Theory of Condensed Matter
Collegejaar:  20182019 

Studiegidsnummer:  4403CONDE 
Docent(en): 

Voertaal:  Engels 
Blackboard:  Ja 
EC:  6 
Niveau:  500 
Periode:  Semester 2 
Onderwijstijd in uren (excl. zelfstudie): 
43:00 uur 
 Wel Keuzevak
 Wel Contractonderwijs
 Wel Exchange
 Wel Study Abroad
 Geen Avondonderwijs
 Wel AlaCarte en Aanschuifonderwijs
 Geen Honours Class
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 meanfield theory the course introduces a number of fundamental concepts such as longrange 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 twofluid model, elementary excitations and the Landau criterion.
* BoseEinstein condensation
* Bogoliubov's theory of a superfluid
* Condensate depletion
* The Gross–Pitaevskii equation
* The linear sigmamodel
* Topological excitations in a superfluid
* Thermodynamic properties of a Fermi gas
* Magnetic properties of a Fermi gas
* The HartreeFock approximation
* Renormalization of the parameters of a Fermi liquid in the HartreeFock approximation
* The Landau FermiLiquid theory
* The RPA approximation
* Collective excitations in a Fermi liquid
* Superfluidity
* The LandauGinzburg theory of a superfluid
* The electronphonon interaction
* The Cooper instability
* The BCS theory
Course objectives
The course will provide students with a working knowledge of the mathematical
framework of quantum manybody theory, including the second quantization formalism, quantum statistical mechanics, linear response theory, and the meanfield theory.
The course will also familiarize the students with the key ideas of quantum liquid phenomenology including spontaneous symmetry breaking, longrange order, elementary excitations, hydrodynamics, and the effective lowenergy Hamiltonians.
At the end of the course you will be able to
 Construct secondquantized models of quantum manybody 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 manybody system
 Calculate scattering cross sections of elementary excitations and relaxation rates
 Calculate form factors for scattering experiments (e.g. neutron scattering)
 Apply meanfield theory to interacting systems of bosons and fermions
 Use the semiclassical theory for the longrange 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 LandauGinzburg 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 ULCNaccount.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
Contactdetails Teacher(s):Dr. Vadim Cheianov
Maakt deel uit van  Soort opleiding  Semester  Blok 

Physics  Master  2  
Physics: Research in Physics, Quantum Matter and Optics  Master  2  
Physics: Research in Physics, Theoretical Physics  Master  2 