COURSE GOALS: Acquire basic insights into perturbation theory and linear response, based on the examples of particlehole response, plasmons, and superconductivity.
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. Understand Lindhard's function through the density of states of particlehole excitations and the KramersKronig relations
2. Understand the connections between retarded, advanced, and causal response functins at the level of a harmonic oscillator with one degree of freedom
3. Describe the connection between linear response, the fluctuationdissipation theorem, and Kubo's formula
4. Explain the appearance of the plasmon collective mode by an elementary electrostatic argument, a classical equationofmotion argument, and a quantum RPA approach.
5. Understand the superconducting instability as a resonance in headon collisions, in the presence of a filled Fermi sea
6. Describe the ground state of a superconductor both from the variational (BCS) and meanfield (Bogoliubov) point of view.
COURSE DESCRIPTION:
1 Scattering electrons on nuclei, or the density of states of particlehole excitations
1.1 The phenomenon
1.2 Particlehole excitations
1.3 Phase space
1.4 Density of states
1.5 Entropy in quantum mechanics
1.6 Quasiparticles as collective excitations
1.7 Particlehole excitations as density oscillations
2 Scattering of electrons on metals, or the linear response to Coulomb excitation
2.1 Elementary argument for a plasmonic mode
2.2 Plasmon in the classical limit
2.2 General linear response formulation
2.3 Response to a variation of the density
2.4 Connection between response functions
2.6 General formalism of perturbation theory
2.7 Plasmon as a resonance
3 Superconducting instability
3.1 Phenomenology
3.2 Electron attraction
3.3 Superconducting instability in electronelectron scattering
3.4 Wave function of the ground state
3.5 Lowtemperature state as a mean field
3.6 Electrical conduction in the superconducting state
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.
