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Coherent evolution in noisy environments [electronic resource] / A. Buchleitner, K. Hornberger (eds.).

Published
Berlin ; New York : Springer, [2002]
Copyright Date
©2002
Physical Description
xiii, 293 pages : illustrations ; 24 cm.
Additional Creators
Buchleitner, A. (Andreas), 1964- and Hornberger, K. (Klaus), 1971-
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Contents
Machine generated contents note: Gert-Ludwig Ingold -- 1.1 Introduction -- 1.2 Path Integrals -- 1.2.1 Introduction -- 1.2.2 Propagator -- 1.2.3 Free Particle -- 1.2.4 Path Integral Representation of Quantum Mechanics -- 1.2.5 Particle on a Ring -- 1.2.6 Particle in a, Box -- 1.2.7 Driven Harmonic Oscillator -- 1.2.8 Semiclassical Approximation -- 1.2.9 Imaginary Time Path Integral -- 1.3 Dissipative Systems -- 1.3.1 Introduction -- 1.3.2 Environment as a Collection of Harmonic Oscillators -- 1.3.3 Effective Action -- 1.4 Damped Harmonic Oscillator -- 1.4.1 Partition Function -- 1.4.2 Ground State Energy and Density of States -- 1.4.3 Position Autocorrelation Function -- References -- Berthold-Georg Englert, Giovanna Morigi -- Introductory Remarks -- 2.1 First Lecture: Basics -- 2.1.1 Physical Derivation of the Master Equation -- 2.1.2 Some Simple Implications -- 2.1.3 Steady State -- 2.1.4 Action to the Left -- Homework Assignments -- 2.2 Second Lecture: Eigenvalues and Eigenvectors of L -- 2.2.1 A Simple Case First -- 2.2.2 The General Case -- Homework Assignments -- 2.3 Third Lecture: Completeness of the Damping Bases -- 2.3.1 Phase Space Functions -- 2.3.2 Completeness of the Eigenvectors of L -- 2.3.3 Positivity Conservation -- 2.3.4 Lindblad Form of Liouville Operators -- Homework Assignments -- 2.4 Fourth Lecture: Quantum-Optical Applications -- 2.4.1 Periodically Driven Damped Oscillator -- 2.4.2 Conditional and Unconditional Evolution -- 2.4.3 Physical Significance of Statistical Operators -- Homework Assignments -- 2.5 Fifth Lecture: Statistics of Detected Atoms -- 2.5.1 Correlation Functions -- 2.5.2 Waiting Time Statistics -- 2.5.3 Counting Statistics -- Homework Assignments -- Appendix -- References -- Kurt Wiesenfeld, Thomas Wellens, Andreas Buchleitner -- 3.1 Introduction -- 3.2 Some Mathematical Tools -- 3.3 Example: Driven Linear System -- 3.4 Mean First Passage Time and Kramers Escape Formula -- 3.5 Rate Equation Description -- 3.6 Two State Theory of Stochastic Resonance -- 3.7 The Unmodulated Case -- 3.8 Time Dependent Rates -- 3.9 Two-State Examples: Classical and Quantum Stochastic Resonance -- 3.10 Quantum Stochastic Resonance in the Micromaser -- 3.11 Stochastic Resonance in Excitable Systems -- 3.12 The Frontier of Stochastic Resonance -- References -- Burkhard Kummerer -- Introduction -- 4.1 An Example -- 4.1.1 The System -- 4.1.2 One Time Step -- 4.1.3 Many Time Steps -- 4.1.4 Outlook -- 4.2 Markovian Behaviour on General State Spaces -- 4.2.1 Transition Probabilities with Densities -- 4.2.2 Transition Kernels -- 4.2.3 Transition Operators -- 4.2.4 Continuous Time -- 4.3 Random Variables and Markov Processes -- 4.3.1 Example and Motivation -- 4.3.2 One Random Variable -- 4.3.3 Two Random Variables -- 4.3.4 Many Random Variables -- 4.3.5 Conditional Expectations -- 4.3.6 Markov Processes -- 4.4 Quantum Mechanics -- 4.4.1 The Axioms of Quantum Mechanics -- 4.4.2 An Example: Two-Level Systems -- 4.4.3 How Quantum Mechanics is Related to Classical Probability -- 4.5 Unified Description of Classical and Quantum Systems -- 4.5.1 Probability Spaces -- 4.5.2 Random Variables and Stochastic Processes -- 4.5.3 Conditional Expectations -- 4.5.4 Markov Processes -- 4.5.5 Relation to Open Systems -- 4.6 Constructing Markov Processes -- 4.6.1 A Construction Scheme for Markov Processes -- 4.6.2 Other Types of Markov Processes in the Literature -- 4.6.3 Dilations -- 4.7 An Example on M2 -- 4.7.1 The Example -- 4.7.2 A Physical Interpretation: Spins in a Stochastic Magnetic Field -- 4.7.3 Further Discussion of the Example -- 4.8 Completely Positive Operators -- 4.8.1 Complete Positivity -- 4.8.2 Interpretation of Complete Positivity -- 4.8.3 Representations of Completely Positive Operators -- 4.9 Semigroups of Completely Positive Operators and Lindblad Generators -- 4.9.1 Generators of Lindblad Form -- 4.9.2 Interpretation of Generators of Lindblad Form -- 4.9.3 Quantum Stochastic Differential Equations -- 4.10 Repeated Measurement and Its Ergodic Theory -- 4.10.1 Measurement According to von Neumann -- 4.10.2 Indirect Measurement According to K. Kraus -- 4.10.3 Measurement of a Quantum System and Concrete -- Representations of Completely Positive Operators -- 4.10.4 Repeated Measurement -- 4.11 The Micromaser as a Quantum Markov Process -- 4.11.1 The Experiment -- 4.11.2 The Micromaser Realizes a Quantum Markov Process -- 4.11.3 The Jaynes-Cummings Interaction -- 4.11.4 Asymptotic Completeness and Preparation of Quantum States -- References -- Walter T. Strunz -- 5.1 Introduction -- 5.1.1 Open Quantum Systems -- 5.1.2 Decoherence: Two Simple Examples -- 5.1.3 First Conclusions -- 5.1.4 Decoherence and the "Measurement Problem" -- 5.1.5 The Paris and Boulder Experiments -- 5.2 Decoherence in Quantum Brownian Motion -- 5.2.1 Classical Brownian Motion -- 5.2.2 High Temperature Limit -- 5.2.3 Decoherence -- 5.3 Robust States -- 5.3.1 Robustness in Terms of Hilbert-Schmidt Norm -- 5.3.2 Example: Lindblad Master Equation -- 5.3.3 Quantum Brownian Motion (Simplified) -- 5.3.4 Robustness Based on Entropy -- 5.3.5 Stochastic Schrodinger Equations and Robust States -- 5.3.6 Some Remarks about Stochastic Schrodinger Equations -- 5.4 Decoherence of Macroscopic Superpositions -- 5.4.1 Soluble Model -- 5.4.2 Universality of Decoherence -- 5.5 Conclusions -- References -- Hans Aschauer, Hans J. Briegel -- 6.1 Introduction -- 6.2 Quantum Error Correction -- 6.3 Entanglement Purification -- 6.3.1 2-Way Entanglement Purification Protocols -- 6.3.2 Purification with Imperfect Apparatus -- 6.4 Quantum Cryptography -- 6.4.1 The BB84 Protocol -- 6.4.2 The Ekert Protocol -- 6.4.3 Security Proofs -- 6.5 Private Entanglement -- 6.5.1 The Lab Demon -- 6.5.2 The State of the Qubits Distributed Through the Channel -- 6.5.3 Binary Pairs -- 6.5.4 Bell-Diagonal Initial States -- References -- Michael Keyl, Reinhard F. Werner -- 7.1 Introduction -- 7.2 Quantum Channels -- 7.3 Channel Capacities -- 7.3.1 The cb-Norm -- 7.3.2 Achievable Rates and Capacity -- 7.3.3 Elementary Properties -- 7.4 Quantum Error Correction -- 7.4.1 An Error Corrector's Dream -- 7.4.2 Realizing the Dream by Unitary Transformation -- 7.4.3 The Knill-Laflamme Condition -- 7.4.4 Example: Localized Errors -- 7.5 Graph Codes -- 7.6 Discrete to Continuous Error Model -- 7.7 Coding by Random Graphs -- 7.8 Conclusions -- 7.8.1 Correcting Small Errors -- 7.8.2 Estimating Capacity from Finite Coding Solutions -- 7.8.3 Error Exponents -- 7.8.4 Capacity with Finite Error Allowed -- References.
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ISBN
3540443541 (acid-free paper)
Bibliography Note
Includes bibliographical references and index.
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