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 mathématiques of the Université de Montréal (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.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students and research mathematicians interested in mathematical methods of control of molecular processes; chemical engineers; chemists.

Table of Contents

• O. Atabek and C. M. Dion -- Molecular alignment and orientation: From laser-induced mechanisms to optimal control
• A. Auger, A. Ben Haj-Yedder, and M. Schoenauer -- Overview and software guide of evolutionary algorithms; A case study in quantum control
• A. D. Bandrauk, F. Légaré, and H. T. Yu -- Laser control of molecular states--Nonperturbative examples
• V. S. Batista and P. Brumer -- Coherent control: Principles and semiclassical implementations
• G. Chen, D. A. Church, B.-G. Englert, and M. S. Zubairy -- Mathematical models of contemporary elementary quantum computing devices
• M. C. Delfour -- Addendum and remarks on doubly conservative numerical schemes for the nonlinear Schrödinger equation and its control
• R. Illner, H. Lange, and H. Teismann -- A note on the exact internal control of nonlinear Schrödinger equations
• C. Le Bris, Y. Maday, and G. Turinici -- Towards efficient numerical approaches for quantum control
• H. Lefebvre-Brion -- Multichannel quantum defect study of the control in the frequency domain: Example of HI
• Y. Ohtsuki and H. Rabitz -- Development of solution algorithms for quantum optimal control equations in product spaces
• X.-G. Wang and T. Carrington, Jr. -- Using contracted basis functions to solve the Schrödinger equation
• E. Zuazua -- Remarks on the controllability of the Schrödinger equation