Quantum Control: Mathematical and Numerical Challenges: Mathematical and Numerical Challenges : CRM Workshop, October 6-11, 2002, Montréal, CanadaAmerican Mathematical Soc., 2003 - 211페이지 An entirely new branch of science now known as Laser Control of Molecular Processes is steadily making an impact on the experimental and technological worlds, with internationally distinguished scientists making many outstanding contributions. In parallel, mathematicians from control theory and numerical simulation are getting progressively involved and making their contributions to this scientific endeavor. This volume presents the proceedings of the workshop, ``Quantum Control: Mathematical and Numerical Challenges'', held at the Centre de recherches mathematiques of the Universite de Montreal (CRM). The workshop concentrated on advanced numerical methods and new mathematical control and optimization approaches and tools for the quantum control of matter at the molecular level using current laser technology. It brought together mathematicians, theoretical chemists, and physicists working in the area of control and optimization of systems to address the outstanding numerical and mathematical problems. The volume is suitable for graduate students and research mathematicians interested in mathematical methods of control of molecular processes. It will also be useful to chemical engineers and chemists working in control and optimization of systems. |
목차
From LaserInduced Mechanisms to Optimal Control | 1 |
Overview and Software Guide of Evolutionary Algorithms A Case Study in Quantum Control | 23 |
Laser Control of Molecular StatesNonperturbative Examples | 41 |
Principles and Semiclassical Implementations | 59 |
Mathematical Models of Contemporary Elementary Quantum Computing Devices | 79 |
Addendum and Remarks on Doubly Conservative Numerical Schemes for the Nonlinear Schrödinger Equation and Its Control | 119 |
A Note on the Exact Internal Control of Nonlinear Schrödinger Equations | 127 |
Towards Efficient Numerical Approaches For Quantum Control | 139 |
Example of HI | 155 |
Development of Solution Algorithms for Quantum Optimal Control Equations in Product Spaces | 163 |
Using Contracted Basis Functions to Solve the Schrödinger Equation | 177 |
Remarks on the Controllability of the Schrödinger Equation | 193 |
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A. D. Bandrauk alignment applied approximation Atabek atom bend Brumer C. M. Dion calculate CANADA cavity Chem coherent control components control of molecular control problem convergence cost functional crossover denotes discrete dissociation dynamics E-mail address eigenvalue eigenvectors electric field electron energy levels evolution Evolutionary Algorithms exact controllability excitation experimental frequency Hamiltonian initial datum interaction interference ionization iteration laser control laser field laser pulses Lett linear mathematical Mathematics Subject Classification matrix matrix-vector products mechanism method molecular system molecule mutation nonlinear nonlinear Schrödinger equation numerical obtained optimal control orientation oscillator parameters phase lag photodissociation photon Phys potential quantum computing quantum control quantum dots quantum gates qubit Rabitz resonance rotational scheme Schrödinger equation search space Section semiclassical solution solve stretch TDSE Theorem time-dependent transition Université de Montréal Université de Sherbrooke variation operators vector vibrational wavefunctions