Admission Requirements
Quantum Theory a
Bachelor of Physics with an introduction to solid state physics and (preferably) some knowledge on semiconductors and electron bands
Description
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)
Timetable
Mode of instruction
Lectures and tutorials
Course load
Assessment method
written examination with short questions
Blackboard
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”
Contact
Lecturer:Dr.Vadim Cheianov