COURSE GOALS: Understanding the quantum and thermodynamical causes of the behavior of many particle systems in the limit when the number of available states is much smaller than the number of particles. Acquaintance with the actual behavior of three such systems: Fermi liquid, suprafluid helium, and low-temperature superconductors.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.1 formulate, discuss and explain the basic laws of physics including mechanics, electromagnetism and thermodynamics
1.2 demonstrate a thorough knowledge of advanced methods of theoretical physics including classical mechanics, classical electrodynamics, statistical physics and quantum physics
1.3 demonstrate a thorough knowledge of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.2 evaluate clearly the orders of magnitude in situations which are physically different, but show analogies, thus allowing the use of known solutions in new problems;
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
2.4 adapt available models to new experimental data
3. MAKING JUDGEMENTS
3.1 work with a high degree of autonomy, even accepting responsibilities in project planning and in the managing of structures
3.2 develop a personal sense of responsibility, given the free choice of elective/optional courses
4. COMMUNICATION SKILLS
4.1 work in an interdisciplinary team
4.2 present one's own research or literature search results to professional as well as to lay audiences
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
5.3 carry out research by undertaking a PhD
5.4 participate in projects which require advanced skills in modeling, analysis, numerical calculations and use of technologies
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
1. To understand the quasiparticle construction, including the description of the avoided crossing of two levels.
2. Describe the physical origin of the effective mass and of Landau's parametrization of the effective interaction in Fermi liquids.
3. Acquaintance with the phenomenology and physical origin of zero sound in Fermi liquids.
4. Acquaintance with the phenomenology of liquid helium.
5. Describe the microscopic excitations of liquid helium, phonons and rotons.
6. Understanding the role of the Bose-Einstein condensate in the maintenance of long-range order in liquid helium.
7. Acquaintance with the phenomenology of superconductors.
8. Understanding of the Landau-Ginzburg thermodynamical description of superconductors, including the appearance of critical currents and fields.
9. Acquaintance with the elements of the microscopic description of superconductors, in particular the BCS wave-function and Bogoliubov quasiparticles.
10. Understand the origin of the physical length scales of a superconductor: London's, Pippard's, and Landau's.
COURSE DESCRIPTION:
1 Liquids in general
1.1 Introduction. Basic notions
1.2 Hydrodynamics
2 Fermi liquids
2.1 Landau liquid
2.2 Landau's description of 3He
3 Suprafluid helium
3.1 Introduction
3.2 Phenomenology
3.3 Quantum hydrodynamics
3.4 Microscopic picture
4 Superconductivity
4.1 Phenomenology
4.2 London's picture
4.3 Pippard's insight
4.4 Macroscopic description of Landau and Ginzburg
4.5 Vortices
4.6 Microscopic theory
REQUIREMENTS FOR STUDENTS:
Obligatory written seminar work on a chosen subject, the seminar grade is recorded as the written examination grade. Oral examination.
GRADING AND ASSESSING THE WORK OF STUDENTS:
The course instructor oversees exercises in which students work autonomously on simple problems. The seminar is written in consultation with the course instructor.
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