Lecture Notes in Theoretical Solid-State Physics

Elementary excitations in solid state physics.- Ideal Bose gas.- Interacting Bogoliubov Bose gas.- Superfluid helium Sounds and vortices.- Superfluidity of the two dimensional systems. Berezinskii Kosterlitz Thouless BKT phase transition.- Phonons in the solid state physics.- Density of the phonon states Debye approximation.- Phonon spectrum in crystals with pairwise interaction. Quantization of the lattice vibrations.- Phonon distribution function. Specific heat of the crystal.- Mossbauer effect. Diagonal processes with respect to phonon occupation numbers.- Neutron scattering on crystals.- An harmonic interactions. The damping of the phonon spectrum.- Phonon thermos conductivity in crystals.- Spin waves in ferromagnets. Exchange interaction.- Basic interactions in metals. Ion ion and electron ion interaction.- Electron electron interaction. Exchange hole for the wave function of two electrons with parallel spins.- Correlation energy for the interaction of electrons with opposite spins.- Charge screening in metals in the Random phase approximation.- Metallic hydrogen.- One electron excitations in metals.- Thermodynamics of metals.- Magnetic oscillations in metals.- The Cooper problem.- Many particle problem in the theory of superconductivity.- Thermodynamics of the superconductor.
This textbook explores foundational and cutting-edge topics in condensed matter physics. Inspired by the influential work of Prof. Yuri Kagan, the book spans key areas such as Bose-Einstein condensation, superfluid helium, crystal lattice dynamics, and phonon physics. It also addresses electronic excitations in metals and superconductors, including the BCS theory, electron-phonon interactions, and metallic hydrogen. Professor Maxim Kagan extends this work with advanced lectures on strongly correlated electron systems, quantum hydrodynamics, and mechanisms of unconventional superconductivity. The book concludes with a focus on groundbreaking research by Prof. Yuri Kagan, covering topics such as quantum gases, metallic hydrogen, and high-temperature superconductivity. This textbook serves as both a tribute to Prof. Kagan's legacy and a comprehensive resource for students and researchers in theoretical condensed matter physics.