__Solid-state physics III.__**Credits:** 5**Responsible for the course: **Dr. Attila Virosztek*Abstract:*

This is one of the fundamental courses of the condensed matter module,
and its aim is to deepen and enrich the knowledge of the previous solid-state
physics I. and II. courses for students who are particularly interested
in solid-state physics. It gives an introduction to the second quantization,
linear response theory and their application to interacting electron systems
(ferromagnetism of metals, collective excitations, spin density waves)
in the framework of mean-field approach.

__Statistical physics II.__**Credits: **3**Responsible for the course: **Dr. János Kertész*Abstract:*

Correlation- and response functions, fluctuation-dissipation theorem,
Kubo formula, generalized hydrodynamics, broken symmetries, mode coupling,
continuous phase transitions, the two dimensional Ising model, real-space
renormalization group transformation, s^{4} model, basics of critical
dynamics, first order phase transitions, nucleation, spinodial decomposition,
disordered systems: percolation, fractals, localization, spin glasses,
far from equilibrium systems, hydrodynamic instabilities, stability analysis,
pattern formation, fundamentals of non-linear dynamics, turbulence models.

__Many-body problem__**Credits: **3**Responsible for the course: **Dr. Alfréd Zawadowski*Abstract:*

Correlation functions, definition and their measurement. Zero and finite
temperature Green function technics Application in solid-state physics:
superconductivity, plasmons, Kondo-effect, etc.

__Lectures on the mathematical physics of one dimensional
systems__**Credits:** 3**Responsible for the course: **Dr. Ferenc Woynarovich*Abstract:*

Real-space Bethe Ansatz for the 1D Heisenberg chain and 1D delta-gas.
Solution of Bethe-Ansatz equation for the 1D Heisenberg chain, higher order
Bethe-Ansatz equations, fully integrable finite temperature models, the
algebraic Bethe-Ansatz, solution of impurity models using Bethe-Ansatz.

__Magnetic theory of complex systems__**Credits: **3**Responsible for the course: **Dr. Alfréd Zawadowski*Abstract:*

Ferri- meta- and super-magnetism, multilayers, spin glasses.

__Dynamic systems__**Credits: **2**Responsible for the course: **Dr. Zoltan Noszticzius*Abstract:*

The concept and types of the dynamic systems, chemical examples, examination
of dynamical system described by ordinary differential equations, local
stability analysis of non-linear dynamical systems, various types of stationary
points, dissipative dynamic systems, mechanical and electrodynamical examples.
Classification of attractors; point, periodic, quasiperiodic, strange attractors,
chaos, bifurcations, stationary point and bifurcation of periodic attracts,
Poincare cuts, one dimensional map as a dynamic system, logistic map.

__Fractal structures__**Credits:** 3**Responsible for the course: **Dr. János Kertész*Abstract:*

Basics of fractal geometry, self-affinity, multifractals, random walks,
linear polymers, percolation, structure of infinite clusters conductivity
of percolation lattice, droplet theory of phase transition, growth phenomena,
diffusion, diffusion limited aggregation, surface roughening, continuum
theory, 1/f noise, self-organized criticality, scaling in exotic systems
(biology, traffic, economy).

__Theory of magnetism I.__**Credits: **3**Responsible for the course:** Dr. Patrik Fazekas*Abstract:*

Classification of solids into metals and insulators. Mott insulators.
Definition of the Hubbard model, and the simplest description of the Mott
transition. Derivation of the antiferromagnetic Heisenberg model (kinetic
exchange) and the ferromagnetic Heisenberg model (direct exchange with
orthogonal orbits), non-orthogonal orbits, Wigner theorem for the ground
states of two electrons, spin wave theory of the antiferromagnetic Heisenberg
model, Holstein-Primakoff theorem, thermal properties, ground state and
excitation spectrum of the antiferromagnetic Heisenberg model (spin wave
theory), discussion of spontaneous symmetry breaking. Remark: this course
includes homework assignments.

__Theory of magnetism II.__**Credits: **3**Responsible for the course: **Dr. Patrik Fazekas*Abstract:*

This course builds on the knowledge of the previous one and treats
three topics: 1. Crystal field theory, 2. Magnetism of metals, 3. Some
interesting examples of strongly correlated electron systems. Role of the
symmetry in quantum mechanics, point groups, properties of weak, average
and strong crystal fields, splitting of orbit degeneration, origin of magnetic
anisotropy, Kramers theorem, Jan-Teller effect, magnetic effect on d and
f electrons, magnetism in Hubbard model, mean field theory of spin waves,
conditions of ferromagnetism, strong correlation in metallic, heavy-metalic
ions, two band models, valence mixing, f electron systems, RKKY interaction,
magnetism of rare-earth elements. Remark: this course also includes homework
assignments.

__Disordered systems__**Credits: **3**Responsible for the course:** Dr. János Kertész*Abstract:*

The main goal of the course is to provide an introduction to disordered
systems, especially to the statistical physics of spin glasses. Following
the overview of some fundamental experiments about spin glasses, it treats
theoretical methods (quenched averages, replica trick, ergodicity- and
parity breaking , Parisi-theory, ultrametric property, loop expansion),
application inside the physics (random ensembles) and outside (neuron network,
combinatorial optimization) as well.

__Order, diffusion and conductivity__**Credits: **3**Responsible for the course: **Dr. János Kertész

Superionic conductors, metallic hydrogen, alloys, surface monolayers,
driven lattice gas model stochastic cellular automates.

__Structure determination methods in solids__**Credits: **3**Responsible for the course: **Dr. György Mihály*Abstract:*

Production X-rays, their properties and detection, diffraction type
of local methods (EXAFS,XANES), exotic methods. (X-ray holography, Mössbauer
diffraction)

__Resonance methods__**Credits: **3**Responsible for the course: **Dr. András Jánossy*Abstract:*

Fundamentals of the theory of spin and magnetic resonance. Equipments
of spin resonance. Resonance in metals and insulators. Relaxation processes.
Special applications.

__Nuclear methods in solid-state research__**Credits: **3**Responsible for the course: **Dr. Sándor Kugler*Abstract:*

Neutron sources, spectrometers, coherent and incoherent scattering,
elastic and inelastic scattering, correlation functions, structure determination,
measuring phonon spectrum with neutron scattering, neutron spin-echo method
and applications, crystal diffraction, amorphous and liquid structures,
Mössbauer spectroscopy, electromagnetic properties and transitions
of nuclei, hyperfine interaction, resonance absorption and emission without
phonon back-scattering, isomer shift, magnetic split, magnetic structures
and phase transitions, examples and applications, outline of other methods
and their comparison with Mössbauer spectroscopy.

__Electron-microscopy__**Credits:** 3**Responsible for the course: **Dr. János Kertész*Abstract:*

Transmission electron-microscopy, electron diffraction LEED, RHEED,
electro-microscopic mapping high-resolution, analytical and scanning tunnelling
electro-microscopy, electron beam X-ray microanalysis.

__Surface analytical methods__**Credits: **3**Responsible for the course**: Dr. János Kertész*Abstract:*

Low-energy electron diffraction, experimental setup, two dimensional
lattices, kinematic theory of LEED, dynamic theory of LEED, surface structures.
Auger electron spectroscopy (AES), Auger-effect, experimental apparatus,
explanation of spectras, concentration calculation, applications,
intrusive profiling . Microelectronic application. Metal physics. X-ray
excitation, photo-electric spectroscopy: principles, instruments, concentration
calculation, applications. Secondary-ion spectroscopy: principles, instruments,
concentration calculation, applications.

__Liquid crystals__**Credits: **2**Responsible for the course: **Dr. György Mihály*Abstract:*

Liquid crystalline materials and properties, phase transitions in liquid
crystals, electronic properties of liquid crystals, transport phenomena,
optical properties of liquid crystals.

__Band structure calculation I.__**Credits:** 3**Responsible for the course: **Dr. Béla Vasvári*Abstract:*

Reducing the many-body problem, Hohenberg-Kohn theorems, electron structures
of metals, geometry of Fermi surface, electron structures of alloys, the
method of coherent potentials, electron structures of amorphous metals.

__Band structure calculation II.__**Credits: **3**Responsible for the course: **Dr. Béla Vasvári*Abstract:*

Electron system of mesoscopic systems, clusters, fullerens, electron
structure of carbon nanotubes, collective electron states, plasma oscillations
in metals, fullerens and nanotubes.

__Special laboratory I.__**Credits: **6**Responsible for the course: **Dr. György Mihály*Abstract:*

The subject of the course is the experimental study and explanation
some of the quantum phenomena in solids. Typical topics are:

During the laboratory work students should acquire the knowledge of the following methods: detecting, using computer controlled measurement technics, liquid helium based criotechnics and superconductor apparatus.

__Special laboratory II.__**Credits: **10**Responsible for the course: **Dr. György Mihály*Abstract:*

The subject of the course is the experimental study and explanation
some of quantum phenomena n solids Typical topics are:

During the laboratory work students should acquire the knowledge of the following method: detecting, using computer controlled measurement technics, liquid helium based criotechnics and superconductor apparatus.

__Selected lectures on theoretical physics I. II.__**Credit scores:** 4+3**Responsible for the course: **Dr. Alfréd Zawadowski*Abstract:*

The `` Selected lectures on theoretical physics I. II.'' courses have
changing subjects. Their purpose is to give insight into some special fields
based on the knowledge from fundamental courses. The following topics are
some examples of the previous and future ones: Green-function technics,
correlation functions, Van Hove-formula, Kubo-formula, superconductors,
d-type superconductors, light scattering, point contacts, Josephson junctions.

__Selected lectures on experimental solid-state physics
I.__**Credits: **3**Responsible for the course:** Dr. György Mihály*Abstract:*

This course aims to give a year by year review of some topics of the
modern experimental solid-state physics such as spin density waves, high
temperature superconductors and C60. The subject is connected to the institute's
current research topics.

__Selected lectures on experimental solid-state physics
II.__**Credits: **3**Responsible for the course: **Dr. György Mihály*Abstract:*

This course aims to give a year by year review of some topics of the
modern experimental solid-state physics such as spin density waves, high
temperature superconductors and C60. The subject is connected to the institute's
current research topics.

__Seminars I. - IV.__**Credits:** 2**Responsible for the course: **Dr. Alfréd Zawadowski*Abstract:*

The purpose of the seminars is not only to broaden the knowledge but
to improve the students' lecturing skills. Subject of the seminar is changing
year by year, some examples are:

__Physics of metals (joint course with Material Science
Module)__**Credits:** 4**Responsible for the course: **Dr. Péter Deák*Abstract:*

Structure of metals, periodic systems, electronic states in metals,
methods for determining electron energies in metals, theory of metallic
bonds, cohesion of metals, density of states, Fermi surface, methods of
measuring the Fermi surface, calculation of dielectric constant, phonon
spectra, Kohn anomaly, Friedel oscillations, optical, thermal and transport
properties of metals (resistivity, specific heat, etc.) magnetic properties
of metals (Pauli paramagnetism, itinerant magnetism of the iron group,
Stoner model, magnetism of rare earth elements) superconductivity.

__Physics of semiconductors (joint course with Material
Science Module)__**Credits: **4**Responsible for the course: **Dr. Péter Deák*Abstract:*

Structure of metals, periodic system, electron states in metals, methods
for determining electron energies in metals, theory of metallic bonds,
cohesion of metals, density of states, Fermi surface, methods of measuring
the Fermi surface, calculation of dielectric constant, phonon spectra,
Kohn anomaly, Friedel oscillations, optical, thermal and transport properties
of metals (resistivity, specific heat, etc.) magnetic properties of metals
(Pauli paramagnetism, itinerant magnetism of the iron group, Stoner model,
magnetism of rare earth elements) superconductivity.

__Computer simulations in statistical physics__**Credit scores: **3**Responsible for the course:** Dr. János Kertész*Abstract:*

Monte-Carlo methods (random number generators, time- and ensemble averages,
importance sampling, finite size scaling, various ensembles, multi-spin
coding, Swendsen-Wang cluster dynamics, Monte-Carlo renormalization group,
relaxation problems). Molecular dynamics (solving the equations of motion,
potentials and scales, stabilizing the temperature, calculation of time-
and ensemble averages, measuring time dependent quantities, non-equilibrium
molecular dynamics, Car-Parinello method) Simulation of fractals (Percolation
model, spanning cluster analysis, large cell renormalization group for
percolation, directed percolation, self- avoiding walk, Eden model, diffusion
limited aggregation, methods for measuring the fractal dimension).

__Beyond the crystalline state__**Credits: **3**Responsible for the course:** Dr. György Mihály*Abstract:*

Variety in structures: crystals, incommensurate and long period structures,
quasicrystals, liquid crystals, glasses, systems with quasi long range
order. Order out disorder: symmetry breaking, defects and fluctuations,
Goldstone modes, generalized rigidity, orientation order vs. translational
order. Landau theory: ordered atomic structures, amorphous structures,
liquid crystals, defect mediated structures.

__Group theory in solid-state research__**Credits:** 3**Responsible for the course: **Dr. György Kriza*Abstract:*

Basics: symmetry groups, important theorems of finite groups, representation,
character chart. Vibrational spectroscopy: normal coordinates, selection
rules, direct product representation, situs group, factor group. Electron
transition: crystal space spallation, correlation diagrams. Molecule orbits:
hybridization, chemical bonds, chemical reactions, Woodward-Hoffmann rules.
Crystal lattice symmetries: space groups, crystallographic methods, international
tables, band structure calculation.

__Interacting electronic systems__**Credit:** 3**Responsible for the course: **Dr. György Mihály*Abstract:*

Electronic states in a solid state. The success and the limits of the
band picture. Mott insulator, Andersen localization. Extended and localized
electronic states. Bloch and Wannier functions. Instability of low dimensional
metals. Lindhard function, Kohn anomaly. Charge and spin density waves.
Two dimensional electron gas. Quantum Hall effect, Wigner crystal.

__Charge and spin density waves I.__**Credits: **3**Responsible for the course: **Dr. György Mihály*Abstract:*

Electron-electron interaction treated by perturbation theory. Lindhard
function. The nesting properties of Fermi-surface, low-dimensional systems.
Electron-phonon coupling. Peierls distortion, formation of charge density
waves. Experimental indications of charge density waves. Incommensurate
charge density waves, NMR experiments. Weak and strong pinning of charge
density waves. Collective conductivity. Narrow-band noise, mode locking.

__Charge and spin density waves II.__**Credits: **3**Responsible for the course: **Dr. György Mihály*Abstract:*

Excitation spectrum of charge density waves. Application of Kramers-Kronig
relation. Microwave resonance, sum rule, effective mass. Dielectric constant,
polarization relaxation. Linear response theory. Two-fluid model of charge
density waves. AC conductivity, thermal voltage. Hall constant. Wide band
noise, application of fluctuation-dissipation theorem. Low temperature
charge density wave conductivity.

__Selected problems in the many-body theory__**Credits: **3**Responsible for the course: **Dr. Gergely Zaránd*Abstract:*

The course aims to practice of the methods of many-body phenomena.
Following a short review of the methods of many-body problems (Green function
technics, formalism of second quantization) the lecturer can choose one
from the topics listed below: Theory of localization, quantum impurity
models, Bose condensation, quantized Hall effect, Cher-Simon gauge theories,
path integral technics, one dimensional interacting electrons, renormalization
group methods, bosonization.

__Physics of mesoscopic systems__**Credits: **3**Responsible for the course: **Dr. Gergely Zaránd*Abstract:*

- Theory of localization: localized and delocalized states, localizational step, length of localization, the theory of weak localization, diffusions and Cooperons, the scale theory of localization, the metal-insulator transition, fundamentals of the field theory of localization, the supersymmetric model and the non-linear sigma model, the saddle-node method, the order parameter, the way of symmetry breaking, the role of Goldstone modes, localization theory on the Bethe lattice.
- Introduction to supersymmetric technics: Grassman integrals, supervectors, supertrance and superdeterminants, handling of appearing divergencies.
- Behaviour of mesoscopic metallic systems: Finite size scaling of conductivity, Thouless energy, global and local corrections to the density of states, level repulsion, the universal corrections to conductivity, conductivity of quantum wire, the zero dimensional sigma model, connection with quantum chaos.
- Random matrix theory: spectral statistics, the principle of maximum entropy, universality classes, the stiffness of spectrum, level repulsion, scattering processes, statistics of the scattering matrix, conductivity fluctuations, transfer matrix formalism, the Mello-Pichard equation.
- Single charge phenomena: the one electron quantum box, (charging energy, discrete charge states, charge fluctuation) the one electron transistor, description of superconducting islands, measuring the Cooper energy.
- One dimensional electronic systems: edges states and quantum wires, the g-ology model, scaling, renormalization group, Luttinger model, description of bosonization and Luttinger phase? liquids, potential scattering in Luttinger liquids, persistent currents.
- Point contacts: theoretical basis of point contacts dynamic conductivity fluctuations. Systems with two states, 1/f noise, quantization of conductivity, local density of states fluctuations, measuring energy dependent life-time.