**CRM Proceedings & Lecture Notes**

Volume: 33;
2003;
211 pp;
Softcover

MSC: Primary 49; 81; 78;
Secondary 35; 37; 46; 47

**Print ISBN: 978-0-8218-3330-8
Product Code: CRMP/33**

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

**Electronic ISBN: 978-1-4704-3947-7
Product Code: CRMP/33.E**

List Price: $71.00

AMS Member Price: $56.80

MAA Member Price: $63.90

# Quantum Control: Mathematical and Numerical Challenges

Share this page *Edited by *
*André D. Bandrauk; Michel C. Delfour; Claude Le Bris*

A co-publication of the AMS and Centre de Recherches Mathématiques

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

## Quantum Control: Mathematical and Numerical Challenges

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- List of participants vii8
- List of speakers xi12
- Molecular alignment and orientation: From laser-induced mechanisms to optimal control 114
- Overview and software guide of evolutionary algorithms; A case study in quantum control 2336
- Laser control of molecular states—Nonperturbative examples 4154
- Coherent control: Principles and semiclassical implementations 5972
- Mathematical models of contemporary elementary quantum computing devices 7992
- Addendum and remarks on doubly conservative numerical schemes for the nonlinear Schrödinger equation and its control 119132
- A note on the exact internal control of nonlinear Schrödinger equations 127140
- Towards efficient numerical approaches for quantum control 139152
- Multichannel quantum defect study of the control in the frequency domain: Example of HI 155168
- Development of solution algorithms for quantum optimal control equations in product spaces 163176
- Using contracted basis functions to solve the Schrödinger equation 177190
- Remarks on the controllability of the Schrödinger equation 193206
- Back Cover Back Cover1225