The course provides theoretical tools for understanding the properties of aggregate quantum systems with huge number of particles. In particular during the course the crystalline solid, characterized by the lattice and the electronic degrees of freedom, is described at microscopic level, starting from the Schroedinger equation. Its low temperature ordered phases, the response to external perturbation, and its transport and optical properties are investigated, with reference to more recent topics, such as hight Tc superconductivity, quantum Hall effect, entanglement and topological phases. A basic introduction to their numerical study by means of Quantum Monte Carlo technique is also provided.

Knowledge of the microscopic mechanisms, models and tools for describing the behavior of interacting ions, electrons and excitations. Ability to apply the tools to the study of reference systems in condensed matter physics, such as graphene or ultracold atomic and molecular gases.

Basic knowledges of quantum and statistical physics

1. From condensed matter to solid state physics. The fundamental Hamiltonian of a solid in first quantization; the Born Oppenheimer approximation. The crystalline solid; Bravais and reciprocal lattice. (6 hs) 2. Review of basic concepts of quantum statistical physics. Second quantization, density matrix, grand canonical ensamble, chemical potential. (6 hs) 3. Free Fermi and Bose gases. Bose-Einstein condensation; superfluids. (6 hs) 4. Single electron approximation. The Sommerfeld model; Bloch theorem; bands and Fermi surface; weak potential and tight binding approximations; graphene bands. (9 hs) 5. Lattice dynamics. The dynamical matrix; phonons; optical and acoustic modes; the Debye model and specific heat. (9 hs) 6. Electron-phonon interaction. The electron-phonon Froelich Hamiltonian; polarons; the Holstein model; second order processes and effective electronic Hamiltonian. (6 hs) 7. Electron-electron interaction in mean field. The Hartree-Fock approximation; exchange interaction, the jellium model, ferromagnetism. Screening and Thomas Fermi treatment. . Introduction to Fermi and Luttinger liquid theories. (10 hs) 8. Models for electron-electron interaction. Mott insulator and the Hubbard model. Ferromagnetism and the Heisenberg Hamiltonian. Quantum phase transitions. Entanglement. (9 hs) 9. Conventional superconductors. The Cooper instability. BCS microscopic theory. (9 hs) 10. High Tc superconductors. Role of electron-electron interaction and modelization. (6 hs) 11. Numerical simulations: the quantum Monte Carlo technique. (6 hs) 12. Transport properties: Drude conductivity, thermal conductivity and Wiedemann- Franz law. Classical and Quantum Hall effect. (6 hs) 13. Optical properties. Macroscopic formulation of electrodynamics in dispersive media: complex refraction index, absorption coefficient and dissipated power. Microscopic formulation: interaction of electrons with electromagnetic radiation; (6 hs) 14. The concept of Nanostructures. K-dot-p theory, envelope function, quantum wells, wires and dots. (6 hs)

The course consists of frontal lectures accompanied by exercises.

N.W. Ashcroft, N.D. Mermin, Solid State Physics, Hartcourt Courtrige Pubiher, 1976 H. Bruus, and K. Flensberg, Introduction to many body quantum theory in condensed matter physics, 2002 C. Di Castro, R. Raimondi, Statistical mechanics and applications in condensed matter, Cambridge University Press, 2015 R.P. Feynman, Statistical mechanics: a set of lectures, Benjamin Cummings Publishing Company, 1972 U. Roessler, Solid state theory: an introduction, Physica Verlag, 2009 J. Solyom, Fundamentals of the physics of solids, vols 1,2,3, Springer, 2007-2010 A. Montorsi, Notes of the course, 2018

Modalità di esame: Prova orale obbligatoria; Progetto individuale;

Exam: Compulsory oral exam; Individual project;

... The exam consists of two parts: one oral exam on topics 1-7, with two questions. A second part, on topics 8-14, which depending on students’ choice, may either consists of two questions, or an individual project on some of the topics.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.