FYSS5550 Kollektiiviset kvantti-ilmiöt tiiviin aineen fysiikassa (5 op)

Opinnon taso:
Syventävät opinnot
Arviointiasteikko:
0-5
Suorituskieli:
englanti
Vastuuorganisaatio:
Fysiikan laitos
Opetussuunnitelmakaudet:
2020-2021, 2021-2022, 2022-2023

Kuvaus

  • 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. 

Osaamistavoitteet

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 

Esitietojen kuvaus

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. 

Oppimateriaalit

Textbooks, lecture slides and notes, excercises. 

Kirjallisuus

  • 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

Suoritustavat

Tapa 1

Kuvaus:
Given every two years.
Arviointiperusteet:
Total points from course elements (for example 30 % assignments, 10 % participation, 10 % project work, 50 % examination).
Opetusajankohta:
Periodi 3
Valitaan kaikki merkityt osat
Suoritustapojen osat
x

Osallistuminen opetukseen (5 op)

Tyyppi:
Osallistuminen opetukseen
Arviointiasteikko:
0-5
Arviointiperusteet:
Total points from course elements (for example 30 % assignments, 10 % participation, 10 % project work, 50 % examination).
Suorituskieli:
englanti
Työskentelytavat:
  • Lectures

  • Assignments

  • participants teach each other (presentation)

  • small project work

  • examination 

Ei julkaistua opetusta