Irreversible Quantum Dynamics

✍ Scribed by Fabio Benatti; Roberto Floreanini

• Publisher: Springer Science & Business Media
• Year: 2003
• Tongue: English
• Leaves: 349
• Category: Library

✦ Synopsis

The idea of editing the present volume in the Lecture Notes in Physics series arosewhileorganizingthe“ConferenceonIrreversibleQuantumDynamics”that took place at The Abdus Salam International Center for Theoretical Physics, Trieste, Italy, from July 29 to August 2, 2002. The aim of the Conference was to bring together di?erent groups of - searcherswhoseinterestsandpursuitsinvolveirreversibilityandtimeasymmetry in quantum mechanics. The Conference promoted open and in-depth exchanges of di?erent points of view, concerning both the content and character of qu- tum irreversibility and the methodologies used to study it. The following main themes were addressed: • Theoretical Aspects of Quantum Irreversible Dynamics • Open Quantum Systems and Applications • Foundational Aspects of Irreversible Quantum Dynamics • Asymmetric Time Evolution and Resonances Eachthemewasreviewedbyanexpertinthe?eld,accompaniedbymorespeci?c, research-like shorter talks. The whole topic of quantum irreversibility in all its manifold aspects has always raised a lot of interest, starting with the description of unstable systems in quantum mechanics and the issue of quantum measurement. Further, in - cent years a boost of activity concerning noise, dissipation and open systems has been prompted by the fast developing ?eld of quantum communication and information theory. These considerations motivated the editors to put together a volume that tries to summarize the present day status of the research in the ?eld, with the aim of providing the reader with an accessible and exhaustive introduction to it.

✦ Table of Contents

Chapter 1
1 Introduction
2 On Irreversible Dynamical Systems
2.1 The General Picture
2.2 Phenomenological Picture of Open Quantum Systems
3 Conservative Quantum Dynamics and Microscopic Reversibility
4 Irreversibility in Subsytems of Conservative Systems
5 Irreversibility in Open Quantum Systems
6 Irreversible Macroscopic Continuum Mechanics
7 Some Consequences of Irreversibility: Ordered and Chaotic Structures Far from Equilibrium
8 Concluding Remarks
References
Chapter 2
1 Introduction
2 Irreversibility in Markovian Equations
3 Entropy Production
4 Regularization of Relative Entropy
5 Time-Dependent Generators
6 Entangled Initial States
7 Complete Non-Markovian Equations
Acknowledgement
References
Chapter 3
1 Liouville Space Notation
1.1 Involutions
2 Closed Evolution Supops
3 Reduced Dynamics
3.1 Memory Equation
3.2 Cumulant Equation
3.3 Cumulant vs. Memory
4 Examples
4.1 Wigner-Weyl Bases
4.2 Quadratic Hamiltonians
4.3 Pure Decoherence in a Bath of Oscillators
4.4 Oscillator in a Bath of Oscillators
4.5 Static Model Again
Acknowledgments
References
Chapter 4
1 Introduction
2 Dynamics of Open Systems: Microscopic Theory
3 Dynamical Maps and Quantum Markov Processes
4 Quantum Operations, Continuous Measurements and Stochastic Processes in Hilbert Space
5 Non-Markovian Processes
References
Chapter 5
1 Introduction
2 Historical Background
3 A Simple Example of Decoherence-Free Subspaces: Collective Dephasing
4 Formal Treatment of Decoherence
5 The DFS Conditions
5.1 Hamiltonian Formulation
5.2 Operator-Sum Representation Formulation
5.3 Lindblad-Semigroup Formulation
5.4 Quantum Error Correction Formulation
5.5 Stabilizer Formulation
5.6 Relative Merits of the Various Formulations
6 Further Examples of Decoherence-Free Subspaces
6.1 Electromagnetically Induced Transparency
6.2 Spin Boson Model with Strong Collective Decoherence
6.3 DFS and Dicke Subradiance
6.4 Multiple Qubit Errors
7 Decoherence-Free (Noiseless) Subsystems
7.1 Formal Theory
7.2 Examples
8 Protection Against Additional Decoherence Sources
9 Conclusions
Acknowledgements
References
Chapter 6
1 Introduction
2 Ergodic Properties of Quantum Dynamical Maps and Semigroups
2.1 Complete Positivity
2.2 C*-Algebras and Group Representations
2.3 Decoherence-Free Subalgebras
2.4 Limited Relaxation
3 Examples
3.1 N-Particle Systems with Permutation Invariance
3.2 Superradiance Model with SU(3) Symmetry
4 Non-Markovian Controlled Open Systems
4.1 Errors in CQOP
4.2 Reduced Dynamics in Born Approximation
4.3 Error Formula
5 Conclusions
Acknowledgements
References
Chapter 7
1 Introduction
2 Projective Measurements
3 Unitary Kicks
4 Continuous Coupling
5 Dynamical Superselection Rules
6 An Example
7 More Examples
7.1 Simplified Scheme
7.2 Spontaneous Decay in Vacuum
7.3 Decohering Levels
8 Outlook
References
Chapter 8
1 Introduction
2 Separability, Entanglement, Statistical Consistency
3 Total Disentanglement
4 The Disentanglement Time
5 Discussion and Outlook
Acknowledgment
References
Chapter 9
1 Introduction
2 Path Integrals for Dissipative Quantum Systems
3 Initial State and Influence Functional
4 General Conditions for Markovian Master Equations
5 Weak Damping Regime
6 Strong Friction Range
7 Conclusions
Acknowledgments
References
Chapter 10
1 Motivation
2 Dynamical Systems
3 Entropy Constructs
3.1 The CNT Entropy
3.2 The ALF Entropy
4 Quantum Entropies for Classical Stochastic Dynamics
4.1 The Hudetz Construction
4.2 The ALF Construction
References
Chapter 11
1 Introductory Considerations
2 Irreversibility and Measurement: A Naive Example
3 A Concise Sketch of the Proposed Solutions
4 The Proposed Solutions and Irreversibility
5 Irreversibility in the Case of a Modified Dynamics
6 The Original Dynamical Reduction Model and Its Developments
7 The Physics of the Spontaneous Reduction Models
8 CSL with the Mass Density as the Preferred Basis
9 A Useful Elementary Example
10 Issues of Interpretation: The Onthology of Dynamical Reduction Models
11 Objective Mass Densities
12 Deepening the Analysis: The Unfolding of the Macro-Objectification Process
13 Macroscopic Similarity
14 Relativistic Aspects
15 Concluding Remarks
References
Chapter 12
1 Reduction Theories
2 Sharpening Markov Processes in Hilbert Space
3 The Nonrelativistic Mass Process
4 The Tomonaga–Schwinger Equation
5 Relativistic Stochastic Equation
6 Stuff
7 Stuff Operators
8 Open Problems and Conclusions
References
Chapter 13
1 Introduction
2 Repeated Gedanken Measurements on a Single System: Jumps and Random Trajectories
3 Reset Operation and Bloch Equations
4 Systems with Quantized Center-of-Mass Motion
5 Application to Quantum Arrival Times
References
Chapter 14
1 Introduction
2 Rigged Hilbert Spaces
3 Characterizations of Resonances
3.1 Resonances as Poles of the Resolvent
3.2 Resonances as Poles of the Continued S-Matrix
3.3 Resonances as Complex Eigenvalues of the Hamiltonian
3.4 The Complex Scaling Method
4 Types of Resonances
4.1 Simple or Nondegenerate Resonances
4.2 Relation Between Poles of the S-Matrix and Poles of the Resolvent
4.3 Multiple or Degenerate Resonances
4.4 Resonances as Branch Cuts
4.5 Resonances in Liouville Spaces
4.6 Resonances in Chaotic Systems
4.7 Lax-Phillips Resonances
5 Resonances and Intrinsic Irreversibility
6 Concluding Remarks
Acknowledgments
References
Chapter 15
1 Introduction
2 Preliminaries
2.1 The Hilbert Space Case
2.2 The Banach Space Case
3 Markovian Limit of Reduced Dynamics
4 Markovian Master Equation
4.1 The Hilbert Space Case
4.2 The Banach Space Case
References
Chapter 16
1 Introduction
2 Scattering Theory and the New Axiom
3 Time Evolution from the New Axiom
Acknowledgments
References
Chapter 17
1 Introduction
2 Boundary Conditions upon the Time-Independent Schrodinger Equation
2.1 Standing-Wave Eigenfunctions
2.2 Lippmann-Schwinger Eigenfunctions
2.3 Gamow Eigenfunctions
3 The Arrow of Time of Quantum Electrodynamics
4 Conclusions
Acknowledgment
References
Chapter 18
1 Introduction
2 Theoretical Framework
3 Rigged Hilbert Space for the Unstable States
4 The Derivation of the Relativistic Gamow State
5 Physical Properties of the Relativistic Gamow States
6 The Problem of the Z Boson Mass
6.1 Phenomenology of Resonances
6.2 Standard Model
6.3 Detailed Analysis of the Z-Boson Mass
7 Conclusions
Acknowledgment
References
Chapter 19
1 Quasi-localization Inside the Continuous Spectrum of Multiparticle Systems
2 Hermitian and Non-Hermitian Structures in the Theory of Decaying States
3 The Complex Eigenvalue Schrodinger Equation (CESE) for Resonance States
4 Norms, Energy Distributions and Computation

6 Time-Asymmetry in Irreversible Decay, Energy Distributions and Nonexponential Decay
7 Time-Dependent Tunnelling via Path Integrals: Connection to the Previous Results
References