Modern trends in Superconductivity and Superfluidity

<p>Introduction.- Part I.- Hydrodynamics of rotating superfluids with quantized vortices.- The foundation of Landau theory for superfluid hydrodynamics.- Hydrodynamics of rotating superfluids.- Hydrodynamics of fast rotations.- Opposite case of a single bended vortex line for extremely slow rotations (Ω ~ Ω_C1).- Experimental situation and discussion. How to achieve the limit of the fast rotations at not very high frequencies in He II – ³He mixtures and in superfluid ³He-B.- Reference list to Chapter 1.- 2. Quantum crystals. The search of supersolidity.- Quantum crystals. Phase diagram. The search of supersolidity.- The surface physics of quantum crystals. Atomically smooth and atomically rough surfaces.-Reference list to Chapter 2.- Melting-crystallization waves on the phase-interface between quantum crystal and superfluid.- Surface hydrodynamics for rough surface at low temperatures.- Surface hydrodynamics of the mobile rough interface at  and in the presence of ³He impurities.- Reference list to Chapter 3.- Quantum hydrodynamics of the p-wave superfluids with the symmetry of ³He-A.- Orbital hydrodynamics of bosonic and fermionic superfluids with the symmetry of A-phase of ³He.- Two approaches to a complicated problem of chiral anomaly, anomalous current in fermionic (BCS) A-phase.- Reference list to Chapter 4.- Part II.- Bose-Einstein condensation and Feshbach resonance in ultracold quantum gases and mixtures.- BEC in trapped Bose-gasses.- Feshbach resonance in ultracold quantum gases and mixtures.- Experiments on molecular BEC in ⁶Li and ⁴⁰K.- Reference list to Chapter 5.- Composed particles, trios and quartets in resonance quantum gasses and mixtures.- Two-particle pairing and phase-separation in Bose-gas with one or two sorts of bosons.- Composed fermions in the Fermi-Bose mixture with attractive interaction between fermions and bosons.- Bound states of three and four resonantly interacting particles.- Reference list to Chapter 6.- BCS-BEC crossover and the spectrum of collective excitations in s-wave and p-wave resonance superfluids.- Phase-diagram of the resonance Fermi-gas in 3D and 2D.- Self-consistent Leggett theory for T = 0 in 3D and 2D case.- Anderson-Bogolubov theory for collective excitations.- Feshbach resonance and phase-diagram for p-wave superfluid Fermi-gas.- Reference list to Chapter 7.- Phase diagrams and the physics of the pseudogap in the superconductors with attractive interaction.- Attractive-U fermionic Hubbard model.- Attracting fermions in 2D.- T-matrix approximation.- Experimental predictions of the model.- Reference list to Chapter 8.- Part III.- Superconductivity in the low-density electron systems with repulsion.- Kohn-Luttinger mechanism of SC in purely repulsive Fermi-systems.- Unconventional (anomalous) superconductive materials.- SC in 3D and 2D Hubbard model with repulsion at low electron density.- SC in the jelly model for Coulomb electron plasma.- SC and phase separation in Shubin-Vonsovsky model.- Reference list to Chapter 9.- Strong T_C enhancement in spin-polarized Fermi-gas and in the two-band superconductors.-  T_Cenhancement in a spin-polarized neutral Fermi-gas.-  T_Cenhancement in quasi-2D charged SC in a parallel magnetic field.- Strong T_Cenhancement in the two-band model.- Reference list to Chapter 10.- Fermionic superfluidity in three- and two-dimensional solutions of ³He in ⁴He.- Bardeen-Baym-Pines theory for the solutions of ³He in ⁴He. Direct and exchange interactions.- Two-dimensional case. ³He submonolayers.- Superfluidity in polarized solutions.- Experimental situation and limitations on the existing theories.- Two-dimensional monolayers as a bridge between superfluidity and high-T_C superconductivity.- Reference list to Chapter 11.- Triplet pairing and superfluid phase-diagram in Fermi gas of neutral particles and in superfluid ³He.- Fermionic superfluidity of ⁶Li in magnetic traps at ultralow temperatures.-  p-wave pairing in the Fermi-Bose mixture of ⁶Li-⁷Li with repulsive interaction between the different isotopes.- Ginzburg-Landau functional for triplet superfluid Fermi gas and for the superfluid ³He.- GL-functional and global phase-diagram of the 2D superfluid Fermi gas with repulsion.- Reference list to Chapter 12.- Spin-charge separation and confinement in ladder systems and in high-T_C superconductors.- Spin-charge separation and Luttinger liquid in doped spin-chains.- Two-leg ladder systems. Spin-charge confinement. Luther-Emery liquid.- Three-leg ladders. Anisotropic t-J model for strong-coupling along the rungs.- Superconductivity in isotropic 2D t-J model.- Reference list to Chapter 13.- Part IV.- The search for non-Fermi liquid behavior in the normal state of the low density fermion systems.- The search for non-Fermi liquid behavior in 2D models at low density.- Antibound state of Hubbard-Anderson on the lattice. Manifestation of the upper Hubbard band at low density.- The search for marginal Fermi liquid behavior in the two-band models.- Weak-localization corrections in the 2D case.- Reference list to Chapter 14.- Nanoscale phase separation in complex magnetic oxides.- Inhomogeneous states and nanoscale phase separation in complex magnetic oxides. Similarities with cuprates.- Crystal structure. Electronic and transport properties of manganites.- The minimal theoretical model for manganites.- Temperature ferrons. FM-polarons in a layered case.- Free and bound magnetic polarons.- Phase separation in charge-ordered manganites.- Orbital ferrons.- Experimental confirmation of the gross phase-diagram and phase separation in manganites.- Reference list to Chapter 15.- Mesoscopic transport properties in the phase-separated manganites.- Mesoscopic transport properties in strongly-correlated systems.- 1/f - noise power spectrum. Discussion. Comparison with experiments.- Comparison of the theoretical predictions for tunneling conductivity with experimental results in different families of CMR-systems.- Reference list to Chapter 16.- Conclusion. Unresolved problems in condensed-matter physics. Encouragement to young researches to stay in the field.</p>