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Máster Universitario en Física Avanzada: Partículas, Astrofísica, Nanofísica y Materiales Cuánticos

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Teoría Cuántica de Campos en Física Aplicada, Física Atómica y Física de la Materia Condensada

Código asignatura
MFIAVPAN-1-008
Curso
Primero
Temporalidad
Primer Semestre
Carácter
Optativa
Créditos
6
Itinerarios
  • Especialidad de Nanofísica y Materiales Cuánticos
Pertenece al itinerario Bilingüe
No
Actividades
  • Prácticas de Aula/Semina (7 Hours)
  • Clases Expositivas (38 Hours)
Guía docente

Context:

This is an optional subject within the Nanophysics and Quantum Materials branch.

Its intends to provide an introduction to the formalism of non-relativistic quantum field theory. This is the natural languaje for the description of interacting many-particle systems,

incluiding electrons, phonons, excitons, magnons, plasmons, cold atoms and so on.

This subject is the basis upon which Solid-state theory builds on, and as so it is common lore among the scientific community.

The subject is the non-relativistic counterpart of "Quantum Field Theory" as delivered in the complementary branch.

Any student enroll in this master can take the course freely. It is however recommended to enroll in the relativistic counterpart.

  • Learn the second quantization formalist and the most popular Hamiltonians in non-relativistic quantum physics.
  • Learn the mathematical techniques relavant to solving problems in quantum field theory and quantum transport.
  • Gain an in-depth knowledge of the most relevant phenomena in magnetism, the underlaying maths and the best-suited approximation strategies. Learn how to navigate this dammed non-sensical extra piece of bullshit bureaucracy.
  • Learn the mean-field description of the Hubbard model and the ensuing physical phenomena of strongly correlated electrons.
  • Learn about the different theoretical approaches to superconductivity, including BCS and Ginsburg-landau theories.
  • Learn about the physical description of phase transitions and of topological matter.
  • 5.5.1.3 CONTENIDOS

    Parte I: Introducción y Métodos en Teoría Cuántica de Campos no relativista

    1. Segunda cuantización y Hamiltonianos.

    2. Funciones de Green y Teoría de Perturbaciones.

    3. Integrales de Camino.

    4. Teoría de Transporte Electrónico

    Parte II: Modelos en Física de la Materia Condensada y Física Atómica

    5. Modelos de magnetismo localizado.

    6. Modelo de Hubbard.

    7. Superconductividad y Condensados de Bose-Einstein.

    8. Física de Puntos Cuánticos y Efecto Kondo.

    9. Fenómenos Topológicos en Física de la Materia Condensada.

Part I: Introduction

1. Second quantization formalism.

2. Green's functions.

3. Path integrals.

4. Quantum transport.

Part II: models

5. Models in localised magnetims.

6. Hubbard model.

7. Superconductivity and BEC.

8. Qunatum point contacts and Kondo.

9. Phase transitions and topological matter

Teaching languaje will be spanish intermixed with english.

Teaching activities

Hours

In-person percentage

Lectures

35

100 %

Seminars and the like

7

100 %

Grading/marking

3

100 %

Collaborative work

50

0 %

Study

55

0 %

Total

150

There will be

a) Lectures

b) Seminars, problem solving.

c) Personal work: notes, books and papers.

Basic

  1. G. D. Mahan. Many-Particle Physics.
  2. A. L. Fetter & J. D. Walecka. Quantum Theory of Many-Particle Systems.
  3. J. W. Negele & H. Orland. Quantum Many-Particle Systems.
  4. E. N. Economou. Green’s Functions in Quantum Physics.

Advanced

  1. The Theory of Quantum Liquids. D. Pines & P. Nozieres.
  2. P. G. de Gennes. Superconductivity of Metals and Alloys.
  3. The Kondo Problem to Heavy Fermions. A. C. Hewson.
  4. Field Theories of Condensed Matter systems. E. D. Fradkin.
  5. A Short Course on Topological Insulators. J. Asboth, L. Oroszlany & A. Palyi.
  6. Quantum Transport: Atom to Transistor. S. Datta.
  7. Interacting Electrons and Quantum Magnetism. A. Auerbach.
  8. Theory of Magnetism. K. Yosida.