Banerjee Open Quantum Systems

Dynamics of Nonclassical Evolution
1. Auflage 2018
ISBN: 978-981-13-3182-4
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 20, 289 Seiten

Reihe: Texts and Readings in Physical Sciences

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

SUBHASHISH BANERJEE is an assistant professor and head of the Department of Physics, Indian Institute of Technology Jodhpur, India. He obtained his PhD degree from the School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India, in 2003. He has been involved in the study of the quantum theory of open systems since his PhD. A major theme of his work has been to see how the theory of open quantum systems provides a common umbrella to understand various facets of quantum optics, quantum information processing, quantum computing, quantum cryptography, the foundations of quantum mechanics, relativistic quantum mechanics and field theory. He has published two books and more than 67 articles in national and international journals of repute. 

Autoren/Hrsg.

Banerjee, Subhashish

Inhaltsverzeichnis

1;Contents;6
2;List of Figures;10
3;About the Author;15
4;Preface;16
5;1 Introduction;18
6;2 A Primer on Quantum Statistical Mechanics and Path Integrals;21
6.1;2.1 Introduction;21
6.2;2.2 Quantum Statistical Mechanics;21
6.2.1;2.2.1 States, Operators, Evolutions and Transformations;22
6.2.2;2.2.2 Various Pictures;25
6.2.3;2.2.3 Baker Campbell Hausdorff (BCH) Theorem;26
6.2.4;2.2.4 Density Matrices;28
6.2.5;2.2.5 Harmonic Oscillator;31
6.2.6;2.2.6 Partition Function;33
6.2.7;2.2.7 Entropy;35
6.3;2.3 Path Integrals;37
6.3.1;2.3.1 Introduction to the Path Integral;38
6.3.2;2.3.2 Illustrative examples;41
6.3.3;2.3.3 Partition Function as a Path Integral;44
6.3.4;2.3.4 Density Matrix Evolution as a Path Integral;46
6.4;2.4 Guide to advanced literature;47
7;3 Master Equations: A Prolegomenon to Open Quantum Systems;48
7.1;3.1 Introduction;48
7.2;3.2 Liouville Equation;49
7.3;3.3 Langevin Equation;50
7.4;3.4 Fokker-Planck Equation;54
7.5;3.5 Boltzmann Equation;57
7.6;3.6 Master Equation;58
7.7;3.7 Quantum Dynamical Semigroups and Markovian Master Equation;61
7.7.1;3.7.1 Derivation of the Lindblad-Gorini-Kosakowoski-Sudarshan Master Equation;62
7.7.2;3.7.2 Examples;65
7.7.3;3.7.3 Connection to the Pauli Master Equation;67
7.8;3.8 Quantum Non-Demolition Master Equations;68
7.9;3.9 Projection Operator Techniques;70
7.9.1;3.9.1 Nakajima-Zwanzig Technique;71
7.9.2;3.9.2 Time-Convolutionless Technique;72
7.10;3.10 Guide to advanced literature;77
8;4 Influence Functional Approach to Open Quantum Systems;78
8.1;4.1 Introduction;78
8.2;4.2 A Primer to the Influence Functional (IF) formalism;79
8.3;4.3 Influence Functionals: An Explicit Evaluation;84
8.3.1;4.3.1 Conventional Derivation of IF;84
8.3.2;4.3.2 Basis Independent Derivation of IF;89
8.3.3;4.3.3 Semiclassical Interpretation of the Influence Functional;98
8.4;4.4 Propagator for linear Quantum Brownian Motion;99
8.5;4.5 Master Equation for Quantum Brownian Motion;102
8.6;4.6 Guide to advanced literature;105
9;5 Dissipative Harmonic Oscillator;106
9.1;5.1 Introduction;106
9.2;5.2 Lindbladian Approach to the Damped Oscillator;106
9.3;5.3 Quantum Brownian Motion;112
9.3.1;5.3.1 Weak coupling, high T regime;112
9.3.2;5.3.2 Strong coupling regime;118
9.3.3;5.3.3 Fluctuation-Dissipation Theorem;121
9.4;5.4 Foundational Issues;122
9.4.1;5.4.1 Quantum Phase Distribution;122
9.4.2;5.4.2 Number-Phase Complementarity;127
9.5;5.5 Guide to advanced literature;131
10;6 Dissipative Two-State System;132
10.1;6.1 Introduction;132
10.2;6.2 Spin-Boson Model;133
10.2.1;6.2.1 Hamiltonian;133
10.2.2;6.2.2 Shifted Oscillators;135
10.2.3;6.2.3 Polaron Transformation;137
10.3;6.3 Examples of two-state systems based on Josephson tunnel junctions;137
10.3.1;6.3.1 Charge Qubit;138
10.3.2;6.3.2 Flux Qubit;139
10.3.3;6.3.3 Phase Qubit;140
10.4;6.4 Thermodynamics;141
10.4.1;6.4.1 Partition Function;142
10.5;6.5 Dynamics;143
10.5.1;6.5.1 Exact Solution;143
10.5.2;6.5.2 Noninteracting-Blip Approximation;148
10.6;6.6 Coupling to Reservoir via an Intermediate Harmonic Oscillator;149
10.6.1;6.6.1 Effective Spectral Density;150
10.6.2;6.6.2 Application of the Effective Spectrum Method: Asymptotic behavior of the Spin-Boson Model;152
10.7;6.7 Guide to Advanced Literature;155
11;7 Quantum Tunneling;157
11.1;7.1 Introduction;157
11.2;7.2 Semiclassical Approximation;158
11.3;7.3 Double Well Potential;164
11.4;7.4 Quantum Tunneling;171
11.5;7.5 Transition to Open Systems;177
11.6;7.6 Guide to further reading;181
12;8 Open Quantum System at Interface with Quantum Information;183
12.1;8.1 Introduction;183
12.2;8.2 Role of Noise in Quantum Information: Introduction to Tools and Techniques;184
12.2.1;8.2.1 Quantum noise;187
12.2.2;8.2.2 Channel-State Duality;191
12.3;8.3 Selected Applications of Open Quantum Systems to Quantum Information Processing;196
12.3.1;8.3.1 Environment-Mediated Quantum Deleter;196
12.3.2;8.3.2 Geometric Phase (GP) in Open Quantum Systems;197
12.3.3;8.3.3 Classical Capacity of a Squeezed Generalized Amplitude Damping Channel;201
12.3.4;8.3.4 Application to Quantum Cryptography;203
12.3.5;8.3.5 Dynamics of Quantum Correlations under Open Quantum System evolutions;207
12.3.6;8.3.6 Quantum Walk;214
12.3.7;8.3.7 Quasiprobability distributions in open quantum systems;216
12.3.8;8.3.8 Quantum error correction;220
12.4;8.4 Guide to Further Literature;231
13;9 Recent Trends;232
13.1;9.1 Application of Open Quantum System to Unruh Effect and Sub-Atomic Physics;232
13.1.1;9.1.1 Unruh Effect;233
13.1.2;9.1.2 Neutrinos;237
13.1.3;9.1.3 Mesons;241
13.2;9.2 Non-Markovian Phenomena;245
13.2.1;9.2.1 Non-Markovian Master Equations;245
13.2.2;9.2.2 Information backflow and breakdown of CP divisibility of the intermediate map;247
13.2.3;9.2.3 Illustrative Examples;250
13.3;9.3 Quantum Thermodynamics;256
13.4;9.4 What next?;258
14;References;259
15;Index;286