Doktorske studium

(Post-graduate studies)

General information on PhD-studies at Astronomical Institute, Charles University (F1) and Masaryk University.

Oficialni seznam pozadavku ke statni doktorske zkousce na MFF UK


U doktoranda zamereneho prevazne na teoretickou astrofyziku ci astronomii se predpokladaji znalosti za zakladniho okruhu c. 10 a k tomu si voli bud okruh 8 ci okruh 9 a jeden z fyzikalnich okruhu 1-7.

1. Matematicka fyzika
Hilbertuv a Banachuv prostor. Teorie linearnich operatoru. Omezene a nomezene operatory. Spektralni analyza. Rovnice matematicke fyziky. Schrodingerovy operatory. Teorie zobecnenych funkci. Relativisticka invariance v kvantove teorii (Lorentzova a Poincare grupa a jejich representace). Topologicke prostory. Teorie rozptylu. Teorie dynamickych systemu. Matematicka statisticka fyzika. Teorie fazovych prechodu a kriticke jevy. Geometricke metody ve fyzice. Symetrie ve fyzice a teorie grup. Teorie algeber. Supersymetricke algebry.

2. Relativisticka fyzika a kosmologie
Zakladni principy obecne teorie relativity (princip ekvivalence, obecne kovariance a minimalni vazby). Rovnice geodetiky a geodeticke deviace. Einsteinovy rovnice pole. Alternativni teorie gravitace. Experimentalni overeni relativistickych teorii gravitace. Linearizovana teorie a aproximacni metody. Teorie gravitacnich vln: asymptoticka struktura prostorocasu a presna zariva reseni; zdroje a detekce gravitacnich vln. Relativisticka teorie stelarni struktury (bili trpaslici, neutronove hvezdy, pulsary). Gravitacni kolaps a fyzika cernych der v astrofyzice. Standardni kosmologicke modely a zakladni kosmologicke testy. Fyzika raneho vesmiru. Teorie linearnich perturbaci kosmologickych modelu.

3. Kvantova teorie pole a fyzika elementarnich castic
Kanonicky formalismus teorie pole. Feynmanuv drahovy integral. Feynmanova pravidla a poruchova teorie. Kalibracni invariance. Kvantova elektrodynamika. Renormalizace v teorii pole. Relativisticka invariance. CTP teorem, spin a statistika. Neabelovske kalibracni teorie. Metoda renormalizacni grupy. Asymptoticka volnost. Spontanni naruseni symetrie. Standardni model. Modely sjednocenych interakci. Supersymetricka polni teorie a strunove modely.

4. Teorie pevnych latek
Plyn interagujicich elektronu v kovech a polovodicich: stinena elektron-elektronova a elektron-fononova interakce, tesnovazebni modely. Teorie Fermiho kapaliny. Greenovy funkce a jejich analyticke vlastnosti, Kramersovy-Kronigovy relace a fluktuacne-dispacni teorem. Teorie linearni odezvy, Kubovy formule. Supravodivost a supratekutost. BSC teorie supravodivosti.

5. Nerelativisticka kvantova teorie
Hermitovske operatory a jejich spektrum, Schrodingerova rovnice, kvasiklasicka aproximace, princip superposice, relace neurcitosti, stacionarni stavy, pohyb v centralne symetrickem poli, teorie poruch, spin, spinory, identicke castice, energeticke hladiny atomu, jemna struktura atomovych hladin, atomy v elektrickych a magnetickych polich, hustota toku, elasticke srazky castic, amplituda rozptylu, opticky teorem, Bornova rada, S-matice a jeji analyticka struktura, kvazistacionarni stavy, Jostova funkce a Levinsonuv teorem.

6. Hydrodynamika, magnetohydrodynamika a teorie plazmatu
Boltzmannova a Vlasovova kineticka rovnice, soustava fluidnich a magnetohydrodynamickych rovnic, driftove priblizeni pohybu castic v elektromagnetickych polich, rovnovaha a stabilita plazmatu, disperzni rovnice pro sireni vln ve studenem plazmatu, kineticka teorie sireni v horkem plazmatu, Landauv utlum a nestabilita vln, nelinearni interakce vln s plazmatem; zachycene castice a kvazilinearni aproximace ponderomotivni sily v plazmatu, slaba a silna turbulence plazmatu, vzajemna interakce vln, deterministicky chaos - uvod do teorie a aplikace v modelech anomalnich jevu v plazmatu, plazma nizkoteplotni, termonuklearni a astrofyzikalni.

7. Statisticka fyzika a termodynamika
Interagujici statisticke systemy: klasicke a kvantove kapaliny a plyny, distribucni funkce a poruchove metody - virialovy a klasterovy rozvoj, poruchove metody kvantove statisticke mechaniky. Modely a teorie fazovych prechodu: Isinguv a Heisenberguv model magnetismu, statisticka teorie stredniho pole, skalovaci hypoteza a teorie renormalizacni grupy.

8. Experimentalni metody v astronomii
Zaklady optiky. Teleskopy, spektrografy, fotometry, interferometry, detektory (deleno podle jednotlivych oboru elektromagnetickeho zareni). Primarni redukce dat: zpracovani signalu a obrazu, analyza casovych rad mereni vcetne statistickych metod. Specialni analyzy dat (reseni krivek radialni rychlosti a svetelnych krivek, dopplerovske zobrazeni povrchovych struktur atp.).

9. Klasicka astrofyzika
Stavba a vyvoj hvezd, tvoreni hvezd, vyvoj dvojhvezd, zaverecne faze vyvoje hvezd. Pulsace a kmity hvezd, helioseismologie. Slunecni fyzika. Hvezdne atmosfery: pole zareni, absorpce, emise, zdrojova funkce, rovnice statisticke rovnovahy, pojem LTE a non-LTE, modely hvezdnych atmosfer (zakladni rovnice), formovani spektralnich car, Einsteinovy koeficienty, zakazane cary. Atomy a molekuly v kosmickem prostoru, elektronova, vibracni a rotacni spektra. Plazma a magneticke pole, vlny v plazmatu, rovnice magnetohydrodynamiky. Tepelne a netepelne zareni plazmatu. Stavove rovnice, degenerace. Jaderne reakce ve hvezdach, nukleogeneze. Akrecni jevy, fyzika akrecnich disku. Fyzika razovych vln.

10. Klasicka astronomie, mechanika a dynamika kosmickych teles a soustav
Nebeska mechanika: problem dvou a tri teles, teorie potencialu. Sfericka astronomie: soustavy souradnic a vlivy, ktere na ne pusobi, cas a jeho mereni. HR diagram, rovnice prenosu zareni, zareni absolutne cerneho telesa, zakladni predstavy o vyvoji hvezd, metody urcovani vzdalenosti kosmickych teles, zakladni informace morfologicke (Slunce, slunecni soustava vcetne malych teles, hvezdy, typy promennych hvezd, dvojhvezdy), elementy visualnich, zakrytovych a spektroskopickych dvojhvezd, hvezdokupy, dynamika. Galaxie, hvezdokupy, slozky galaxii, hvezdne populace, urcovani stari, Hubbleuv zakon, typy galaxii, zdroje vysokych energii, mezihvezdny plyn a prach, tvorba hvezd, vznik a vyvoj galaxii.

Official list of requirements for state doctoral examination at Faculty of Mathematics and Physics of Charles University


The knowledge from the basic item No. 10 is required from PhD-student oriented mainly on theoretical astrophysics or astronomy. In addition, he has to choose either item No. 8 or 9 and one of physics items 1-7.

1. Mathematical physics

2. Relativistic physics and cosmology
Basic principles of general relativity (principle of equivalence, of general covariance and minimum coupling). Equations of geodesics and geodesic deviation. Einstein's field equations. Alternative theories of gravitation. Experimental tests of relativistic theories of gravitation. Linearized theory and approximation methods. Theory of gravitational waves: asymptotic structure of space-time and exact radiative solutions; sources and detection of gravitational waves. Relativistic theory of stellar structure (white dwarfs, neutron stars, pulsars). Gravitational collapse and physics of black holes in astrophysics. Standard cosmological models and basic cosmological tests. Physics of early universe. Theory of linear perturbations of cosmological models.

3. Quantum field theory and physics of elementary particles

4. Theory of solid state

5. Non-relativistic quantum theory

6. Hydrodynamics, magnetohydrodynamics and plasma theory

7. Statistical physics and thermodynamics

8. Experimental methods in astronomy
Fundaments of optics. Telescopes, spectrographs, photometers, interferometers, detectors (according to different regions of electromagnetic radiation). Primary data-reduction: signal- and image-processing, analysis of time series of measurements including statistical methods. Special analysis of data (solution of radial-velocity and light curves, doppler imaging of surface structures etc.).

9. Classical astrophysics
Structure and evolution of stars, star formation, evolution of binaries, final stages of stellar evolution. Stellar pulsations, helioseismology. Solar physics. Stellar atmospheres: radiation field, absorption, emission, source function, equations of statistical equilibrium, LTE and non-LTE, models of stellar atmospheres (basic equations), formation of spectroscopic lines, Einstein coefficients, forbidden lines. Atoms and molecules in cosmic space, electron, vibration and rotational spectra. Plasma and magnetic fields, plasma waves, equations of magnetohydrodynamics. Thermal and non-thermal radiation of plasma. Equation of state, degeneracy. Nuclear reactions in stars, nucleogenesy. Accretion effects, physics of accretion discs. Physics of shock waves.

10. Classical astronomy, mechanics and dynamics of cosmic bodies and systems
Celestial mechanics: problem of two and three bodies, theory of potential. Spherical astronomy: systems of coordinates and effects acting on them, time and its measurement. HR diagram, equation of radiative transfer, black-body radiation, basic notions about evolution of stars, methods of determination of distances of cosmic bodies, basic information about morphology (the Sun, solar system including small bodies, stars, types of variable stars, binaries), elements of visual, eclipsing and spectroscopic binaries, stellar clusters, dynamics. Galaxy, stellar clusters, components of galaxies, stellar populations, age determination, Hubble law, types of galaxies, high-energy sources, interstellar gas and dust, star formation, origin and evolution of galaxies.

Studijni okruhy, konzultanti a literatura doporucovane AsU AVCR


Petr Hadrava,
Astronomical Institute of the Academy of Sciences of the Czech Republic,
251 65 Ondrejov,
Czech Republic
had@sunstel.asu.cas.cz,
tlf.: +420 - 323 620 141;
fax: +420 - 323 620 110.
Revised 16.10.2002