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Theory of Condensed Matter


Admission Requirements

Quantum Theory a
Bachelor of Physics with an introduction to solid state physics and (preferably) some knowledge on semiconductors and electron bands


The course gives an introduction into the theory of quantum phenomena in condensed matter systems.

With the help of the second quantization approach, perturbation theory and the mean-field theory the course introduces a number of fundamental concepts such as long-range order, spontaneous symmetry breaking, elementary, collective and topological excitations. These general concepts are illustrated on a range of archetypal examples such as crystalline dielectric solid, superfluid, normal metal and superconductor.

The detailed list of topics includes

  • Second quantization of bosonic/fermionic fields

  • Elementary excitations in harmonic crystals

  • Thermodynamics of harmonic crystals

  • Effects of anharmonicity in real crystals

  • Probing elementary excitations with neutron scattering and other techniques

  • Elements of kinetic theory

  • Linear response theory and the Kubo formula

  • Superfluidity, the two-fluid model, elementary excitations and the Landau criterion.

  • Bose-Einstein condensation

  • Bogoliubov's theory of a superfluid

  • Condensate depletion

  • The Gross–Pitaevskii equation

  • The linear sigma-model

  • Topological excitations in a superfluid

  • Thermodynamic properties of a Fermi gas

  • Magnetic properties of a Fermi gas

  • The Hartree-Fock approximation

  • Renormalization of the parameters of a Fermi liquid in the Hartree-Fock approximation

  • The Landau Fermi-Liquid theory

  • The RPA approximation

  • Collective excitations in a Fermi liquid

  • Superfluidity

  • The Landau-Ginzburg theory of a superfluid

  • The electron-phonon interaction

  • The Cooper instability

  • The BCS theory

Course objectives

The course will provide students with a working knowledge of the mathematical
framework of quantum many-body theory, including the second quantization formalism, quantum statistical mechanics, linear response theory, and the mean-field theory.

The course will also familiarize the students with the key ideas of quantum liquid phenomenology including spontaneous symmetry breaking, long-range order, elementary excitations, hydrodynamics, and the effective low-energy Hamiltonians.

At the end of the course you will be able to

  • Construct second-quantized models of quantum many-body systems

  • Calculate thermodynamic properties of model systems

  • Calculate linear response functions (e.g. magnetic susceptibility) of model systems

  • Describe elementary excitations of a model system

  • Use perturbation theory in a many-body system

  • Calculate scattering cross sections of elementary excitations and relaxation rates

  • Calculate form factors for scattering experiments (e.g. neutron scattering)

  • Apply mean-field theory to interacting systems of bosons and fermions

  • Use the semiclassical theory for the long-range dynamics of a quantum fluid

  • Construct topological excitations of a quantum fluid

  • Use the random phase approximation

  • Calculate the properties of a superconductor within the Landau-Ginzburg theory

  • Derive and solve the BSC equation for the superconducting gap

Generic skills (soft skills)


Physics Schedule

Mode of instruction

Lectures and tutorials

Course load

Assessment method

written examination with short questions


Blackboard will be used for the provision of lecture notes, distribution of home assignment worksheets, and announcements.
To have access to Blackboard you need a ULCN-account.Blackboard UL

Reading list A set of lecture notes prepared by the lecturer and

R. Feynman, Statistical Mechanics: A Set of Lectures
C. Kittel, Quantum Theory of Solids
D. Pines, Elementary Excitations in Solids
D.R. Tilley and J Tilley, Superuidity and Superconductivity
P. Nozieres and D. Pines, Theory of Quantum Liquids
M. Tinkham “Introduction to superconductivity”


Contactdetails Teacher(s):Dr. Vadim Cheianov