Armer, T.: Cambridge English for Scientists
Regular and active presence at the seminars, student’s professional presentations in various formats. The course will be classified provided that the PhD student proves the fulfilment of obligations at the level of at least 51 %. The conditions for successful completion of the course are in accordance with the Study Regulations of the Faculty of Mathematics, Physics and Informatics.
English
Knowledge of English minimum at B1 level.
The students will be trained to deliver various formats of professional communication tools: Elevator talk (1 min). Brief poster talk (3-5 min overview of the student’s research topic and key achievements), flash (3 min) and full (15-45 min) oral presentation. Technique and delivery of a good (scientific) presentation. Asking questions and adding comments, addressing peers’ questions and comments. The students’ topics for presentation: their current research activities or other related topics to the student’s field of study. By the end of the course the student will be able to present and discuss their topic effectively in English with using a variety of tools and tips.
The aim of the course is to help the student improve his/her communication and presentation skills and stimulate discussion in a simulated scientific conference/symposium setting.
Lecture covers the study of a wide spectrum of processes in ionosphere and magnetosphere induced by solar activity. Stress is laid upon modern methods of description and processing of ground and satellite measurements. Part of the study is devoted to resonance phenomena in Earth-ionosphere cavity. Contents of lecture will be arranged according to demands of supervisors and the aims of doctoral thesis.
W. Baumjohann, R.A. Treumann: Basic space plasma physics. Imperial College Press 1996
H.M. Hastings, G. Sugihara: Fractals: a Users Guide for the Natural Scientists.
Oxford University Press 1993
M.G. Kivelson, Ch.T. Russel: Introduction to space physics. Cambridge University Press 1995
J. Galejs: Terrestrial propagation of long electromagnetic waves. Pergamon Press 1972
J. R. Wait: Electromagnetic waves in stratified media. Pergamon Press 1962
Selected articles from J.Geophys. Res., Planet. Space Sci., Geophys. Res. Lett., Nonl. Proc.Geophys.
test
The evaluation of the subject is individual by the supervisor, according to the individual study plan of the doctoral student. The evaluation reflects the sufficient orientation of the student in the subject. The conditions for successful completion of the course are in accordance with the Study Regulations of Faculty of Mathematics, Physics and Informatics.
Dynamics of middle atmosphere, QBO, NAO, ENSO, ionization, interaction of solar radiation with neutral atmosphere. Chemical processes in the lower ionosphere. Variations of solar activity and their influence on changes in ionosphere and middle atmosphere. Earth’s magnetosphere and selected processes, solar wind interaction with magnetosphere. Time and space structure of wave processes in magnetosphere, non-linear character of geomagnetic pulsations development, resonance phenomena. Energy transfer. Processes in magnetosphere on micro- and macro scales, processes of self-organisation and synergism. Fractal dimensions and chaos, scaling. Turbulence. Intermittence and coherence. Non-linear analysis of time series. Method of neuron networks. Cosmic weather. Space satellite research. Propagation of electromagnetic waves along the curved surface and between the surface and ionosphere, eigenmodes of Earth-ionosphere resonator. Schumann resonances. Observatory measurements, analysis and processing of time records and interpretation.
After completing the course, students will be able to work on a dissertation. The lecture covers the study of a wide range of processes in the ionosphere and magnetosphere induced by solar activity. The dominant focus will reflect the focus of the dissertation
exam
To provide with explanation of mechanisms of magnetic field generation in the rotating systems by magnetohydrodynamic processes, an arising of various instabilities and dynamo theory.
J. A. Jacobs: Geomagnetism, Vol. 2. Academic Press 1987
H. K. Moffatt: Magnetic field generation in electrically conducting fluids. Cambridge University Press 1978
P. H. Roberts: An Introduction to Magnetohydrodynamics. Longman 1967
S. Chandrasekhar: Hydrodynamic and hydromagnetic stability. Clarendon Press 1961
Selected papers in Phys. Earth Planet. Int., Geophys. Astrophys. Fluid Dyn.
test
Basic equations of MHD, Boussinesqu and inelastic approximation, density stratification and conditions for convection. Toroidal and poloidal vectors, decay modes. Dimensionless parameters, scaling. Non-diffusion waves, the effect of diffusion on MHD waves. Boundary layers (Ekman, Hartmann, Stewartson). Magnetoconvection in rotating systems, linear stability theory. Stationary convection and periodic instabilities. Horizontal rotating layer model, stability studies in cylindrical and spherical layers. MAC and MC waves. Finite amplitude convection, nonlinear stability theory. MHD in the middle fields.
Convection and dynamo drive mechanisms. Kinematic dynamos and antidynamic theorems. Alpha-effect and omega-effect, alpha-omega dynamos, dyna models with strong and weak field, dynamo number, Taylor condition, Taylor state. Z-dynamo. Computer dyna models, self-consistent self-exciting dynamo. Numerical implementation and solution methods. Geodynamic inversions and their control and regulation mechanisms.
By completing the course, students will master the mechanisms of magnetic field generation in rotating systems based on magnetohydrodynamics, methods of linear analysis of instabilities of various types and the principles of dynamo theory.
oral exam
To explain advance methods and techniques based on non-Fourier ideas in the area of the time-frequency analysis of the seismic signals and images, and to adopt time-frequency methods to real (1D) seismic signals, stationary and non-stationary seismic process and usefulness of the standard algorithm of image processing in seismology.
S. Mallat: A Wavelet Tour of Signal Processing. Academic Press 1999
P. Flandrin: Time-Frequency / Time-Scale Analysis. Academic Press 1999
R. Carmona, W.L. Hwang, B. Torésani: Practical Time-Frequency Analysis. Academic Press 1998
R.C. Gonzales, R.E. Woods: Digital Image Processing. Addison-Wesley Publishing Co. 1993
test
The evaluation of the subject is individual by the supervisor, according to the individual study plan of the doctoral student. The evaluation reflects the sufficient orientation of the student in the subject. The conditions for successful completion of the course are in accordance with the Study Regulations of Faculty of Mathematics, Physics and Informatics.
Time-frequency analysis, Heisenberg-Gabor uncertainty principle, windows Fourier transform, continuous wavelet transform, marginal distributions (Wigner-Ville) for real seismic signals and their discrete versions, adaptive pursuit methods-orthogonal/non-orthogonal matching pursuit. Discrete wavelet transform, definition of multi-resolution analysis (MRA). Approximation spaces, scaling function, and the dilation equation, detail spaces. Mother wavelet and the wavelet equation. A view from the frequency domain. Orthogonal wavelets, Daubechies wavelets, Daubechies' least asymmetric filters, coiflets, biorthogonal wavelets. Local trigonometric bases and transforms - discrete sine and cosine transforms. Wavelet packet transform (WPT) and local sine and cosine packet transform. Shift-invariant wavelet transform (MODWT) and WPT's algorithms for pattern recognition. Image segmentation, signal detection and edge identification in seismic signals and images.
Wavelet threshold and noise reduction, the minimum squared error threshold. General cross validation (GCV) methods and their applicability for seismic signals. The Bayesian approach for denoising signals and images. Wavelet packet and best basis methods for compression of seismic signals.
Algorithms and methods for identification and clustering methods in automated identification of seismic phases, phase and group delay, polarization analysis, locally earthquakes effects.
After completing the course, students will be able to use advanced nonFourier methods of time-frequency analysis (TFA) signals and methods used in image processing and analysis.
exam
To provide with overview of theories and models of long-term preparation of tectonic earthquakes, initialization of the rupture process and rupture process.
Ch. H. Scholz: The mechanics of earthquakes and faulting. Cambridge Univ. Press 2002
B.V. Kostrov, S. Das: Principles of earthquake source mechanics. Cambridge Univ. Press 1988
J.R. Rice: The mechanics of earthquake rupture. North-Holland 1980
J. Koyama: The complex faulting process of earthquakes. Kluwer 1997.
R. Teisseyre (ed.): Continuum theories in solid earth physics. Elsevier 1986
L.B. Freund: Dynamic fracture mechanics. Cambridge Univ. Press 1998
B. Lawn: Fracture of brittle solids. Cambridge Univ. Press 1998
selected articles in Bull. Seism. Soc. Am., J. Geophys. Res., Geophys. J. Int., Rev. Geophysics
test
The evaluation of the subject is individual by the supervisor, according to the individual study plan of the doctoral student. The evaluation reflects the sufficient orientation of the student in the subject. The conditions for successful completion of the course are in accordance with the Study Regulations of Faculty of Mathematics, Physics and Informatics.
Tectonic movements of the lithosphere, stress in the lithosphere, cohesion and internal friction, Coulomb's criterion, Anderson's theory of fracture formation, population of fractures, structure and rheology of fracture zone, stress and deformation in fracture zone, thermodynamics of fracture zone, asseismic movements. Breaking surface, initial stress. Crack initialization and formation, crack propagation modes, spontaneous crack propagation and boundary conditions on the fracture surface. Friction - microscopic and macroscopic view. Results of laboratory measurements. Laws of friction and crack propagation on the fracture surface. The process of stopping crack propagation. Energy balance of crack formation and propagation. Seismic crack propagation efficiency. Influence of initial stress, material inhomogeneity, fracture surface geometry. Influence of fluid pressure in pores. Friction heating. Small and large earthquakes in terms of crack propagation and seismic efficiency.
By completing the course, students will gain an overview of current models of long-term preparation of the tectonic earthquake, the initiation of the fault process and the fault process itself.
exam
To provide with overview of alternative efficient methods of simulation of seismic wavefields and seismic motion.
K. Aki, P.G. Richards: Quantitative seismology – Theory and methods I, II. W.H. Freeman 1980
O.C. Zienkiewicz, R.L. Taylor: The finite element method. McGraw-Hill 1989
G.C. Cohen: Higher-order numerical methods for transient wave equations. Springer 2002
P. Moczo: Introduction to modeling seismic wave propagation by the finite-difference method. Kyoto University 1988.
B.L.N. Kennett: The seismic wavefield I and II. Cambridge University Press 2001 a 2002.
J.M. Carcione: Wave field in real media: Wave propagation in anisotropic, anelastic and porous media. Pergamon 2001
selected articles in Geophysics, Bull. Seism. Soc. Am., Geophys. J. Int., J. Geophys. Res., Wave Motion
test
The evaluation of the subject is individual by the supervisor, according to the individual study plan of the doctoral student. The evaluation reflects the sufficient orientation of the student in the subject. The conditions for successful completion of the course are in accordance with the Study Regulations of Faculty of Mathematics, Physics and Informatics.
The problem of solving the equation of motion of a viscoelastic continuum with realistic attenuation for structurally complex models. Models of the whole earth body, regional models, local models. Boundary, domain and hybrid methods. Finite difference method, met. finite elements, met. spectral elements, met. boundary elements, met. finite volumes and their application to the solution of the equation of motion of the viscoelastic continuum and the calculation of crack propagation at the fracture. Discrete wave number method. Hybrid approach combining met. finite elements and finite differences.
Upon completion, students will have an overview of alternative effective methods of numerical simulation of seismic wave fields and seismic motion.
exam
To give a synthetic view on physical processes on a seismoactive fault and on forming of seismic motion with relation to the parametric model of time-space occurrence of earthquakes. Explain methods of computation of probabilistic seismic hazard characteristics.
R.K. McGuire: The practice of earthquake hazard assessment. IASPEI/ESC 1993
L. Reiter: Earthquake hazard analysis. Issues and insights.Columbia University Presss 1990
C.A. Cornell: Engineering seismic risk analysis. Bull. Seism. Soc. Am. 58,1538-1606,1968
K.W. Campbell: Near-source attenuation of peak horizontal acceleration. Bull. Seism. Soc. Am.71, 2039-2070, 1981
D.L. Wells, K.J. Coppersmith: New empirical relationships among magnitude, rupture length, rupture width, rupure area, and surface displacement. Bull. Seism. Soc. Am. 84, 974-1002,1994
S.-C. Wu et al: A hybrid recurrence model and its implication on seismic hazard results. Bull. Seism. Soc. Am. 85, 1-16,1995
the whole No: Seism. Res. Lett. 68, No. 1, 1997
selected papers in Bull. Seism. Soc. Am., J. Geophys. Res., J. European Engng., Nat. Haz.
test
The evaluation of the subject is individual by the supervisor, according to the individual study plan of the doctoral student. The evaluation reflects the sufficient orientation of the student in the subject. The conditions for successful completion of the course are in accordance with the Study Regulations of Faculty of Mathematics, Physics and Informatics.
Seismoactive fault, structure of active focal zone, spatio-temporal mode of focal zone, long-term physical processes of earthquake preparation, fault process - crack initialization and propagation, elements of seismic threat, parameterization of seismoactive fault and focal zone in relation to earthquake probability model, , seismotectonic model, epistemic and aleatoric uncertainties of focal zone parameters, attenuation of seismic hazard characteristics, logical tree of seismic hazard parameters - seismic hazard scenarios, probabilistic calculations of seismic hazard characteristics, probabilistic calculation deagregation.
After completing the course, students will be able to apply current methods of seismic hazard analysis.
exam
To add and advance the knowledge acquired in the master study and to explain specific mathematical methods applicable in geophysical research. To give review on a new methods.
T. Rikitake, R. Sato, Y. Hagiwara: Applied Mathematics for Earth Scientists. Kluwer 1987
M. Abramowitz, I.A. Stegun: Handbook of mathematical functions. National Bureau of Standards, Applied Mathematics Series, 1964
V.J. Arsenin: Matematická fyzika, Alfa 1977 (in Slovak)
M. Hvoždara, M. Gajdošová (R. Pašteka): Matematické základy teórie geofyzikálnych metód I (II), Lecture notes PriFUK 1998 (2000) (in Slovak)
A. Ralston: Základy numerické matematiky, Academia 1973
A.H. Nayfeh: Introduction to Perturbation Techniques, J. Wiley 1981
A.H. Nayfeh, B.Balachandran: Applied Nonlinear Dynamics, J. Wiley 1995
P. Glendinning: Stability, Instability and Chaos. Cambridge University Press 1994
A. Angot: Užitá matematika pro elektrotechnické inženýry. SNTL 1971, (in Czech)
P.M. Morse, H. Feshbach: Methods of Theoretical Physics. McGraw-Hill 1953
H. Jeffreys, B. Swirles: Methods of Mathematical Physics. Cambridge University Press 1966
test
The evaluation of the subject is individual by the supervisor, according to the individual study plan of the doctoral student. The evaluation reflects the sufficient orientation of the student in the subject. The conditions for successful completion of the course are in accordance with the Study Regulations of Faculty of Mathematics, Physics and Informatics.
The equations of mathematical physics (in geophysics) – partial differential equations and the methods to solve them. The methods of potential theory, the Green functions method. Qualitative analysis of ordinary differential equations. Application of integral transforms (in mathematical physics and in the data and signal processing…). The methods of signal processing – linear, non-linear, statistical approaches, wavelet transform and analysis. The method of boundary integral equations. Perturbation and asymptotic methods – their application in solving of nonlinear equations (algebraic, differential). Numerical methods – finite difference method, boundary element method, spectral method. Interpolation and approximation.
After completing the course, students will have knowledge of specific mathematical methods applicable in geophysical research.
exam
To explain principles of measuring methods and systems and to provide to postgraduate students with possibility of personal observational and experimental measurement and its data processing according to the goals of PhD dissertation.
Selected articles in the geophysical journals.
test
Physical principles of geophysical measurement systems in gravimetry, seismology, geomagnetism, paleomagnetism and electromagnetic sounding. Sensors, calibration, analog-digital conversion, time marks and synchronization, DCF and GPS time marks. Precision and sensitivity of apparatus. Absolute and relative measurements, data acquisition by computer, international rules, requirements and standards for data formatting and archivation. Data postprocessing, transfer of data to the local, regional and international collecting centers.
Protection of analog and digital data lines against overvoltages and their attendant problems in geophysical observatories. Disturbances, noise and electromagnetic smog. Elimination of antropogeneous influences by electronic and/or computational postprocessing, digital filtration. The selection of a locality for continual and temporary measurements, the analysis of a suitable locality for recording.
After completing the course, students will be able to perform and evaluate their own observatory and experimental measurements according to the focus of the dissertation.
oral exam
http://www.st.fmph.uniba.sk/~hlubina1/
Green’s functions and condensed matter / G. Rickayzen. Academic Press, 1980
Fundamentals of the Physics of Solids, Vols. 1-3 / J. Sólyom. Springer 2007 - 2010
Principles of condensed matter physics / P. M. Chaikin, T. C. Lubensky. Cambridge Univ. Press, 1995
Basic notions of condensed matter physics / P. W. Anderson. Addison Wesley, 1984
2-FTL-107 Structure and mechanical properties of solids
2-FTL-108 Electronic and optical properties of solids
2-FTL-205 Many body physics
seminars, homeworks + oral exam
minimal score: 50%
english
Linear response theory and correlation functions. Green's functions: relation to observables, formal properties. Perturbation theory and Feynman diagrams. Adiabatic continuity, renormalization group, and effective Hamiltonians. Variational methods. Upon agreement with the students, these notions and methods will be illustrated in the context of quantum magnetism, superfluidity and superconductivity, disordered systems, correlated electrons, and/or coupled electron-phonon problems.
http://www.st.fmph.uniba.sk/~hlubina1/
55/45
The students will be able to formulate the many-body problems in the language of quantum field theory. They will know the basic principles of selected theoretical techniques used in condensed matter theory and they will know in which circumstances they can be applied.
F. Giustino, Materials Modelling using Density Functional Theory, Oxford University Press 2014
D.S. Sholl, J.A. Steckel, Density functional theory (A practical introduction), John Wiley & sons, 2009
Wolfram Koch, Max C. Holthausen, A Chemist's Guide to Density Functional Theory, 2001 Wiley‐VCH Verlag GmbH
The course requires knowledge of standard classical MD/MC simulation methods on the level of the course FMFI.KEF/2-FTL-110/22 Computer simulations of condensed matter.
At the end of the semester a simulation problem will be assigned and the student will provide a written report on the solution. The score will be based on the evaluation of the report. Minimal score: 50%
Slovak, English
materials modeling, structural prediction, calculation of properties
density functional theory (DFT), Hohenberg - Kohn theorems
Kohn - Sham method and equations
approximate DFT functionals - LDA, GGA, hybrid
practical approach to solving Kohn-Sham equations - plane-wave basis expansion of wavefunctions, pseudopotentials
ab initio molecular dynamics
evolutionary algorithms and crystal structure prediction
Diffusion Quantum Monte Carlo approach (DMC)
Path Integral Monte Carlo methods
machine-learning-based methods of generating force-fields
further applications of machine learning in materials simulations
0/100
The course provides an introduction to current methods of materials modeling based on ab initio approaches. It focuses on static and dynamical simulations (ab initio molecular dynamics) based on the density functional theory (DFT) for electrons and their applications to various condensed matter systems. Quantum Monte Carlo methods for electrons (Diffusion Monte Carlo) and ions (Path Integral Monte Carlo) will be mentioned too. Besides that new approaches to force-field generation based on machine learning will be shown, as well as other possible applications of machine learning in materials simulations. The methods will be illustrated on a number of examples and in the exercises the student will learn to use the freely available ab initio code Quantum Espresso.
An introduction to quantum field theory / Michael E. Peskin, Daniel V. Schroeder. Boulder : Westview Press, 1995 The quantum theory of fields : Volume 1 : Foundations / Steven Weinberg. Cambridge : Cambridge University Press, 2005 The quantum theory of fields : Volume 2 : Modern applications / Steven Weinberg. Cambridge : Cambridge University Press, 2005
2-FTF-116/00 Kvantová elektrodynamika
Continuous assessment, problem solving A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Relativistic quantum fields: bosons and fermions. Examples of tree-level processes, Feynman diagrams and details of perturbation theory. Regularization and renormalization. Example of calculation at the level of one loop.
100/0
Students completing the course will be able to use the material covered by the course - as listed below.
An introduction to quantum field theory / Michael E. Peskin, Daniel V. Schroeder. Boulder : Westview Press, 1995 The quantum theory of fields : Volume 1 : Foundations / Steven Weinberg. Cambridge : Cambridge University Press, 2005 The quantum theory of fields : Volume 2 : Modern applications / Steven Weinberg. Cambridge : Cambridge University Press, 2005
2-FTF-116/00 Kvantová elektrodynamika
continuous assessment A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Relativistic quantum fields, bosons and fermions in non-abelian gauge theory. Aspects of renormalization: beta function in non-abelian gauge theory and running of gauge coupling constants in the standard model.
100/0
Students completing the course will be able to use the material covered by the course - as listed below.
Ch.W.Misner, K.S.Thorne, J.A.Wheeler: Gravitation, W.H.Freeman, 2003, New York
I.D.Novikov, K.S.Thorne: Astrophysics of Black Holes, in Black Holes,
eds. C. DeWitt, B. DeWitt, Paris : Gordon and Breach, 1973
Continuous assessment: solving problems
Completion: exam
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
SK, EN
Kerr metric (dragging of inertial frames, Penrose process, ring siingularity), disks around black holes
http://davinci.fmph.uniba.sk/~balek1
40/60
After completing the course, students will have a detailed knowledge of the applications of general theory of relativity in astrophysics
L.D.Landau, E.M.Lifschitz: The Classical Theory of Fields, Oxford, Butterworth-Heinemann, 1980
A.R.Liddle, D.H.Lyth: Cosmological Inflation and Large-Scale Structure, Cambridge, Cambridge University Press, 2000
Continuous assessment: solving problems
Completion: exam
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
SK, EN
generation and propagation of gravitational waves, theory of cosmological perturbations
http://davinci.fmph.uniba.sk/~blazek1
40/60
After completing the course, students will have a detailed knowledge of the applications of general theory of relativity in cosmology.
M.Fecko: Differential Geometry and Lie Groups for Physicists,
Cambridge University Press, 2006, 2011
M.Fecko: Modern geometry in not-so-high echelons of physics: Case studies,
Acta Physica Slovaca 63, No.5, 261 - 359 (2013) (arXiv:1406.0078)
Ch.Misner, Kip S.Thorne, J.A.Wheeler: Gravitation, W.H.Freeman, 1973
Continuous assessment: solving problems
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
SK, EN
Geometric approach to hydrodynamics,
2D vector analysis
energy-momentum tensor
Nöther's theorem
Kaluza-Klein geometry,
http://davinci.fmph.uniba.sk/~fecko1/studenti.html
100/0
Continuous assessment: solving tasks
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
SK, EN
Einstein-Cartan gravity
Newton-Cartan gravity,
cohomology of Lie algebras
Lie algebroids
quantum dynamics as a ("classical") Hamiltonian system
http://davinci.fmph.uniba.sk/~fecko1/studenti.html
100/0
After completing the course, students will be able to use modern geometry in the areas listed in the Brief syllabus.
according to the seminar schedule
active presence
SK / EN
according to the seminar schedule
abs
the student will be acquainted with the results of active research
active presence
SK / EN
according to the seminar schedule
abs
the student will be acquainted with the results of active research
active presence
SK / EN
the student will be acquainted with the results of active research
abs
active presence
SK / EN
according to the seminar schedule
abs
the student will be acquainted with the results of active research
Roman Orus, A practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States, Annals of Physics 349 (2014) 117-158
Continuous assessment: continuous test
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Interacting systems written by the matrix formalism of the second quantization. Reduced density matrix and von Neumann entropy of quantum coupling. Renormalization group in real space. Matrix product states. Decompositions into singular values. Quantum-classical correspondence. Phase transition theory. Classification of universality classes. Fractal systems of interacting spins. Hyperbolic systems (Anti-de Sitter space) of interacting spins. Quantum gravity.
100/0
Students will learn about current theories of tensor networks, which are used to obtain very accurate descriptions of quantum states of fermion and boson strongly correlated systems. They will learn to analyze systems using renoralization methods based on decomposition into singular values by maximizing the quantum entropy of coupling.
S. W. Hawking, Comm. Math. Phys. 43, 199 (1975);
J. B. Hartle, S. W. Hawking, Phys. Rev. D 28, 2960 (1983)
2-FTF-117 General Theory of Relativity
Exam: final work
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Hawking radiation (scalar field modes against a black hole, Hawking temperature), wave function of the universe (ADM formalism, diffeomorphism and Hamiltonian coupling, Hawking - Hartl boundary condition, minispace).
http://davinci.fmph.uniba.sk/~balek1/
100/0
After completing the course, students will know the success to date on the way to combine quantum mechanics with general theory of relativity.
M. Nielsen and I.Chuang: Quantum Computation and Quantum Information (CUP, 2000)
J. Preskill: Quantum Computing (http://www.theory.caltech.edu/people/preskill/ph229/)
Continuous assessment: homework
Exam: test and oral
Indicative assessment scale: A 85%, B 70%, C 55%, D 40%, E 20%
Fundamental concepts of quantum mechanics, basics of computer science, quantum logic networks, quantum Fourier transform, quantum search algorithms, physical implementation of quantum computers, CP maps and quantum processes, open quantum systems and decoherence, quantum communication channels and their capacity.
100/0
Students will get acquainted with the basic principles of quantum information processing and quantum communication theory.
T.Heinosaari, M.Ziman: Guide to mathematical concepts of quantum theory, Acta Physica Slovaca 58, 487-674 (2008)
T.Heinosaari, M.Ziman: The Mathematical Language of Quantum theory (Cambridge, 2012)
Continuous assessment: homework
Exam: test and oral
Indicative assessment scale: A 85%, B 70%, C 55%, D 40%, E 20%
Slovak, English
1. Mathematical foundations (Hilbert spaces, transformation groups, convex sets, measure theory) 2. States and effects (density matrix, state space, duality, automorphism groups, Wigner theorem, Gleason's theorem) 3. Quantum observable (POVM, relations between observable , Naimark's theorem) 4. Quantum operations (complete positivity, Stinespring's theorem, Choi-Jamiolkowski isomorphism, quantum channels, Kraus representation) 5. Quantum measurement models (instruments, Luders measurements) 6. Quantum dynamics (control equations, Lindblad's equation)
100/0
The graduate of this course will be able to use mathematical tools and formalism of modern quantum theory.
R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Acad. Press, 1982 (rus. Mir, 1985).
L. D. Faddeev, How Algebraic Bethe Ansatz works for integrable model, in "Les Houches lectures" (Elsevier, 1997); arXiv:hep-th/9605187.
T. Deguchi, Introduction to solvable lattice models in statistical and mathematical physics, in "Classical and Quantum Integrable Systems: Theory and Application" (IOP Publishing, 2003); cond-mat/0304309.
Continuous assessment: continuous test
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Bethe ansatz method. Analysis of Bethe equations and determination of ground state energy (free energy) as well as the first excited levels depending on the model parameters. Formalization of Bethe ansatz via Yang-Baxter equations, "inverse method of quantum scattering matrix". Model systems: two-dimensional Ising model, one-dimensional quantum Heisenberg model and Hubbard model.
100/0
After completing the course, students will be able to explain under what circumstances the system of interacting particles (or spins) is exactly solvable.
Solution of several model systems.
Selection of recent papers from the field relevant to the PhD work
Ongoing evaluation based on homework
Approximate marking: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
independent active scientific activity based on the recommendation of the advisor
1. Work on a publication sent to a professional journal, conference proceedings, contribution to a collaborative note. Development of a new software product related to the dissertation. 2. Presentation at a conference, summer school, professional event, presentation of preliminary results at a departmental seminar or equivalent event for the named events. 3. Submission of a UK grant, participation of at least 20% in the submission of other research grants. The percentage will be confirmed by the advisor.
100/0
The student will learn to work individually and in a team on a research project in the following areas: 1. Publishing activities, 2. Active presentation of results, 3. Grants, responses and others
Selection of recent papers from the field relevant to the PhD work
Ongoing evaluation based on homework Approximate marking: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
independent active scientific activity based on the recommendation of the advisor
1. Work on a publication sent to a professional journal, conference proceedings, contribution to a collaborative note. Development of a new software product related to the dissertation. 2. Presentation at a conference, summer school, professional event, presentation of preliminary results at a departmental seminar or equivalent event for the named events. 3. Submission of a UK grant, participation of at least 20% in the submission of other research grants. The percentage will be confirmed by the advisor.
100/0
The student will learn to work individually and in a team on a research project in the following areas: 1. Publishing activities, 2. Active presentation of results, 3. Grants, responses and others
Selection of recent papers from the field relevant to the PhD work
Ongoing evaluation based on homework Approximate marking: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
independent active scientific activity based on the recommendation of the advisor
1. Work on a publication sent to a professional journal, conference proceedings, contribution to a collaborative note. Development of a new software product related to the dissertation. 2. Presentation at a conference, summer school, professional event, presentation of preliminary results at a departmental seminar or equivalent event for the named events. 3. Submission of a UK grant, participation of at least 20% in the submission of other research grants. The percentage will be confirmed by the advisor.
100/0
The student will learn to work individually and in a team on a research project in the following areas: 1. Publishing activities, 2. Active presentation of results, 3. Grants, responses and others
Selection of recent papers from the field relevant to the PhD work
Ongoing evaluation based on homework Approximate marking: A 90%, B 80%, C 70%, D 60%, E 50%
independent active scientific activity based on the recommendation of the advisor
1. Work on a publication sent to a professional journal, conference proceedings, contribution to a collaborative note. Development of a new software product related to the dissertation. 2. Presentation at a conference, summer school, professional event, presentation of preliminary results at a departmental seminar or equivalent event for the named events. 3. Submission of a UK grant, participation of at least 20% in the submission of other research grants. The percentage will be confirmed by the advisor.
100/0
The student will learn to work individually and in a team on a research project in the following areas: 1. Publishing activities, 2. Active presentation of results, 3. Grants, responses and others