Summer Term 2024

1300142101
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Content

* Structure of solids in real and reciprocal space
* Lattice dynamics and phonon band structure
* Thermal properties of insulators
* Electronic properties of metals and semiconductors: band structure and transport
* Optical properties from microwaves to UV
* Magnetism
* Superconductivity
* Defects, surfaces, disorder
(each chapter includes experimental basics)

Goal

After completing the course the students - have gained a thorough understanding of the fundamentals of condensed matter physics and can apply concepts of many-particle quantum mechanics to pose and solve relevant problems. - will be able to describe the priciples of formation of solids and can propose appropriate experimental methods to study structural properties. They are familiar with and can apply the concept of reciprocal space. - they can apply fundamental electronic models to explain and predict properties of crystalline materials as metals, semiconductors, and insulators. - they can ascribe optical, magnetic properties of matter to electronic and structure degrees of freedom. - they can describe and theoretically explain fundamental properties of superconductivity. - they are able to choose appropriate experimental methods for probing structural, optical, magnetic, and electronic properties of condensed matter and can analyse the experimental results.

1300142209
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Content

The course is a general introduction to the physics of matter at low temperatures and will provide a discussion of phenomena that uniquely occur near absolute zero. For example, when the thermal energy becomes small new macroscopic quantum states like superfluidity and superconductivity are formed. The course is divided into three sections: Quantum fluids, Properties of Solids and Refrigeration Techniques.

1300172204
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Content

- Introductory materials: bosons, fermions and second quantisation
- Green's functions approach
- Exactly solvable problems: potential scattering, Luttinger liquids etc.
- Theory of quantum fluids, BCS theory of superconductivity
- Quantum impurity problems: Kondo effect, Anderson model, renormalisation group approach
Depending on the lecturer more weight will be given to solid state theories or to soft matter.

Goal

After completing the course the students - have a thorough knowledge and understanding, of the nowadays 'traditional' diagrammatic technique and the problems solved by this technique, including Landau's theory of quantum liquids and BCS theory of superconductivity, - of advanced non-perturbative approaches such as renormalization group transformations, bosonisation and Bethe Ansatz and there application to examples of quantum impurity problems such as potential scattering in Luttinger liquids, inter-edge tunneling in fractional quantum Hall probes and Kondo effect in metals and mesoscopic quantum dots, - have acquired the necessary mathematical knowledge and competence for an in-depth understanding of this research field, - have advanced competence in the fields of theoretical physics covered by this course, i.e. the ability to analyze physical phenomena using the acquired concepts and techniques, to formulate models and find solutions to specific problems, and to interpret the solutions physically and communicate them efficiently, - are able to broaden their knowledge and competence in this field of theoretical physics on their own by a systematical study of the literature.

1300142205
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Content

Introduction, final decision to participate in this seminar, and assignment of topics will be done during the first seminar session. 

Typical topics are:
- Probing Magnons by Electron Spin Resonance Studies
- 1D Quantum Spin Systems
- Quantum Spin Liquids in Magnetically Frustrated 2D Materials
- Cathode Materials for Lithium-ion Batteries: Relevance of the Electronic Structure
...

1300172224
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Content

Motivation:
Have you ever wondered why it is so hard to get ketchup out of its bottle or why you need to whip egg whites to make meringue? Why Cheerios floating on milk seem to attract each other? Why a gel can swell to many times its own size, while a crystal already breaks at a deformation of few percents? How large scale complex structures can assemble out from simple nano-scale units?  Or how your LCD display works? Soft matter is the physics of everyday life! 
Soft matter systems are characterized by a characteristic energy that is on the order of thermal energy at room temperature. They display unique physics, including fractality, phase transitions, and self-organization, as well as peculiar material properties and dynamics. We will discuss the main theoretical concepts needed to describe soft condensed matter systems like polymers, liquid crystals, membranes, complex fluids and colloids.

Goal

Possible topics: Polymers				     1. Basics of single chains: random walk, Gaussian chain, entropic elasticity, solvent effects     2. Many chains: mixtures, semi-dilute systems, polymer melts     3. Dynamics: Rouse model, Zimm model, reptation     4. Polymer networks: rubbers, elastomers, gels  Liquid crystals     5. isotropic-nematic phase transition, Frank elastic energy, LCD displays     6. Defects, dynamics  Membranes/Surfactants      7. Helfrich energy, shape diagram, membrane fluctuations     8. surfactants, self-assembly Theory of soft systems dynamics 		      9. basics of non-equilibrium: force-flux relations, examples: hydrodynamics, diffusion     10. Langevin equation, Mori-Zwanzig formalism, Fokker-Planck equation     11. Correlation and response, Fluctuation Dissipation theorem, scattering     12. Liquid-state theory: g(r), Ornstein-Zernike equation, Density functional theory (DFT),   Complex fluids      13. continuum mechanics, viscoelasticity     14. suspensions, emulsions Electrostatic effects in Soft Matter 	     15. Debye Hückel/Poisson-Boltzmann equation; Manning condensation     16. Colloids: effective interactions, stabilization, colloidal effects Computational methods		     17. Particle-based: molecular dynamics (MD) vs. Monte Carlo (MC)     18. (Navier-)Stokes: Lattice Boltzmann method, Oseen tensor, boundary integral method