Period: Second ECTS: 4
Course contents
Topic 1 Introduction to path integrals
Feynman path integral in quantum mechanics. Functional integrals in quantum field theory. Fermion and boson propagators. Perturbation theory: Feynman diagrams and Dyson equation.
Topic 2 Applications of the functional integral to condensed matter
RPA approximation to the electron gas. Fermi liquid theory. Broken symmetry and mean field theory.
Topic 3 Criticality and the renormalization group
Phase transitions and criticality. Introduction to the renormalization group in quantum field theory. Applications of the renormalization group to simple problems.
Topic 4 The Hubbard model and bosonization
The 1D Hubbard model with the renormalization group. Bosonization. Luttinger liquid and spin-charge separation.
Topic 5 Diagrammatic approach to out-of-equilibrium systems
The Keldysh formalism. Diagrammatic expansions in out-of-equilibrium systems. The triangular representation.
Topic 6 Applications to electronic transport
Electronic transport in nano structures. Stationary and time-dependent transport. Analysis of fluctuations: full counting statistics.
Topic 7 Out-of-equilibrium systems with broken symmetry
Superconductivity. Nambu representation. Andreev reflection, Andreev states and multiple Andreev reflection. Basic concepts about topological superconductors.
Topic 8 Out-of-equilibrium systems of interacting electrons
Transport in quantum dots. Coulomb blockade and Kondo effect.
Bibliography
- J. W. Negele, and H. Orland, “Quantum Many-Particle Systems”, Frontiers in Physics (1997).
- A. Altland and B. Simons, “Condensed Matter Field Theory”, 2nd Edition, Cambridge (2010).
- P. Coleman, “Introduction to Many-Body Physics”, Cambridge (2015).
- A.A. Abrikosov, L.P. Gorkov y I.E. Dzyaloshinski: “Methods of Quantum Field Theory in Statistical Physics” (Dover Books).
- A. M. Tsvelik: “Quantum Field Theory in Condensed Matter Physics” (Cambridge, 1996).
- A. Kamenev: “Field Theory of Non-Equilibrium Systems” (Cambridge 2011).
- H. Bruus, K. Flensberg, “Many-Body Quantum Theory in Condensed Matter Physics: An Introduction” (Oxford Graduate Texts 2004).
Faculty
Coordinator Jaime Merino
Email jaime.merino@uam.es
Website http://dep.ftmc.uam.es/members/name/jaime-merino/
More info on the course official guide (Guía docente)