* 1. Superconductivity:

Introduction to superconductivity (electrical resistance, critical parameters, ideal conductivity and Meissner effect, London theory, type 1 and 2. superconductors, thermodynamic properties, isotope effect, interaction with electromagnetic radiation).

Microscopic theory (origin of attractive interaction, Bardeen-Cooper-Schrieffer theory, variation method, ground state energy, coherence coefficients, calculation of the critical temperature and critical thermodynamic field, temperature dependence of the gap, density of states, gap-less superconductivity, electron tunneling, coherence effects).

Ginzburg-Landau theory (order parameter, energy, coherence length, flux penetration length, limits of validity of GL theory, surface energy) Magnetic properties of type 2 superconductors (flux quantization, quantized vortices, structure of the mixed state, interaction energy of vortices, magnetization loop, interaction of vortices with surface, coexistence of mixed and intermediate state, transport properties of type 2 superconductors, pinning and critical currents, resistive state).

Weak superconductivity (Josephson effect, calibration transformation, influence of static magnetic filed, electrodynamics, voltage-current characteristics, macroscopic quantum interference).

Applications of weak superconductivity (SQUIDs, analog and digital circuits).

High temperature superconductivity (history, structural and chemical properties of materials, magnetic and transport properties, theory).

* 2. Superfluidity:

Basic properties of 4 He and 3He, liquifaction of 4He, Fermi-Dirac and Bose - Einstein quantum statistics. Ideal Bose gas, Bose - Einstein condensation (BEC). Ideal Fermi gas, Fermi liquid, zero sound. Phase diagrams of 4He a 3He, zero oscillations. 3He-4He mixtures, dilution refrigerator.

Superfluid He II - Fountain effect, mechano-caloric effect. Andronikashvili experiment, two-fluid model and Landau equations of motion, energy spectrum, criterion of superfluidity. Superfluid film. Collective modes - first, second, third and fourth sounds. Macroscopic wave function, quantization of circulation - quantized vortices, mutual friction, Kelvin and Tkachenko waves, introduction into superfluid hydrodynamics, superfluid turbulence. Positive and negative ions, ionic mobility, two-dimensional pools of ions below the surface of superfluid helium, plasma oscillations, crystallization.

Superfluid 3He - basic ideas of generalized BCS theory, paramagnons, equal spin pairing, order parameter for the A, B, and A1 phases. Textures and orienting forces, solitons. Nuclear magnetic resonance. Phase-slips and Josephson phenomena in 3He. Rotating 3He- continuous and singular vortices. Superfluid hydrodynamics in 3He, Kelvin-Helmholtz instability, transition to superfluid turbulence. Relationship between superfluidity and cosmology, Kibble-Zurek mechanism.

BEC - hydrogen, alcali atoms, experiments, principles of laser cooling, BEC and superfluidity. Quantized vortices in BEC.

Superconductivity: Phenomenology, Ginzburg-Landau a BCS theories, Josephson effect, high temperature superconductivity, applications.

Superfluidity: Superfluid He II- two fluid model, collective modes, macroscopic wave function, quantization of circulation- quantized vortices, superfluid hydrodynamics and turbulence. Superfluid 3He - basic ideas of generalized BCS theory, order parameter, NMR, phase-slips and Josephson phenomena in 3He, rotating 3He. BEC - hydrogen, alcali atoms, principles of laser cooling.

For PGDS.

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