Control of Quantum-Mechanical Processes and Systems

Inhaltsverzeichnis

• 1. The Problem of Control on the Quantum Level.
• 1.1. Introduction.
• 1.2. A Quantum Process as the Object of Control.
• 1.3. Problems of Control in Different Descriptions.
• 1.4. Obtaining a Prescribed Pure State or a State in its Vicinity.
• 1.5. Control with the Aim of Obtaining a Specified Probability of a Given Pure State.
• 1.6. Obtaining the Maximum (or Minimum) Probability of a Specified Value of a Physical Quantity.
• 1.7. Obtaining a Desired Distribution of Probability Amplitudes for Values of Given Physical Quantities.
• 1.8. Control of Quantum Averages and Moments of Physical Quantities.
• 1.9. Control of the Distributions of Eigenvalues of Physical Quantities.
• 1.10. Control of Operators of Physical Quantities.
• 1.11. Measurement in Systems with Feedback.
• 2. Controllability and Finite Control of Quantum Processes (Analytical Methods).
• 2.1. Control of Pure States of Quantum Processes.
• 2.2. Local Controllability in the Vicinity of a Pure State.
• 2.3. Global Asymptotic Controllability of Pure States.
• 2.4. Control of the Electron in a Rectangular Potential Well.
• 2.5. Control of a Two-Spin System.
• 2.6. Finite Control of a Particle Spin State.
• 2.7. Control of Quantum Averages of Physical Quantities.
• 2.8. Control of Coherent States of a One-Dimensional Quantum Oscillator by Means of an External Force.
• 2.9. Control of a One-Dimensional Quantum Oscillator by Varying its Eigenfrequency.
• 2.10. Obtaining a Specified Probability of a Given State of a Charged Particle by Means of an External Magnetic Field.
• 2.11. Control of the State of a Free Particle by an External Force.
• 2.12. Control of the Coefficients of Linear Differential Equations Impulse Control.
• 2.13. Control of Magnetization.
• 3. Controllability and Finite Control (Algebraic Methods).
• 3.1. Algebraic Conditions for the Controllability of a Quantum Process.
• 3.2. Control on the Motion Groups of Quantum Systems.
• 3.3. The Structure of the Algebra of a Quantum System.
• 3.4. The Accessible Set of Evolution Matrices.
• 3.5. Designing Discrete Automata on Controlled Transitions of Quantum Systems.
• 4. Optimal Control of Quantum-Mechanical Processes.
• 4.1. General Formulation of the Control Problem for a Quantum Statistical Ensemble.
• 4.2. Variational Control Problems.
• 4.3. Necessary Conditions for an Extremum.
• 4.4. Methods of Solving Boundary Value Optimization Problems.
• 4.5. Methods of Direct Optimization on Unitary Groups.
• 4.6. Maximization of the Probability of Observing a Given State of a Quantum System.
• 5. Dynamical Systems with Stored Energy and Negative Susceptibility.
• 5.1. The Effect of Negative Susceptibility of Dynamical Systems and its Applications.
• 5.2. Synthesis of Bipolar Circuits with Negative Impedance and Negative Conductivity.
• 5.3. Negative Susceptibility in Gyroscopically Related Systems.
• 5.4. Transverse Susceptibility of a Rigid Dipole in an Inversely Directed Constant Field.
• 5.5. Negative Susceptibility of a Parametrically Modulated Oscillator.
• 5.6. Systems with Stored Energy.
• 5.7. Static Susceptibility of Adiabatically Invariant Control Systems.
• 5.8. Conditions for Negative Static Susceptibility in Quantum Systems.
• 6. Negative Susceptibility in Parametrically Induced Magnetics.
• 6.1. Induced Superdiamagnetism and its Application to Distributed Control.
• 6.2. Superdiamagnetic States in Inversely Magnetized Ferromagnetic Media.
• 6.3. Superdiamagnetism and Parametrically Stimulated Anomalous Gyrotropy.
• 6.4. Low-Frequency Susceptibility of a Gyromagnetic Medium.
• 6.5. Stability of Spin Waves in Longitudinal Pumping of Ferromagnetic Crystals.
• 6.6. Applications.
• Appendix 1. Mathematical Models of Quantum Processes.
• Appendix 2. Controllability and Finite Control of Dynamical Systems.
• A2.1. Controllability and Finite Control of Linear Finite-Dimensional Systems.
• A2.2. Finite Control of Linear Distributed Systems.
• A2.3. A New Differential Geometric Method of Solving the Problems of Finite Control of Non-Linear Finite-Dimensional Dynamical Systems.
• Appendix 3. Continuous Media and Controlled Dynamical Systems (CDS’s). The Maximum Principle for Substance Flow. The Laplacian of a CDS.
• References.