Information for students started before 2020 can be found on this link
The final examination consists of two parts: the thesis defense and a comprehensive exam. The duration of the examination is about half an hour. The topics of the comprehensive exam comprise the topics of the field of the given program/specialization/module (as listed below). The final exam will be taken inperson at the Northen building of the Lágymányosi Campus (1117 Budapest, Pázmány P. stny. 1/A.).
Research Physicist Specialization
Topics 
Date and Time 
Location 
Astrophysics 
2024. jun. 24. (Mo) 8:00 
3.139 
Biological Physics 
2024. jun. 24. (Mo) 14:00 
3.74 
Condensed Matter Physics 
2024. jun. 26. (We) 9:00 
4.70 
Nuclear Physics 
2024. jun. 25. (Tu) 9:00 
3.139 
Particle Physics 
2024. jun. 26. (We) 9:00 
6.85A 
Statistical Physics 
2024. jun. 25. (Tu) 9:00 
5.128 
Other Specializations
Specialization 
Date and Time 
Location 
Scientific Data Analytics and Modeling 
2024. jun. 27. (Th) 10:00 
5.128 
Biophysics 
2024. jun. 24. (Mo) 14:00 
3.74 
Committees and topics for each specialization and topics
Committee:
chair 
Frei Zsolt 
egy. tanár 
Atomfizikai Tsz. 
member (vicechair) 
Csótó Attila 
egy. tanár 
Atomfizikai Tsz. 
member 
Bagoly Zsolt 
egy. doc. 
Komplex Rendszerek Fizikája Tsz. 
member 
Petrovay Kristóf 
egy. tanár 
Csillagászati Tsz. 
member 
Kiss László 
tud. tanácsadó 
CSFK 
member 
Ábrahám Péter 
tud. tanácsadó 
CSFK 
Topics:
 Astronomical observations in visible wavelengths. Photometry, photometric systems in astronomy. Types and construction of telescopes.
 Spectroscopy in astrophysics. Observations in wavelengths outside the visible range. Tools and results of space astronomy.
 Physics of stars: the LaneEmden equation and the polytropic model. Energy production in stars (pp chain and the CNO cycle). The HR diagram. Evolution of stars in the HR diagram.
 End states of stellar evolution. Evolutionary phases of massive stars and nucleosynthesis in stars. Supernovae.
 Types of galaxies and their morphological classification. The structure and components of different galaxies. Spiral arms in disc galaxies.
 Galaxy clusters and superclusters in the Universe. The Abell and Zwicky catalogs.
 The largescale structure of the Universe. Surveys exploring the LSS of the Universe (CfA slice, pencilbeam, SDSS) and their results: the statistical description of the LSS.
 A hierarchical model of formation and evolution of galaxies. The physics of quasars, observational results.
 The basics of cosmological theory: the cosmological principle, the Friedmann equations, the expanding universe and the big bang, cosmological parameters.
 Observations confirming the big bang theory, the questions left open by the theory, and the theory of cosmic inflation as a possible solution.
 Precision cosmological measurements and their results: the fluctuation spectrum of the CMB, SN Ia observations, and the largescale structure of the Universe.
 Active galactic nuclei and their unified model: characteristics of different active galactic nucleus categories (Seyfert galaxies, quasars, blazars, radio galaxies), evidence for the presence of a supermassive black holes, and the unified model.
 Gammaray bursts: observations of different types of GRBs, the fireball model and the afterglow.
 The astrophysics of hot intergalactic gas in galaxy clusters: characteristics of the hot gas, cooling flows and AGN feedback, methods for exploring the hot gas (Xray spectroscopy, SunyaevZeldovich effect).
 The characteristics of gravitational waves, fundamentals of gravitationalwave detection, observations at various wavelengths and with multiple detectors.
 Gravitational waves in astrophysics: signal types, observations so far, multimessenger astronomy. The cosmological application of gravitational waves.
Committee:
chair 
Derényi Imre 
egy. tanár 
Biológiai Fizika Tsz. 
member (vicechair) 
Vicsek Tamás 
prof. emer. 
Biológiai Fizika Tsz. 
member 
Nagy Máté 
tud. fmts. 
Biológiai Fizika Tsz. 
member 
Kardos József 
adjunktus 
Biokémiai Tsz. 
member 
Meszéna Géza 
nyug. egy. tanár 
Biológiai Fizika Tsz. 
Information for the defense: 15 minutes are available for the defense of the dissertation, as well as an additional 5 minutes for answering the questions of the committee and the audience. Using a projectable presentation (PowerPoint, PDF) is recommended, which can be uploaded to the notebook provided for the presentation in advance.
Topics:
 Molecular scale biophysics
 Reaction kinetics and thermodynamics
 Structure and function of proteins and nucleic acids
 Biological membranes
 Membrane potential, ion transport, nerve signaling
 Spectroscopic methods in biology
 Biophysical experimental techniques
 Biophysics of sensation
Committee:
chair 
Groma István 
egy. tanár 
Anyagfizikai Tsz. 
member (vicechair) 
Cserti József 
egy. tanár 
Komplex Rendszerek Fizikája Tsz. 
member 
Nguyen Quang Chinh 
egy. tanár 
Anyagfizikai Tsz. 
member 
Kriza György 
tud. tanácsadó 
Wigner FK 
member 
Lendvai János 
prof. emer. 
Anyagfizikai Tsz. 
member 
Tüttő István 
tud. tanácsadó 
Wigner FK 
Topics:
Solid State Physics
 Bonding in solid states (van der Walls, ionic, covalent, and metallic bonding).
 Crystalline structures, experimental determination of crystalline structures (basic structures, symmetry properties, direct and reciprocal lattice, Xray, electron, and neutrondiffraction).
 Disordered systems ( alloys, amorphous materials, liquid crystals, quasicrystals).
 Lattice vibrations (classic and quantum description, acoustic and optic branches, experimental determination of phonon spectra).
 Thermal properties of crystalline materials (heat capacity of phonon gas, anharmonicity, thermal expansion, heat conductivity by phonons).
 Electron states in periodic systems (Bloch and Wannier functions, band structure and its relation to the symmetry of the crystal, experimental determination of band structure, metals, semiconductors, insulators).
 Pure and doped semiconductors, (Fermi energy, donor and acceptor levels, excitons). Schottky barrier, pn transition, transistor.
 Semiclassical description of the dynamic of electrons. Experimental determination of Fermi surface (motion of the electron in electric and magnetic fields, cyclotron resonance).
 Electron in strong magnetic field (Landau levels, de Haasvan Alphen effect, quantum Hall effect)
 Electronphonon interaction, (limits of adiabatic decoupling, obtaining the electron phonon interaction).
 Theory of conduction (Boltzmann equation, relaxation time approximation and its limitations, transport coefficients in metals and semiconductor, scattering of impurities, phonons and electrons.
 Interaction of solid materials with photons and neutrons (optical properties, Brillouin and Raman scattering, neutron scattering). Experimental methods for studying the properties of solid materials (Mössbauer effect, NMR, ESR, positron annihilation).
 The phenomenological theory of superconductivity (thermodynamics of superconductors, I. and II. type superconductors, GinzburgLandau theory, superconducting vortex).
 BCS theory of superconductivity, tunnel effect, Josephson effect.
 Many electron systems, electronelectron interaction (HartreeFock approximation, correlations, dielectric constant, screening, density function theory).
Magnetism
 Basic properties of magnetism (Hund’s rules, splitting of atomic levels in magnetic field, dia and paramagnetism, paramagnetic resonance, Pauli paramagnetism, exchange interaction).
 Ordered magnetic materials (ferro and antiferromagnets, meanfield theory, spin waves, magnetic anisotropy, magnetic domains).
Materials Physics
 Defects in crystals, and their role in material properties, Point defects (equilibrium concentration, mixing entropy, evolution of point defects), dislocations (topological properties, continuum description, force acting on a dislocation), internal surfaces (grain boundary, phase boundary, energy of the boundaries, nanostructural materials).
 Diffusion in solid states. Macroscopic and microscopic descriptions, Fick's laws, Important specific problems, Kirkendalleffect, generalized approach.
 Mechanical properties, plasticity, work hardening, hardening by solid solution and precipitates.
 Thermodynamic of multicomponent systems, phase rule, phase diagrams, calculating the phase diagram from free energy, homogeneous and heterogeneous nucleation. Irreversible thermodynamics, Onsager relations.
 Molecular dynamics, empirical potentials, embedded potentials, first principle calculations, thermostats, barostat.
 Phase field theories (GinzburgLandau, CahnHilliard ), spinodal decomposition, superalloy, solidification.
 Ceramics and composite materials (chemical structure of ceramics, properties, properties of composites, how to select materials for composites).
Committee:
chair 
Csótó Attila 
egy. tanár 
Atomfizikai Tsz. 
member (vicechair) 
Papp Gábor 
egy. tanár 
Elméleti Fizikai Tsz. 
member 
Csanád Máté 
egy. tanár 
Atomfizikai Tsz. 
member 
Varga Dezső 
tud. fmts. 
Wigner FK 
member 
Wolf György 
tud. tanácsadó 
Wigner FK 
Topics:
 Ground state properties of nuclei and their measurements (binding energy, radius, magnetic moment, quadrupole moment)
 Nuclear forces (the central potential, the mechanism of the interaction, the spindependent interaction, the tensor force)
 Nuclear models (liquid drop model, Fermigas model, shell model, unified model)
 Nuclear reactions (strong, electromagnetic, and weak processes of nuclei, chargedparticle reactions)
 Primordial nucleosynthesis (nuclear statistical equilibrium, the nucleosynthesis temperature, the primordial reaction network, results for the helium abundance, baryonphoton ratio, and baryon density parameter)
 The nuclear physics of the Sun (the energygenerating reactions of the Sun, thermal reaction rate, reaction rate of charged particle reactions)
 The nuclear physics of massive stars and supernova explosions (helium, carbon, neon, oxygen and silicon burning, the mechanisms of supernova explosions)
 Basics of highenergy nuclear physics (highenergy particle accelerators, detectors, complex detector systems, timeline of the collisions, basic measurements and observables)
 Processes in heavyion collisions (soft and hard processes, their physical ingredients and the relevant observables: jets, heavy quarks, photons, momentum distributions, anisotropies, viscosity, femtoscopy)
 Strong interaction in heavyion collisions (basics of QCD, microscopic and effective theories, hydrodynamics, experimental and theoretical results on the QCD phase diagram)
Committee:
chair 
Katz Sándor 
egy. tanár 
Elméleti Fizikai Tsz. 
member (vicechair) 
Veres Gábor 
egy. tanár. 
Atomfizikai Tsz. 
member 
Nógrádi Dániel 
egy. tanár 
Atomfizikai Tsz. 
member 
Forgács Péter 
tud. tanácsadó 
Wigner FK 
member 
Takács Gábor 
egy. tanár 
BME Fizikai Int. 
member 
Balog János 
tud. tanácsadó 
Wigner FK 
Topics:
 Basic principles of particle detection, tracking, calorimetry.
 Complex detector systems, particle identification.
 Particle accelerators and their limitations, (anti)particle beams, focusing. Most important experimental discoveries at accelerators.
 Characterization of elementary particles and their interactions, strangeness, barion and lepton numbers.
 Geometrical symmetries, rotation group, Poincaré group, reflection symmetries.
 Internal symmetry groups: SU(2), SU(3), particle multiplets, the basics of the quark model.
 Quantization of free fields.
 Interaction Lagrangians, Wick theorem, Feynman rules.
 Nonabelian gauge theories, perturbative quantization, Feynman rules.
 Basics of the electroweak theory: spontaneous symmetry breaking, Goldstone bosons, Higgs mechanism, masses and couplings of the W and Z bosons, lepton and quark multiplets.
 Basics of quantum chromodynamics, one loop renormalization, running coupling, asymptotic freedom.
Committee:
chair 
Vattay Gábor 
egy. tanár 
Komplex Rendszerek Fizikája Tsz. 
member (vicechair) 
Csordás András 
egy. tanár 
Komplex Rendszerek Fizikája Tsz. 
member 
Kaufmann Zoltán 
egy. doc. 
Komplex Rendszerek Fizikája Tsz. 
member 
Palla Gergely 
egy. tanár 
Biológiai Fizika Tsz. 
member 
Pollner Péter 
tud. fmts. 
Statisztikus és Biológiai Fizika Kcs. 
member 
Török János 
egy. doc. 
BME Fizikai Int. 
member 
Ódor Géza 
tud. tanácsadó 
HUNREN EK 
Topics:
 Universal properties of complex networks: Sparse and dense networks. Clustering coefficient. Smallworld property. Scale independence and its implications. Quantities measuring centrality. Assortive and disassortive networks.
 Network modeling: ErdősRényi model. WattsStrogatz model. The BarabásiAlbert model and its variations: the fitness models and the HolmeKim model. The configuration model and randomization. The hidden parameter models.
 Percolation properties of networks: Percolation transformation of the giant component and the ErdősRényi graph. Determining the critical point in generator function formalism. Resilience of networks in random node removal processes, targeted attacks on networks.
 Propagation processes in networks: The SIS and SIR models. Behavior of the SIS model on homogeneous networks. The SIS model on scalefree networks.
 Network motifs and groups: Triadic motifs of directed networks and the motif significance profile. The concept of network groups. The concept of the GirvanNewman algorithm and modularity. Modularity optimization.
 Dynamic foundations of statistical physics: Nonlinear dynamics and chaos in dissipative systems. Onedimensional mappings. Autocorrelation, Lyapunov exponent and PerronFrobenius operator. Chaos in conservative systems and the Liouville operator.
 Classical transport and fluctuation dissipation theorem: Classical linear response, classical GreenKubo formula, relationship between diffusion and velocity autocorrelation.
 Characterization of stochastic processes: Markov processes, Master equation, stability of stationary distribution, Htheorem, FokkerPlanck equation, stochastic differential equations, Brownian motion.
 Open quantum systems: Open quantum systems, Markov approximation, Redfield equation and Lindblad equation.
 Theory of linear response: Correlation and response functions. Quantum fluctuationdissipation theorem.
Committee:
chair 
Csabai István 
egy. tanár 
Komplex Rendszerek Fizikája Tsz. 
member (vicechair) 
Papp Gábor 
egy. tanár 
Elméleti Fizikai Tsz. 
member

Oroszlány László 
adj. 
Komplex Rendszerek Fizikája Tsz. 
member 
Palla Gergely 
egy. tanár 
Biológiai Fizika Tsz. 
member 
Pollner Péter 
tud. fmts. 
Statisztikus és Biológiai Fizika Kcs. 
member 
Barnaföldi Gergely 
tud. fmts. 
Wigner FK 
Topics:
 Measurement data and measurement error  Errors and noise, their sources. Statistical and systematic error. Stochastic modelling of error. Data modelling  The basic problem of function fitting. Kernel function estimation.
 Bootstrap methods. The maximum likelihood method. Hypothesis testing. Extreme statistics. Post hoc analysis. Regression. Independence test. Exact tests. Bayesian methods.
 Random number generation. Numerical integration, Newtontype formulas, Gausstype formulas. MonteCarlo method, Markov chain MonteCarlo. Hierarchical Bayesian networks.
 Simulation of thermodynamic systems, Ising model, Metropolis algorithm.
 Fractal dimension, selfsimilar mathematical fractals, naturally occurring fractals, cellular automata.
 Numerical analysis of differential equations, Euler's method, RungeKutta method, stability, partial differential equations.
 Chaotic behaviour of dynamical systems. Population dynamics models, Strange attractor. Chaotic mappings, bifurcation, Lyapunov exponent. Quantum chaotic systems, distributions associated with eigenvalues of random matrices.
 Molecular dynamics, Verlet and velocityVerlet algorithms. Determination of thermodynamic quantities and relaxation.
 Signal processing and time series analysis  Fourier methods, FFT, spectra and spectrogram, transfer and window functions, Wiener filter. Correlation functions, WienerHinchin theorem and power spectrum. Convolution and deconvolution.
 Machine learning  Prediction and classification methods. Supervised and unsupervised learning. The training set, validation and overfitting. Kmeans, Support Vector Machine, Random Forest, kNN method.
 Neural networks  fully connected neural nets, convolutional neural nets, backpropagation, optimizers (SGD, Adam), batch normalisation, autoencoders, word2vec.
 Dimensionality reduction methods  Statistical properties of high dimensional data.
 Relational databases  the relational data model, logical and physical operators (seek, scan and variants of joins, aggregation), data storage models (row store, column store), indexes (clustered index, nonclustered index), the Btree, keys and constraints, transactions. Query optimization. Data loading process.
 Multidimensional data, representation of geographic and spatial data. Basic search problems: interval search, spatial search, nearest neighbours. Spatial indices, spatial filling curves (Zindex, PeanoHilbertindex), kDtree, Rtree, role of bit coding. Spatial celling methods: Delaunay triangulation, Voronoi tessellation.
 Image processing  Digital representation of images, colour models. Interpolation, convolution and deconvolution methods, homomorphic filtering. Edge, corner and speckle detection. Morphological analysis, feature extraction. Perspective correction, noise filtering methods.
 Visualisation  Techniques for two and three dimensional visualisation of scientific data, representation of scalar, vector and tensor data. Use of colours, notation, Gestalt laws, Static and interactive visualisation techniques, Spatial data visualisation, Volumetric and level surface visualisation.
Committee:
chair 
Derényi Imre 
egy. tanár 
Biológiai Fizika Tsz. 
member (vicechair) 
Vicsek Tamás 
prof. emer. 
Biológiai Fizika Tsz. 
member 
Nagy Máté 
tud. fmts. 
Biológiai Fizika Tsz. 
member 
Kardos József 
adjunktus 
Biokémiai Tsz. 
member 
Meszéna Géza 
nyug. egy. tanár 
Biológiai Fizika Tsz. 
Information for the defense: 15 minutes are available for the defense of the dissertation, as well as an additional 5 minutes for answering the questions of the committee and the audience. Using a projectable presentation (PowerPoint, PDF) is recommended, which can be uploaded to the notebook provided for the presentation in advance.
Topics:
 Principles and biological aspects of thermodynamics and statistical physics (BP)
 Structure and function of proteins (BP, BET, CB, IB)
 Structure and function of DNA and RNA, classical and molecular genetics, gene technology (BP, CB, IB)
 Biological membranes (BP, IB)
 Bioenergetics: anaerobic and aerobic processes, chemiosmosis (BP, IB)
 Bioenergetics: photosynthesis (BP, IB)
 Membrane potential, ion transport (BP, IB)
 Neurons and synapses, nerve signaling, HodgkinHuxley theory (BP, IB)
 Spectroscopic methods in biology (BET)
 Biophysical experimental techniques (BP, BET)
 Biophysics of sensation (BP, IB)
 Comparative and population genomics, molecular evolution (CB)
 Collective behavior (synchronization, networks, motion) (BIS)
The topics are based on the following subjects:
BP: Biophysics I. and II.
BET: Biophysical Experimental Techniques
CB: Computational Biology
BIS: Bioinspired Systems
IB: Introduction to Biology 1., 2., 3.