CONTENTS -- Foreword -- Preface -- Control of the Molecular Alignment or Orientation by Laser Pulses Arne Keller -- 1. Introduction - Motivations -- 1.1. Motivations -- 1.2. Experimental methods -- 2. The Model -- 2.1. The free molecule -- 2.2. Molecule-laser interaction -- 2.2.1. Dipole moment interaction -- 2.2.2. Polarizability interaction -- 2.3. Molecular states time dependent evolution -- 2.3.1. Pure state -- 2.3.2. Mixed state -- 2.3.3. Sudden approximation -- 2.4. Alignment or orientation characterization -- 2.4.1. Orientation -- 2.4.2. Alignment -- 3. Control -- 3.1. Control objectives -- 3.2. Control at zero temperature - Pure state control -- 3.2.1. Target states -- 3.2.2. Open questions -- 3.2.3. Strategy of maxima -- 3.2.4. Optimization with an evolutionary algorithm -- 3.3. Control of a thermal ensemble - Mixed state control -- 3.3.1. Target states -- 3.3.2. Strategy of maxima -- 4. Conclusion -- References -- Quantum Computing and Devices: A Short Introduction Zhigang Zhang, Viswanath Ramakrishna and Goong Chen -- 1. Introduction -- 2. A Brief Historical Account, Motivation, and Three Fundamental Principles of Quantum Computing -- 2.1. Spins, the Stern-Gerlach experiment and superposition -- 2.2. Entanglement and the Einstein-Podolsky-Rosen (EPR) Problem -- 2.3. Reversibility and irreversibility, the Landauer principle -- 3. Quantum Computing Devices -- 3.1. The electromagnetic field and its quantization -- 3.2. The interaction between a two-level atom and the optical field -- 3.3. Cavity-QED -- 3.4. Optical lattices -- 3.4.1. Setting up the fields -- 3.4.2. Storing, sorting, and transporting ultra cold neutral atoms using optical latices -- 3.4.3. Entanglement with ultracold atoms in optical lattices -- 4. Universality of Quantum Gates -- 4.1. The Hamiltonian for the cavity-QED system -- 4.2. The coupled quantum dot Hamiltonian.

4.3. An explicit conjugation -- Acknowledgments -- References -- Dynamics of Mixed Classical-Quantum Systems, Geometric Quantization and Coherent States Hans-Rudolf Jauslin and Dominique Sugny -- 1. Introduction -- 2. Hilbert Space Framework of Quantum Dynamics -- 3. Hilbert Space Framework of Classical Dynamics -- 3.1. Koopman-Schr odinger representation -- 3.2. Koopman-Heisenberg representation -- 4. Dynamics of Mixed Classical-Quantum Systems -- 4.1. Example: Stern-Gerlach experiment -- 4.2. Physical interpretation - classical-quantum entanglement -- 5. Berezin-Toeplitz Quantization - Geometric Quantization -- 5.1. Selection of a polarization subspace -- 5.1.1. Construction of a basis of L K -- 5.1.2. Selection of a polarization subspace L LK by the choice of a subset of the basis -- 5.1.3. De nition of an isomorphism between L LK and Fock space -- 5.2. Toeplitz quantization of the observables -- 5.3. Toeplitz quantization of the generators of the dynamics - geometric quantization -- 5.4. Quantization by coherent states -- 5.4.1. Definition of coherent states -- 5.4.2. Construction of the coherent states determined by the selection of a polarization subspace -- 5.4.3. Coherent state quantization of observables -- 5.4.4. Coherent state quantization of the generators of the dynamics -- 6. Dequantization by Coherent States -- 6.0.1. (a) Construction of a phase space manifold from a set of coherent states -- 6.0.2. (b) Construction of the polarization subspace and of the isomorphism from a given set of unnormalized coherent states -- 6.0.3. (c) Dequantization of the observables - covariant and contravariant symbols -- 6.0.4. (d) Dequantization of the Hamiltonian generator of the dynamics -- 7. Conclusions -- Aknowledgments -- References -- Quantum Memories as Open Systems Robert Alicki -- 0. Introduction -- 1. Encoded Qubit.

2. A Generic Model of Classical Memory -- 3. Davies Generators -- 4. Kitaev Models -- 5. Concluding Remarks -- References -- Two Mathematical Problems in Quantum Information Theory Alexander S. Holevo -- 1. Formulation -- 1.1. The additivity problem -- 1.2. The problem of Gaussian optimizers -- 2. Quantum Channels -- 2.1. Additivity and entanglement -- 2.2. Different forms of the additivity property -- 2.3. Nonadditivity of quantum entropy quantities -- 2.4. Infinite-dimensional channels -- 3. Gaussian Systems -- 3.1. Canonical commutation relations, symplectic space and complex structures -- 3.2. Gaussian states and channels -- 3.3. The classical capacity -- Acknowledgments -- References -- Dissipatively Induced Bipartite Entanglement Fabio Benatti -- 1. Introduction -- 2. Two Qubit Master Equation -- 3. Dissipative Entanglement Generation -- 3.1. Persistence of Entanglement -- Appendix -- References -- Scattering in Nonrelativistic Quantum Field Theory Jan Derezi nski -- 1. Introduction -- 2. Basic Abstract Scattering Theory -- 2.1. Moller and scattering operators -- 2.2. Measurement of observables -- 2.3. Physical meaning of the scattering operator -- 2.4. Problem with eigenvalues -- 2.5. Alternative kinds of M ller operators -- 2.7. Other formalisms of scattering theory -- 3. Scattering Theory for 2-Body Schrodinger Operators -- 3.1. Short-range case -- 3.2. Physical meaning of scattering cross-sections -- 3.3. Long-range case -- 3.4. Freedom of the choice of modi ed M ller operators -- 4. Second Quantization -- 4.1. Fock spaces -- 4.2. Creation and annihilation operators -- 4.3. Field and Weyl operators -- 4.4. Wick quantization -- 4.5. Second quantization of operators -- 5. Scattering for Hamiltonians of Quantum Field Theory -- 5.1. QFT Hamiltonians -- 5.2. QFT Hamiltonians that do not polarize vacuum -- 5.3. Ground state.

5.4. Feynman-Dyson approach -- 5.5. The LSZ formalism -- 6. Scattering Theory of Van Hove Hamiltonians -- 6.1. Infra-red case A -- 6.2. Infra-red case B -- 6.3. Infra-red case C -- 6.4. Feynman-Dyson scattering theory for van Hove Hamiltonians -- 6.5. The LSZ formalism for van Hove Hamiltonians -- 7. Representations of the CCR -- 7.1. Definition of a representation of the CCR -- 7.2. Regular representations of the CCR -- 7.3. Creation/annihilation operators associated with a representation of the CCR -- 7.4. The Fock representation -- 7.5. Coherent representations -- 7.6. Coherent sectors -- 7.7. Covariant representations -- 7.8. Coherent sectors of a covariant representation -- 8. Pauli-Fierz Hamiltonians -- 8.1. Definition of Pauli-Fierz Hamiltonians -- 8.2. Spectral properties of Pauli-Fierz Hamiltonians -- 8.3. Scattering theory of Pauli-Fierz Hamiltonians -- 8.4. Asymptotic dynamics -- 8.5. Asymptotic completeness -- 8.6. Relaxation to the ground state -- 8.7. Coherent asymptotic representations -- Acknowledgments -- References -- Mathematical Theory of Atoms and Molecules Volker Bach -- 1. Relative Boundedness and Stability of the First Kind -- 2. Stability of Matter - Stability of the Second Kind -- 3. Hartree-Fock (HF) Theory for Atoms and Molecules -- 4. Bogolubov-Hartree-Fock (BHF) Theory -- Acknowledgment -- References.