CONTENTS -- PREFACE -- Chapter 1 DENSITY FUNCTIONAL THEORY -- 1. Introduction -- 1.1. Units and notation -- 1.2. Hartree-Fock theory -- 1.3. Homogeneous electron gas -- 1.3.1. Free electrons -- 1.3.2. Exchange energy -- 2. What is density functional theory? -- 2.1. Hohenberg-Kohn theorem -- 2.2. A simple example: the Thomas-Fermi theory -- 2.2.1. Variational equation of Thomas-Fermi theory -- 2.2.2. Thomas-Fermi atom -- 2.2.3. An example -- 3. Kohn-Sham theory -- 3.1. Local density approximation -- 3.2. Spin and the local spin density approximation -- 3.3. The generalized gradient approximation -- 4. Numerical methods for the Kohn-Sham equation -- 4.0.1. Exact exchange -- 4.0.2. 0(N) methods -- 5. Some applications and limitations of DFT -- 5.1. Two examples of condensed matter -- 5.2. Vibrations -- 5.3. NMR chemical shifts -- 6. Limitations of DFT -- 7. Time-dependent density functional theory: the equations -- 7.1. Optical properties -- 7.1.1. f-sum rule -- 7.2. Methods to solve the TDDFT equations -- 7.2.1. Linear response formula -- 7.3. Dynamic polarizability -- 7.4. Dielectric function -- 8. TDDFT: numerical aspects -- 8.1. Configuration matrix method -- 8.2. Linear response method -- 8.3. Sternheimer method -- 8.4. Real time method -- 9. Applications of TDDFT -- 9.1. Simple metal clusters -- 9.2. Carbon structures -- 9.3. Diamond -- 9.4. Other applications -- 9.5. Limitations -- References -- Chapter 2 MICROSCOPIC DESCRIPTION OF QUANTUM LIQUIDS -- 1. Introduction -- 1.1. General properties -- 2. Microscopic description -- 3. Hypernetted-chain equations -- 3.1. Results for liquid 4He -- 4. Minimization of the energy: Optimal two-body correlation functions -- 4.1. Asymptotic behavior -- 5. Low excited states -- 6. A 3He impurity in liquid 4He.

6.1. The 3He impurity as a probe in liquid 4He -- 6.2. The excitation spectrum of the 3He impurity -- 6.3. Correlated perturbative approach -- 7. Variational description of Fermi systems -- 7.1. Diagrammatic rules and Fermi hypernetted chain equations -- 7.2. Results for 3He -- 7.3. Excited states and the dynamic structure function -- 8. Summary -- 9. Acknowledgments -- References -- Chapter 3 THE COUPLED CLUSTER METHOD AND ITS APPLICATIONS -- 1. Introduction -- 2. The Coupled Cluster formalism -- 2.1. The exponential form of the wave function -- 2.2. The Configuration Interaction Method (CIM) -- 2.3. The Coupled Cluster equations -- 2.4. The reference state -- 2.5. The Bra Ground state -- 3. Approximation schemes -- 3.1. The SUB(n) or CCn approximation -- 3.2. Applications to Coulomb interacting systems -- 3.3. The HCSUB(n) approximation -- 4. Applications to light nuclei -- 4.1. The TICC2 approximation in configuration representation -- 4.2. TICC2 in coordinate representation -- 4.3. The nuclei 4He and 16O in the TICI2 approximation -- 4.4. Beyond TICI2 -- 5. Helium droplets -- 5.1. The J-TICI3 approximation -- 5.2. Ground state of 4He droplets -- 5.3. Collective states of 4He droplets -- 5.4. 3He droplets -- References -- Chapter 4 EXPERIMENTS WITH A RUBIDIUM BOSE-EINSTEIN CONDENSATE -- 1. Introduction -- 2. Micromotion -- 3. BEC in 1D optical lattice -- 4. Condensate photoionization -- 5. Conclusions and acknowledgments -- References -- Chapter 5 THEORETICAL ASPECTS OF BOSE-EINSTEIN CONDENSATION -- 1. Bosons and condensation -- 2. BEC in 4He -- 3. BEC in dilute systems -- 4. Conclusions -- 5. Acknowledgments -- References -- Chapter 6 ELEMENTARY EXCITATIONS AND DYNAMIC STRUCTURE OF QUANTUM FLUIDS -- 1. Introduction -- 2. Ground state of a quantum Bose fluid -- 2.1. Optimized ground state.

2.2. Euler equation with the Jastrow wave function -- 3. Equation of motion method -- 3.1. Linear response -- 3.2. Time-dependent correlation functions -- 3.3. Action integral -- 3.4. Least action principle -- 3.5. Many-particle densities and currents -- 3.6. One- and two-particle continuity equations -- 4. Solving the continuity equations -- 4.1. Feynman approximation -- 5. CBF-approximation -- 5.1. Convolution approximation -- 5.2. Two-particle equation -- 5.3. One-particle equation -- 5.4. The self-energy and the linear response function -- 5.4.1. Numerical evaluation of the self-energy -- 5.5. Analytic structure of the self-energy -- 5.5.1. Anomalous dispersion in liquid 4He -- 5.5.2. Absolute minimum in the spectrum -- 5.6. Dynamic structure function in the CBF-approximation -- 5.7. Summary -- 6. The full solution -- 6.1. Continuity equations -- 6.2. Continuity equations in momentum space -- 6.3. Phonon-roton spectrum -- 6.4. Sum rules -- 6.5. Results on two-particle currents -- 6.6. Precursor of the liquid-solid transition -- 7. Dynamics of a single impurity -- 7.1. Continuity equations -- 7.2. Linear response and self-energy -- 7.3. Hydrodynamic effective mass -- 8. Summary -- References -- Chapter 7 THEORY OF CORRELATED BASIS FUNCTIONS -- 1. Introduction -- 2. Basics of CBF theory -- 2.1. Motivations basic concepts and definitions -- 2.2. Finite-order correlated basis functions theory -- 3. Techniques for matrix elements -- 3.1. Definitions and notations -- 3.2. Techniques for matrix elements. I. Diagonal quantities -- 3.3. Techniques for matrix elements. II. Off-diagonal quantities -- 4. Interpretation of effective interactions -- 4.1. Quasiparticle interaction -- 4.2. Variational BCS theory -- 4.3. CBF the optimization problem and momentum-dependent correlations -- 5. Infinite order CBF theory -- 5.1. Introduction.

5.2. Correlated coupled cluster theory -- 5.3. CBF ring diagrams -- 6. Dynamics in correlated basis functions -- 6.1. Equations of motion for correlated states -- 6.2. Coherence and the Feynman theory of excitations -- 6.3. Diagrammatic reduction -- 6.4. Local approximations -- 6.5. Averaged CRPA equations -- 6.6. Response function and dynamic structure function -- References -- Chapter 8 THE MAGNETIC SUSCEPTIBILITY OF LIQUID 3He -- 1. Introduction -- 2. The susceptibility of bulk liquid 3He -- 3. Liquid 3He confined in aerogel -- 4. Two-dimensional liquid 3He -- 5. Conclusions -- 6. Acknowledgements -- References -- Chapter 9 THE HYPERSPHERICAL HARMONIC METHOD: A REVIEW AND SOME RECENT DEVELOPMENTS -- 1. Introduction -- 2. Microscopic systems -- 3. Jacobi coordinates -- 4. Hyperspherical coordinates -- 5. Hyperspherical functions -- 6. The coupled equations -- 7. The hyperspherical harmonic expansion in momentum space -- 8. Results for the A = 3 4 nuclei with the hyperspherical harmonic expansion -- 9. Modified hyperspherical harmonic expansions -- 9.1. The potential basis -- 9.2. The correlated expansion -- 9.3. The adiabatic approximation -- 9.4. The extended hyperspherical harmonic expansion -- 9.5. Application of the EHH expansion to the helium atom -- 10. Variational calculations for three- and four-nucleon scattering processes -- 10.1. N - d scattering -- 10.2. Results for the N - d scattering -- 10.3. Results for the low energy n-3H and p-3He scattering -- 11. Electro-weak reaction on few-nucleon systems -- 11.1. The p - d radiative capture -- 11.2. The hep reaction -- 12. Conclusions -- References -- Chapter 10 THE NUCLEAR MANY-BODY PROBLEM -- 1. Introduction -- 1.1. The nuclear interaction -- 1.2. Quantum simulations -- 1.3. Plan of the paper -- 2. The Hamiltonian -- 2.1. Two-body potential.

2.2. Three-body interaction -- 3. The AFDMC method -- 3.1. The auxiliary field breakup for a v6 two-body potential -- 3.2. Break-up for the three-body potential -- 3.3. The spin-orbit propagator -- 3.4. Trial wave function and path constraint -- 3.5. Tail corrections -- 3.6. The AFDMC algorithm -- 3.7. Finite size effects: The periodic box FHNC method -- 4. AFDMC applications to nucleon matter -- 4.1. Equation of state of neutron matter -- 4.2. Symmetry energy of nuclear matter -- 4.3. Spin susceptibility of neutron matter -- 5. Outlook and Conclusions -- References -- INDEX.