Contents -- Preface -- PART 1 -- Chapter 1 Independent-Particle Model -- 1.1 Introduction -- 1.2 Bosons -- 1.3 Fermions -- 1.4 Matrix Elements of One-Body Operators -- 1.5 Matrix Elements of Two-Body Operators -- 1.6 Density Matrices -- 1.7 The Ideal Bose Gas Confined in a Harmonic Potential -- 1.8 The Fermi Gas -- 1.8.1 Excited States -- 1.8.2 Polarized Fermi Gas -- 1.9 Finite Temperature and Quasiparticles -- Chapter 2 The Hartree-Fock Theory -- 2.1 Introduction -- 2.2 The Hartree-Fock Method for Fermions -- 2.2.1 Examples of Physical Systems treated by the Hartree-Fock method -- 2.2.2 Examples of Infinite Systems treated by the Hartree-Fock method -- 2.3 The Hartree-Fock Method for Bosons -- 2.4 The Gross-Pitaevskii Equations -- 2.5 Hartree-Fock in Second Quantization Language -- 2.6 Hartree-Fock at Finite Temperature -- 2.7 Hartree-Fock-Bogoliubov and BCS -- Chapter 3 The Brueckner-Hartree-Fock (BHF) Theory -- 3.1 Introduction -- 3.2 The Lippman-Schwinger Equation -- 3.3 The Bethe-Goldstone Equation -- 3.4 The One-Dimensional Fermion System -- 3.5 Numerical Results of BHF Calculation in Different Systems -- 3.6 The g Matrix for the 2D Electron Gas -- 3.6.1 Decomposition in Partial Waves -- 3.6.2 The Separable Approximation -- 3.6.3 The g Matrix Expansion -- 3.6.4 Numerical Results and Discussion -- 3.6.5 Appendix -- Chapter 4 The Density Functional Theory (DFT) -- 4.1 Introduction -- 4.2 The Density Functional Formalism -- 4.3 Examples of Application of the Density Functional Theory -- 4.3.1 The Thomas-Fermi Theory for the Atom -- 4.3.2 The Gross-Pitaevskii Theory for the Ground State of a Diluted Gas of Bosons -- 4.4 The Kohn-Sham Equations -- 4.5 The Local Density Approximation for the Exchange-Correlation Energy -- 4.6 The Local Spin Density Approximation (LSDA).

4.7 Inclusion of Current Terms in the DFT (CDFT) -- 4.8 Ensemble Density Functional Theory -- 4.9 DFT for Strongly Correlated Systems: Nuclei and Helium -- 4.10 DFT for Mixed Systems -- 4.11 Symmetries and Mean Field Theories -- Chapter 5 Quantum Dots in a Magnetic Field -- 5.1 Introduction -- 5.2 The Independent-Particle Model -- 5.2.1 The Wo >> Wc Case -- 5.2.2 The Wc >> Wo Case -- 5.2.3 The MDD (Maximum Density Droplet) State -- 5.3 Fractional Regime -- 5.4 Hall Effect -- 5.5 Elliptical Quantum Dots -- 5.5.1 Analogies with the Bose-Einstein Condensate in a Rotating Trap -- 5.6 Spin-Orbit Coupling and Spintronics -- 5.7 The DFT for Quantum Dots in a Magnetic Field -- 5.8 The Aharanov-Bohm Effect and Quantum Rings -- Chapter 6 Monte Carlo Methods -- 6.1 Introduction -- 6.2 Standard Quadrature Formulae -- 6.3 Random Variable Distributions and Central Limit Theorem -- 6.4 Calculation of Integrals by the Monte Carlo Method -- 6.5 Markov Chains -- 6.6 The Metropolis Algorithm [M(RT)2] -- 6.7 Variational Monte Carlo for Liquid 4He -- 6.8 Monte Carlo Methods and Quantum Mechanics -- 6.9 Propagation of a State in Imaginary Time -- 6.10 Schrodinger Equation in Imaginary Time -- 6.11 Importance Sampling -- 6.12 Fermion Systems and the Sign Problem -- PART 2 -- Chapter 7 The Linear Response Function Theory -- 7.1 Introduction -- 7.2 General Formalism -- 7.3 Linear Response Function and Sum Rules -- 7.4 Finite Temperature -- 7.5 The Density Response -- 7.6 The Current Response to an Electromagnetic Field -- 7.7 The Density Response for Non-Interacting Homogeneous Systems -- Chapter 8 The Linear Response Function in Different Models -- 8.1 The Linear Response Function in Landau Theory -- 8.2 Time-Dependent Hartree (TDH) for Homogeneous Systems: The RPA.

8.3 TDH for the Density Matrix and the Landau Equations -- 8.4 The RPA for Electron Gas in Different Dimensions: The Plasmon -- 8.5 The RPA for Bosons -- 8.6 The Time-Dependent Gross-Pitaevskii Theory -- 8.7 Time Dependent Hartree-Fock (TDHF) and the Matrix RPAE -- 8.8 Examples of Application of the RPA Theory -- 8.8.1 RPA with Separable Interactions -- 8.8.2 RPAE for Metal Clusters -- 8.9 Adiabatic Time Dependent LSDA (TDLSDA) -- 8.9.1 The TDLSDA Longitudinal Response Function -- 8.9.2 The TDLSDA Transverse Response Function -- 8.10 RPA and TDLSDA Commutators and Symmetry Restoration -- 8.10.1 The Kohn and Larmor Theorems -- 8.10.2 Magneto-Conductivity and Quantum Hall Effect -- 8.11 The Linear Response Based on the Green Functions RPAE -- 8.12 Screened Response Function and Dielectric Constant -- 8.13 Examples of Application of the TDLSDA Theory -- 8.13.1 Quantum Wells under very High External Magnetic Field -- 8.13.2 Quantum Dots under Magnetic Field -- Chapter 9 Dynamic Correlations and Response Function -- 9.1 Introduction -- 9.2 Interaction Energy and Correlation Energy -- 9.3 The RPA Correlation Energy -- 9.3.1 The RPA Correlation Energy for the Cold and Dilute Gases of Bosons and Fermions -- 9.4 Theories Beyond the RPA -- 9.5 STLS Theory -- 9.6 Comparison of Different Theories for Electron Gas in 2D -- 9.7 Quasiparticle Properties -- 9.8 Nonlocal Effects -- 9.9 Mean Energy of Many-Particle Excitations -- 9.10 The Polarization Potential Model -- 9.11 The Gross-Kohn Model -- 9.12 The Method of Lorentz Transforms -- Chapter 10 The Hydrodynamic and Elastic Models -- 10.1 The Hydrodynamic Model for Bosons -- 10.1.1 Backflow -- 10.1.2 Compression and Surface Modes of Spherical Drops -- 10.1.3 Compression and Surface Modes of a Bose Gas in a Magnetic Trap.

10.1.4 Moment of Inertia and the Scissors Mode of a Bose Gas in a Magnetic Trap -- 10.1.5 Vortices in the Bose Gas in a Magnetic Trap -- 10.2 The Fluidodynamic and Hydrodynamic Model for Fermions -- 10.2.1 Dipolar Modes in Metal Clusters -- 10.2.2 The Scalar Quadrupole Mode in Confined Systems -- 10.2.3 The Scissors Mode in Fermi Systems -- 10.2.4 The Moment of Inertia of Quantum Dots -- 10.2.5 The Vibrating Potential Model -- 10.3 The Surface Vibrations of Charged Systems in 2D and 3D -- 10.3.1 Surface Vibrations of Charged Metal Clusters -- 10.3.2 Edge Vibrations of Quantum Dots -- Index.