FYSS5550 Collective Quantum Phenomena in Condensed Matter Physics (5 cr)

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Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Physics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

  • Second quantization, causal, retarded and advanced Green’s function of the many-body system. Free fermion and phonon propagators. Relation to observables. Connection between different types of the Green’s functions: retarded/advanced, real-time and imaginary time.

  • Concept of quasiparticles

  • Perturbation theory: Wick’s theorem, Feynman rules. Self-energy, Dyson’s equation, polarization operator. Example of Coulomb screening and plasma waves

  • Hartree-Fock approximation, ground state energy of interacting system, stability of metals and Stoner criterion of magnetism

  • Fermi liquid theory: susceptibilities, zero sound and spin waves

  • Methods of the many-body theory in superconductivity. Cooper problem and pairing instability in particle-hole channel Green’s functions of a superconductor. Gor’kov equations, Bogolubov-de Gennes equations. Quasiparticles in superconductors.

  • Ginzburg-Landau theory, Meissner effect, Abrikosov vortices and Anderson-Higgs mechanism.

  • Magnetism in Hubbard model

  • Antiferromanetism

  • Bose systems: condensation, superfluidity in weakly interacting Bose gas. Gross-Pitaevskii equation. 

Learning outcomes

At the end of this course, students will be able to

  • Explain the role of interactions in many-body systems: electron in metals, atoms in quantum liquids and gases

  • Explain the most common models of many-body systems such as the concepts of quasiparticles, Hartree-Fock approximation, Fermi liquid theory, Hubbard model

  • Use basic theoretical tools such as the second quantization formalism, many-body Green's functions and Feynman diagram technique

  • Explain superconductivity in metals and superfluidity in quantum liquids. Apply BCS model and Ginzburg-Landau theory to describe magnetic and thermodynamic properties of superconductors.

  • Use Stoner and Hubbard models to describe magnetic phenomena in metals.

  • Give a presentation of the scientific paper related to the topics of the course

Description of prerequisites

Either of FYSS7630 Many-particle quantum mechanics, FYSS7641 Statistical physics in and out of equilibrium, FYSS4510 Quantum Field Theory, FYSS7531-FYSS7532 Quantum Mechanics 2, parts A&B. 

Study materials

Textbooks, lecture slides and notes, excercises. 

Literature

  • J.K. Pathria, Statistical physics, Academic Press, 1996
  • Piers Coleman, Introduction to Many-Body Physics, Cambridge University Press, 2015
  • Assa Auerbach, Interacting electrons and quantum magnetism, 1994, Springer-Verlag

Completion methods

Method 1

Description:
Given every two years.
Evaluation criteria:
Total points from course elements (for example 30 % assignments, 10 % participation, 10 % project work, 50 % examination).
Time of teaching:
Period 3
Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Total points from course elements (for example 30 % assignments, 10 % participation, 10 % project work, 50 % examination).
Language:
English
Study methods:

  • Lectures

  • Assignments

  • participants teach each other (presentation)

  • small project work

  • examination 

Teaching