Lecture Notes of Professor Yuri Kagan in Theoretical Solid-State Physics

Prof. Dr. Maxim Yu. Kagan was born in Moscow in 1961 and is a respected figure in the field of condensed matter physics. He is known for his contributions to the study of superconductivity and superfluidity. A product of the Landau school of Theoretical Physics, Prof. Kagan has built a career that bridges both academic teaching and advanced research.He graduated with honors from the Moscow Engineering Physics Institute (MEPhI) in 1984, specializing in Theoretical Nuclear Physics. Following his studies, he joined the P.L. Kapitza Institute for Physical Problems, where he conducted research under the guidance of Prof. A.F. Andreev. In 1989, he earned his Ph.D. with a thesis focused on superfluid properties in systems with complex ordering.Prof. Kagan has held various research positions at the Kapitza Institute, ultimately earning his Doctor of Science degree in 1994. He was elected as a Corresponding Member of the Russian Academy of Sciences in 2006, recognizing his contributions to physics.In addition to his work in Russia, Prof. Kagan has held visiting positions at institutions around the world, including Amsterdam University, ETH Zürich, and the University of Cambridge. He has also been involved in teaching and research in the UK, Spain, and other European countries.His research has been published in over 160 articles and four books, with topics ranging from low-temperature physics to superconductivity. While maintaining his academic responsibilities, Prof. Kagan continues to contribute to international collaborations and scientific conferences.Prof. Kagan’s work has been recognized with several awards, including the Presidential Award for Young Professors and the Leverhulme Award in the UK. He has also been honored with medals from the Russian Academy of Sciences.Currently, Prof. Kagan is a Distinguished Professor at the National Research University Higher School of Economics (HSE) in Moscow, where he continues to teach and conduct research in condensed matter 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.