Modern many-particle physics [[electronic resource] ] : atomic gases, quantum dots and quantum fluids / / Enrico Lipparini

• Record Nr.: UNINA9910782281903321
• Autore: Lipparini Enrico
• Pubbl/distr/stampa: River Edge, N.J., : World Scientific, c2003
• ISBN: 1-281-95613-9; 9786611956134; 981-279-674-6
• Descrizione fisica: 1 online resource (x, 431 p. ) : ill
• Disciplina: 530.144
• Soggetti: Many-body problem - Approximation methods; Solid state physics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ch. 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. Ideal Bose gas confined in a harmonic potential. 1.8. The Fermi gas. 1.9. Finite temperature and quasiparticles -- ch. 2. The Hartree-Fock theory. 2.1. Introduction. 2.2. The Hartree-Fock method for fermions. 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 -- ch. 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 -- ch. 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. 4.4. 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 -- ch. 5. ; Quantum dots in a magnetic field. 5.1. Introduction. 5.2. The independent-particle model. 5.3. Fractional regime. 5.4. Hall effect. 5.5. Elliptical quantum dots. 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 -- ch. 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)[symbol]]. 6.7. Variational Monte Carlo for liquid [symbol]He. 6.8. Monte Carlo methods and quantum mechanics. 6.9. Propagation of a state in imaginary time. 6.10. Schrödinger equation in imaginary time. 6.11. Importance sampling. 6.12. Fermion systems and the sign problem.; ch. 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 -- ch. 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. 8.9. Adiabatic time dependent LSDA (TDLSDA). 8.10. RPA and TDLSDA commutators and symmetry restoration. 8.11. 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 -- ch. 9. Dynamic correlations and response function. 9.1. Introduction. 9.2. Interaction energy and correlation energy. 9.3. The RPA correlation energy. 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 -- ch. 10. The hydrodynamic and elastic models. 10.1. The hydrodynamic model for bosons. 10.2. The fluidodynamic and hydrodynamic model for fermions. 10.3. The surface vibrations of charged systems in 2D and 3D.
• Sommario/riassunto: A study of modern many-particle physics. It describes homogenous systems, such as electron gas in different dimensions, the quantum well in an intense magnetic field, liquid helium and nuclear matter, and addresses finite systems, such as metallic clusters, quantum dots, helium drops and nuclei.