Introduction to Quantum Control and Dynamics (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)
By: Domenico D'Alessandro (author)Hardback
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The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory. After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. The final chapter covers the implementation of quantum control and dynamics in several fields.
Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematical, physics, and engineering work.
Iowa State University, Ames, USA
QUANTUM MECHANICS States and Operators Observables and Measurement Dynamics of Quantum Systems MODELING OF QUANTUM CONTROL SYSTEMS: EXAMPLES Quantum Theory of Interaction of Particles and Fields Approximations and Modeling: Molecular Systems Spin Dynamics and Control Mathematical Structure of Quantum Control Systems CONTROLLABILITY Lie Algebras and Lie Groups Controllability Test: The Dynamical Lie Algebra Notions of Controllability for the State Pure State Controllability Equivalent State Controllability Equality of Orbits OBSERVABILITY AND STATE DETERMINATION Quantum State Tomography Observability Observability and Methods for State Reconstruction LIE GROUP DECOMPOSITIONS AND CONTROL Decompositions of SU(2) and Control of Two Level Systems Decomposition in Planar Rotations Cartan Decompositions Levi Decomposition Examples of Application of Decompositions to Control OPTIMAL CONTROL OF QUANTUM SYSTEMS Formulation of the Optimal Control Problem The Necessary Conditions of Optimality Example: Optimal Control of a Two Level Quantum System Time Optimal Control of Quantum Systems Numerical Methods for Optimal Control of Quantum Systems MORE TOOLS FOR QUANTUM CONTROL Selective Population Transfer via Frequency Tuning Time Dependent Perturbation Theory Adiabatic Control STIRAP Lyapunov Control of Quantum Systems ANALYSIS OF QUANTUM EVOLUTIONS: ENTANGLEMENT, ENTANGLEMENT MEASURES, AND DYNAMICS Entanglement of Quantum Systems Dynamics of Entanglement Local Equivalence of States APPLICATIONS OF QUANTUM CONTROL AND DYNAMICS Nuclear Magnetic Resonance Experiments Molecular Systems Control Atomic Systems Control: Implementations of Quantum Information Processing with Ion Traps APPENDIX A: POSITIVE AND COMPLETELY POSITIVE MAPS, QUANTUM OPERATIONS, AND GENERALIZED MEASUREMENT THEORY Positive and Completely Positive Maps Quantum Operations and Operator Sum Representation Generalized Measurement Theory APPENDIX B: LAGRANGIAN AND HAMILTONIAN FORMALISM IN CLASSICAL ELECTRODYNAMICS Lagrangian Mechanics Extension of Lagrangian Mechanics to Systems with Infinite Degrees of Freedom Lagrangian and Hamiltonian Mechanics for a System of Interacting Particles and Field APPENDIX C: CARTAN SEMISIMPLICITY CRITERION AND CALCULATION OF THE LEVI DECOMPOSITION The Adjoint Representation Cartan Semisimplicity Criterion Quotient Lie Algebras Calculation of the Levi Subalgebra in the Levi Decomposition Algorithm for the Levi Decomposition APPENDIX D: PROOF OF THE CONTROLLABILITY TEST OF THEOREM 3.2.1 APPENDIX E: THE BAKER-CAMPBELL-HAUSDORFF FORMULA AND SOME EXPONENTIAL FORMULAS APPENDIX F: PROOF OF THEOREM 6.2.1 REFERENCES INDEX Notes and Exercises appear at the end of every chapter.
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