mechanics Revisited
4.2.6 The Evolution Operator
4.2.7 Connection to the Schrödinger Picture, and Revisiting Issues with Ehrenfest's Theorem
4.3 Wigner's Phase‐space Quantum Mechanics
4.3.1 Background
4.3.2 Motivating the Phase‐space Equation of Motion
4.3.3 Quantising Phase Space
4.3.4 Joining the Dots
4.3.5 The Heisenberg Uncertainty Relation
4.3.6 Generalising Wigner Functions to Spins
4.3.7 Axioms of Quantum Mechanics Revisited
4.4 The Path Integral Formulation of Quantum Mechanics
4.5 Closing Remarks
Chapter 5 Vectors and Angular Momentum
5.1 Introduction
5.2 On Curvilinear Coordinates (Using Spherical Coordinates as an Example)
5.2.1 The Coordinate Representation: A Statement of the Problem
5.2.2 Canonical Quantisation in Spherical Coordinates
5.2.3 Spherical Coordinates, Vectors, and Momenta
5.3 The Theory of Orbital and General Angular Momentum
5.3.1 From Classical to Quantum Angular Momentum
5.3.2 General Properties of Angular Momentum
5.3.3 Eigenvalues and Eigenvectors of Angular Momentum
5.3.4 Worked Examples of Matrix Construction
5.3.5 Orbital Angular Momentum Basis
5.4 Addition of Angular Momentum
5.4.1 The General Theory
5.4.2 Two‐particle Systems
5.4.3 Example: Addition of Spins
Chapter 6 Some Analytic and Semi‐analytic Methods
6.1 Introduction
6.2 Problems of the Form Ĥ0+Ŵ
6.2.1 The Interaction Picture
6.2.2 Time‐independent Perturbation Theory
6.2.3 Time‐dependent Perturbation Theory
6.3 The Variational Method
6.4 Instantaneous Energy Eigenbasis
6.5 Moving Basis
6.6 Time periodic Systems and Floquet Theory
6.7 Two‐level Systems
6.7.1 Non‐degenerate Uncoupled System
6.7.2 Non‐degenerate Coupled System
6.7.3 Degenerate Coupled System
Chapter 7 Applications and Examples
7.1 Introduction
7.2 Position Representation Examples of Particles and Potentials
7.2.1 The Free Particle
7.2.2 Infinitely Deep Potential Well
7.2.3 The Finite Potential Barrier
7.2.4 Finite Potential Well
7.3 The Harmonic Oscillator
7.3.1 A Scheme for Creating Ladder Operators
7.3.2 Ladder Operators and Some Eigenvalue Properties of the QHO
7.3.3 A Walk‐through of Repeatedly Applying a^† to 0
7.3.4 The General Form of the Action of a^ and a^† on n
7.3.5 Matrix Representation
7.3.6 The Position Representation of Wave‐functions
7.3.7 Coherent States
7.3.7.1 Introduction
7.3.7.2 Coherent States in the Number Basis
7.3.7.3 Coherent States as Displaced Vacuum States
7.3.7.4 The Position Representation
7.4 The Hydrogen Atom
7.4.1 Introduction
7.4.2 Quantum Analysis
7.4.2.1 Choosing a Representation
7.4.3 Fine Structure of Hydrogen: Spin–Orbit Coupling
7.5 The Dihydrogen Ion
7.6 The Jaynes–Cummings Model
7.6.1 The Hamiltonian
7.6.2 The Eigenstates and Eigenvalues
7.6.3 Dynamics of the Atomic Inversion
7.7 The Stern–Gerlach Experiment
Chapter 8 Computational Simulation of Quantum Systems
8.1 Introduction
8.2 General Points for Consideration
8.2.1 On Code Clarity and Performance
8.2.1.1 On Comments
8.2.1.2 Clear Code
8.2.2 Should I Use Third‐party Libraries?
8.2.3 Choice of Language
8.3 Some Overarching Coding Principles
8.3.1 Have Clear Objectives
8.3.2 Trust Your Code
8.3.3 Plan for the Future
8.3.4 Test, Test, Test
8.3.5 Object‐oriented Design
8.3.6 Be a SOLID Scientific Programmer
8.3.6.1 The Single‐responsibility Principle
8.3.6.2 The Open‐closed Principle
8.3.6.3 The Liskov Substitution Principle
8.3.6.4 The Interface Segregation Principle
8.3.6.5 The Dependency Inversion Principle
8.3.7 Be a Clean Coder
8.3.8 Continue to Master Your Craft
8.4 A Small Generic Quantum Library
8.4.1 Some Swift Basics
8.4.1.1 Comments
8.4.1.2 Primitive Types and Their Declaration
8.4.2 Complex Numbers and the ‘Generic’ Decision
8.4.2.1 Introducing Structure and Classes
8.4.2.2 A First Look at Generics
8.4.2.3 Functions
8.4.2.4 Operator Overloading
8.4.2.5 Introducing Protocols and Extensions
8.4.2.6 An Aside on the Power of Extensions
8.4.3 Adding Quantum Structure to the Code
8.4.3.1 Spaces
8.4.3.2 Vectors
8.4.3.3 Operators
8.4.4 Quantum Functionality
8.4.5 Dynamics
8.4.6 Plotting the Output
8.5 Concluding Remarks
8.6 Appendix I – Some Useful Calculated Quantities
8.6.1 Exponentials of the Annihilation and Creation Operators
8.6.2 The Pauli Vector: Euler Formula and Other Functions
8.6.3 Cosine of the Position Operator
8.7 Appendix II – Wigner Function Code
Chapter 9 Open Quantum Systems
9.1 Introduction
9.1.1 Context
9.1.2 Background
9.1.3 System Plus Bath Models
9.2 Classical Brownian Motion
9.2.1 Brownian Motion from Hamiltonian Mechanics
9.3 Master Equations
9.3.1 The Redfield Master Equations
9.3.2 The Caldeira–Leggett Model
9.3.2.1 Spectral Density
9.3.3 Master Equations of Lindblad Form
9.3.4 Low‐temperature Regime
9.3.5 Lindblads: Strengths and Weaknesses
9.3.6 Effective Hamiltonians
9.4 Master Equation Approximations and Their Implications
9.4.1 The Baker Campbell Hausdorff Approximations
9.4.2 The Born Approximation
9.4.3 Choice of Spectral Density
9.4.4 High Cut‐off Limit
9.5 A Master Equation Derivation Example
9.5.1 Inductive Coupling
9.5.2 Introducing Capacitive Coupling
9.5.3 Where Does the Model Break Down?
9.6 Unravelling the Master Equation
Chapter 10 Foundations: Measurement and the Quantum‐to‐Classical Transition
10.1 Introduction
10.2 The Measurement Problem
10.3 Refining the Idea of Measurement
10.4 My First Foray into Model‐based Measurement
10.5 Two Other Measurement Devices and Their Classical Limit
10.6 The Quantum‐to‐Classical Transition
10.7 A Model‐based Approach to Quantum Measurement
10.8 Questions for the Reader to Ponder
Chapter 11 Quantum Systems Engineering
11.1 Introduction
11.2 What Is Systems Engineering?
11.2.1 An Overview
11.2.2 Notes on Complexity and Interconnectedness
11.2.3 Industry Standard Systems Engineering
11.3 Quantum Systems Engineering
11.3.1 Motivation
11.3.2 Modelling and Simulation Challenges
11.3.2.1 What Is in a Model?
11.3.2.2 Design for Modelability
11.3.2.3 Hierarchical Modelling
11.3.2.4 An Aside on Standards
11.3.2.5 Extensibility
11.3.2.6 State of Play
11.3.3 Reliability Engineering
11.3.4 System‐of‐interest Boundaries
11.3.5 Requirements Analysis
11.3.6 Test and Verification
11.3.7 Device Characterisation
11.3.8 Model‐based Systems Engineering
11.4 Concluding Remarks
Bibliography
Index |
|  |
Affiner la recherche Interroger des sources externes
