Magistracy
Speciality Code:
7M05316
Speciality Name:
Theoretical Nuclear Physics (MEPhI)
Faculty:
of Physics and Technology
Qualification:
- Scientific and pedagogical direction - Master of Natural Sciences
- Model of graduating student
- Mandatory disciplines
- Elective disciplines
- Professional
1. conduct experiments in nuclear physics, process and interpret their results;
2. apply modern physical theories to explain the experimental data;
3. use effective computer technologies, programs, mathematical and numerical methods for the theoretical description of phenomena and processes in the field of theoreticl nuclear physics;
4. effectively apply the mathematical apparatus of the theory of particles and obtain reliable quantitative predictions;
5. to evaluate the results of the obtained calculations, conducted research and experiments, to compile a report on the results of the work performed;
6. to substantiate scientific results on a specific physical problem in order to achieve joint goals and accomplish tasks;
7. effectively demonstrate their knowledge, skills and abilities in front of the listeners, present them in an accessible manner;
8. apply advanced educational teaching and educational technologies in teaching activities;
9. to evaluate learning outcomes using modern technologies;
10. to encourage and motivate students to achieve a productive learning outcomes;
11. create content to provide distance learning;
12. show interest and respect for their profession, achieve high qualifications, evaluate the prospects of teaching and research activities.
2. apply modern physical theories to explain the experimental data;
3. use effective computer technologies, programs, mathematical and numerical methods for the theoretical description of phenomena and processes in the field of theoreticl nuclear physics;
4. effectively apply the mathematical apparatus of the theory of particles and obtain reliable quantitative predictions;
5. to evaluate the results of the obtained calculations, conducted research and experiments, to compile a report on the results of the work performed;
6. to substantiate scientific results on a specific physical problem in order to achieve joint goals and accomplish tasks;
7. effectively demonstrate their knowledge, skills and abilities in front of the listeners, present them in an accessible manner;
8. apply advanced educational teaching and educational technologies in teaching activities;
9. to evaluate learning outcomes using modern technologies;
10. to encourage and motivate students to achieve a productive learning outcomes;
11. create content to provide distance learning;
12. show interest and respect for their profession, achieve high qualifications, evaluate the prospects of teaching and research activities.
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Nuclear Astrophysics
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to form students' knowledge of the modern problem of astrophysics and nuclear reactions in stellar matter. During the study of course, master students should be competent in: 1. to formulate the laws of physics apply to space objects; 2. analyze scientific and technical information, 3. to study domestic and foreign experience in the field of research; 4. to use fundamental knowledge in the field of modern nuclear astrophysics. 5. use physical methods for space objects. Stars and interstellar medium. The birth of stars. Galaxies and quasars. The application of physical laws to the study of cosmic objects (stars, cosmic plasma) and the universe as a whole. Sources of stellar energy. Equations of radiation transfer and their simplest solutions. Nuclear reactions in stars and other astronomical objects. Energy and nuclear fission mechanisms. The luminosity of stars and their mass. Physical methods of research of space objects. Nuclear reactions in astrophysical objects. Modern problems of astrophysics. To study the basic concepts of astrophysics, the laws of the world of stars and modern theoretical concepts about the nature of stars and their systems; to show the effect of fundamental laws in space conditions; to study physical methods of space objects research; to get acquainted with modern problems of astrophysics, the latest discoveries and achievements in the study of the universe in recent years.
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Propagation of waves in random media
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline to provide master students with the basic knowledge from the theory of multiple scattering of waves in random media, which helps explaining the fundamental laws of the interaction of radiation with the medium and does not fit into the framework of the standard theory of transfer. During the study of course, master students should be competent in: 1. to recognize the relationship between the solution of the wave equation and the radiation distribution function over the angles and coordinates of the classical theory of transport; 2. understand the principles of describing wave scattering using the Dyson equation under conditions of weak localization (the radiation wavelength is much less than the mean free path); 3. own methods of averaging the wave equation over the positions of point scatterers in the case of media with different geometry; 4. to study the principles of taking into account the effects of coherent reflection from a semi-infinite medium with point scatterers; 5. to use diagramming techniques to analyze solutions of the wave equation (fan and ladder diagrams). When studying a discipline, master students will study the following aspects: The relationship between the solution of the wave equation (wave field) and the radiation distribution function over the angles and coordinates, which appears in the classical theory of transport. Averaging the moments of the wave field over random realizations of the arrangement of scatterers. Average field and average Green function. Diagram technique and Dyson equation for mean Green's function. Dyson equation in conditions of weak localization. The distribution function of the unscattered field in the case of a point source in an infinite medium. The equation for the distribution function of unscattered radiation in an infinite medium. Dyson equation in a semi-infinite medium with scatterers of finite dimensions. Spatial diffusion of radiation in an infinite medium from a point source. Reflection of radiation from a semi-infinite medium with point scatterers taking into account the effects of coherent reflection and refraction at the boundary of the medium. The nature of the abnormal reflection of x-rays from a rough surface. Coherent backscatter radiation. Coherent backscattering spectrum in the double scattering approximation for point scatterers. The equation for the sum of the upper (cyclic) diagrams (point scatterers). The relationship of the sum of fan diagrams with the sum of ladder diagrams (point diffusers).
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Introduction to the Quantum Theory of a Field
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to form the basic concepts of quantum field theory, actively used in theoretical physics. The course forms the basis of a theoretical understanding of the physical structure of quantum field theories. During the study of course, master students should be competent in: 1. explain the basic principles of quantum field theory; 2. understand the formalism of perturbation theory to construct the corresponding Feynman diagrams, 3. plan, execute and document complex mathematical calculations and solutions to physical problems, 4. еxplain solutions to physical and mathematical problems during lectures and sessions on problem solving; 5. use the apparatus for applying the methods of quantum field theory in practical calculations. The reasons for the development of quantum field theory in a conceptual and a history of science context and possible limitations of a quantum field theoretical description. The formalism of quantum field theory, in particular: field quantisation; field-theoretical description of identical particles; Klein-¬Gordon equation; Lagrange formalism for fields; symmetries, Noether's theorem and conservation laws; Poincare invariance and related discrete symmetries; Dirac fields; introduction into perturbation theory and Feynman diagrams. Сurrent research of nuclear and particle physics.
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Foreign Language (professional)
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose is to acquire and improve competencies by international standards of foreign language education and to communicate in an intercultural, professional, and scientific environment. A master's student must integrate new information, understand the organization of languages, interact in society, and defend his point of view.
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History and Philosophy of Science
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: Understanding of modern philosophy as a system of scientific knowledge, including worldview in rational-theoretical comprehension. The discipline includes aspects of the evolution and development of scientific thinking, historical moments, the contribution of scientists and scientific schools to the formation of science, and ethical and social aspects of scientific activity.
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Basic Principles of Modern Physics
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline Statement of basic principles of modern physics, connections of symmetries of physical systems relatively to different transformations of space-time coordinates with conservation laws. To give the master students a deep understanding of regularities of physical phenomena. A master student is to get a clear representation about basic principles of modern physics. During the study of course, master students should be competent in: 1. relativity principle; Galileo and Lorenz transformations; equations of physics in covariant form; principles of symmetry, superposition, uncertainty; correspondence principle; 2. Formulate law of conservation and time homogeneity; laws of conservation of momentum and angular momentum; mirror symmetry of space and parity conservation law; principle of indistinguishability of identical particles and particles statistics; charge independence of strong interactions; additive and multiplicative laws of conservation; 3. use conversion coefficient in modern physical calculations; apply the correspondence principle in quantum mechanics, atomic physics; to use relativistic invariant and determine thresholds of nuclear processes; 4. determine lifetime of fast unstable particles and thresholds of nuclear processes. 5. Possess: understanding about basic principles of modern physics; about symmetry principles and conservation laws; about relativistic invariant and its use. Relativity principle. Galileo and Lorenz transformations. Equation of physics in invariant form. Correspondence principle as a guide at construction of new physical theories. Conserving quantities in quantum physics. Operator of symmetry and unitary transformations. Laws of conservation of electric charge, baryonic and lepton number. Invariance with respect to rotation and translation motion. Charge independence of strong interactions. Isotopic spin. Indistinguishability principle of identical particles and particles statistics. Conservation of parity and mirror symmetry. Additive and multiplicative laws of conservation. Uncertainty principle in quantum mechanics. Degeneracy in central potentials. Uncertainty relation for energy-time. Conception about virtual particles and processes. A consideration of additive and multiplicative laws of conservation because of the characters of transformation generators remaining the system to be invariant; a consideration of principles of physics (relativity, symmetry, superposition, uncertainty, correspondence). A master student is to be able to explain the relation of laws of conservation of physical quantities with properties of space-time symmetry, be able to apply the correspondence principle for explanation of peculiarities of the micro-world, to use the relativistic invariant when describing the processes at high energies in the micro-world.
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Pedagogy of Higher education
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose is the formation of the ability of pedagogical activity through the knowledge of higher education didactics, theories of upbringing and education management, analysis, and self-assessment of teaching activities. The course covers the educational activity design of specialists, Bologna process implementation, acquiring a lecturer, and curatorial skills by TLA-strategies.
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Psychology of management
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Formation of knowledge about the fundamental concepts of management psychology for the practical application of the most critical aspects of management in professional interaction. Basic principles of management psychology, personality in management interactions, management of personality behavior, modern ideas, psychology of managing group phenomena, motivation, and practical reflection.
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Organization and Planning of Scientific Research (in English)
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to form the research culture of the future specialist, and to study the theoretical and methodological principles of organizing research activities in the context of the development of science and society. The discipline is aimed at developing the ability to conduct independent scientific research using methods and techniques of analysis, and information scientific resources.
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Cosmology
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline to familiarize master students with modern cosmological models including the models of the gravitational instability of the Universe, inflation and the formation of the initial spectrum of density perturbations, and the Universe expansion at very early stages and early stages of its evolution. The skills and knowledge obtained as a result of mastering this discipline will be used in conducting of scientific research. During the study of course, master students should be competent in: 1. recognize the main cosmological models: Friedman, de Sitter, the hot Universe, inflation hypotheses; 2. understand the basic properties of a very early universe: domain walls, strings, hedgehogs, monopoles and textures; 3. apply the basic properties of relativistic star clusters; 4. possess the theory of star evolution: Hertzsprung-Russell diagram, G. Bethe theory of evolution; 5. own the theory of inflation: the superearly Universe, the inflation hypothesis, the problem of dark matter, the inflation model and the formation of the initial spectrum of density perturbations. When studying a discipline, master students will study the following aspects: Homogeneous and isotropic models. The Friedman Universe 1. The form of the metric in the Friedmann record and in the Robertson – Walker record. Christoffels for FRW metrics. Ricci tensor. Friedman Universe 2. Full Hilbert action. The Friedman equation from the variational principle. Practical cosmology. Hubble parameter or constant, density parameter. Decision Behavior in Friedman Models. Cosmography: distances in the universe. Photometric distance, the derivation of the formula for its connection with the cosmological redshift of the source. Forms of matter-energy in the universe. Dark Matter and Dark Energy. The balance of superdense stars, the energy of accretion. Relativistic stars. Metric inside a spherically symmetric star. Relativistic binding energy. The equation of mechanical equilibrium of a star. Particle energy in the field of a star in GR. Rotating black holes, Kerr metric (no output). Circular and radial movement in the field of Schwarzschild and Kerr. Particle orbits and energy release during accretion in the Kerr metric. Physics of supernovae and gamma-ray bursts. Ergosphere. Physics of supernovae and gamma-ray bursts. Active galactic nuclei, supermassive black holes and quasars.
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Methods of statistical physics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline to introduce master students into modern methods for treating of multiparticle systems. These methods include the nonequilibrium diagram technique, continuous integration in the problem of the motion of electrons in a conductor with impurities, and the impurity diagram technique. During the study of course, master students should be competent : 1. understand the basic principles of the theoretical description of multiparticle nonequilibrium systems;; 2. recognize the apparatus of Green functions of non-equilibrium systems; 3. apply skills to calculate the Green's functions of nonequilibrium systems by the methods of continuous integration; 4. own elements of nonequilibrium diagram technique; 5. carry out spatial averaging of physical quantities. When studying a discipline, master students will study the following aspects: Green functions of a nonequilibrium system. Representation of the density matrix of the system in the form of a continuous integral over commuting (bosons) and anti-commuting (fermions) variables. Expressions for nonequilibrium Green functions in terms of the path integral. Generating functionality. Advanced and retarded Green functions, F - function. Diagram technique for nonequilibrium Green functions. Dyson equation. Linear relationships between elements of the mass operator for bosons and fermions. Equation for leading and retarded Green's functions. Representation of the collision integral in the kinetic equation in terms of Green's functions and elements of the mass operator. A series of perturbation theory of interaction for the mass operator. Summation of series of diagrams for vertices. Collision integral. Anti-commuting (Grassmann) variables. Averaging over the position of impurities. The relationship between the potential correlator and the mean free path. Expression for conductivity through a current correlator. Representation of Green's functions through integrals over supervectors. Averaging of Green's functions and their correlators over the position of impurities. Dyson equation for retarded Green's function. Solution of the Bethe - Salpeter equation for δ - correlated potential. Diffusion asymptotics. Long range correlations.
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Modern methods of quantum-mechanical modeling
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline to introduce master students into modern methods of computer simulations of real quantum systems, widely applied in condensed matter physics. The main methods of quantum modeling are considered including the exact diagonalization method and the Monte Carlo method. The problems of numerical analysis of the thermodynamic characteristics of various systems are studied using modern examples of condensed matter physics. During the study of course, master students should be competent : 1. understand the basic principles of computer modeling of quantum systems; 2. know the method of point diagonalization; 3. to apply the Monte Carlo method for solving and modeling quantum-mechanical problems; 4. to conduct numerical analysis of the thermodynamics of many-particle model systems; 5. to apply modern mathematical environments for modeling quantum mechanical processes in many-body problems. When studying a discipline, master students will study the following aspects: The matrix formulation of quantum mechanics. Bra-ket technique. Conversion of bases. The operators. Eigenvectors and eigenvalues. Harmonic oscillator in classical mechanics. Oscillations of the nuclei of a diatomic molecule. Anharmonism. Schrödinger equation for a hydrogen atom. The quantum numbers of a hydrogen atom. Classification and designation of conditions. Selection rules. Spectral series of a hydrogen atom. Spin-orbit interaction. Quantization of angular momenta and their projections. The concept of a self-consistent field. The periodic system. Pauli principle. Addition of orbital and spin moments. Types of communication. Normal connection. Two-level systems. Rabi Oscillations and Rabi Frequency. Three-level systems. Linear quadrupole trap. Mathieu equations. Areas of stability trapped in Paul. Macro movement. Lamb - Dicke mode. Lamb's criterion is Dicke. Trap design. Normal vibrations and their quantization. Dual-ion crystal. Interaction of the ion chain with laser radiation in the Lamb - Dicke mode. Laser and sympathetic cooling. Spectroscopy of atomic states based on quantum logic. The concept of qubit. Examples of the implementation of qubits. Deutsche-Jos task. Logical operations on quantum registers. Deutsche - Josa algorithm. Model quantum computer.
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Relativistic astrophysics and cosmology
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline on teaching master students of modern mathematical models of astrophysical objects. The skills and knowledge obtained within the course can be used in the conducting of research. During the study of course, master students should be competent : 1. recognize the basic principles of the theoretical description of stars: polytropic models, Hertzsprung-Russell diagram, G. Bethe theory; 2. understand the properties of black holes: solutions of Einstein's equations (Schwarzschild and Kerr), accretion onto black holes, principles of observation; 3. apply the principles of observing relativistic objects: white dwarfs, radio pulsars, x-ray sources;; 4. own the methods of theoretical description of relativistic star clusters; 5. use modern models of astrophysical objects, combine the principles of cosmic and microphysics in cosmology. When studying a discipline, master students will study the following aspects: The equilibrium and stability of stars: polytropic models. White dwarfs and neutron stars. Black holes: decisions of Schwarzschild and Kerr. Black hole accretion: spherically symmetric case. Disc accretion onto black holes. Accretion of gas with a large-scale magnetic field onto black holes. Observations of relativistic objects: white dwarfs, radio pulsars, x-ray sources. Accretion on neutron stars. Radio pulsars. Relativistic star clusters. The evolution of massive stars and supernovae. Homogeneous cosmological models. The early stages of the expansion of the universe: baryogenesis. and nucleosynthesis. Gravitational Instability: Jeans and Bonnor Models. Black hole accretion: spherically symmetric case. CMB fluctuations and determination of the global parameters of the universe. Cosmic microphysics. Restrictions on the rest mass of a neutrino. Dark matter and dark energy. Background components of the universe. The connection of the universes of Friedman and de Sitter. Properties of scalar fields. A very early universe: domain walls, strings, hedgehogs, mono field and textures. Relativistic star clusters. Inflation models and the formation of the initial spectrum of density perturbations.
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The problems of stability in General Theory of Relativity (GTR)
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying of discipline is to give an idea of orbital stability and in more detail about a special type of stability in the mechanics of general relativity, such as resistance with respect to vector elements. During the study of course, master students should be competent in: 1. use of the basic concepts of differential geometry applying to general relativity 2. use of affine connection, spin connection, Fock – Ivanenko coefficients, torsion tensor, 3. formulate Einstein – Cartan gravity; 4. apply of obtained knowledge when solving problems in theory of gravity of Einstein – Cartan; 5. own: skills of applying the received knowledge at the solution of problems in the theory of gravitation. There is a brief historical review of the problem of bodies’ motion stability in general relativity and correct formulation of the problem for stability in curved space-time. Various classes of test bodies motion in various gravitational and electromagnetic fields are investigated for stability and instability by Lyapunov and Lagrange.
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Super simmetry in the theory of elementary particles
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying of discipline – provide master students with an introduction to the subject of supersymmetry, introduce them to physics based on the idea of symmetry between bosons and fermions; During the study of course, master students should be competent in: 1. formulate the basics of modern relativistic astrophysics; 2. solve independently applied and theoretical problems; 3. own: skills in the formulation and solution of problems on a given topic. 4. use the current knowledge of the large-scale structure and evolution of the universe 5. demonstrate a thorough understanding of the laws of the macrouniverse. The latest discoveries in astrophysics associated with the detection of exotic compact objects, dark matter and dark energy. The purpose of the course is. The subject and objects of study of relativistic astrophysics. Recent discoveries in astrophysics. The physical structure of the universe. The theory of the expanding universe. Modern problems of cosmology. To study methods of theoretical investigation of structure and evolution of the Universe.
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Introduction to quantum chromodynamics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying of discipline – provide masters students with an introduction to the subject of Quantum Chromodynamics, introduce with physics of gluons and quarks and also modern methods of theories of strong interaction. During the study of course, master students should be competent in: 1. to expand the horizons in physical theories; 2. to examine methods on quarks and gluons; 3. to formulate problems of quantum chromodynamics; 4. to use ways of its solution; 5. to interpret classification of elementary particles in quantum chromodynamics. Abstract оf discipline: Perturbative methods in quantum chromodynamics. Divergence in the quantum theory of the field and methods of their elimination. A method of renormalizatsionny group in quantum chromodynamics. An invariant charge and asymptotic freedom in quantum chromodynamics. Partonny model. The description of processes of strong interaction in the time-like area.
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Pedagogical
- Type of control: Защита практики
- Description: Aim оf discipline: formation of the ability to carry out educational activities in universities, to design the educational process and conduct certain types of training sessions using innovative educational technologies.
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Research
- Type of control: Защита практики
- Description: The purpose of the practice: gaining experience in the study of an actual scientific problem, expand the professional knowledge gained in the learning process, and developing practical skills for conducting independent scientific work. The practice is aimed at developing the skills of research, analysis and application of economic knowledge.