PhD courses offered in English (SPBPPQS)
Statistical Physics, Biological Physics and Physics of Quantum Systems
Statistical physics of polymers and membranes
 Polymers:ideal chains (lattice chain, Gaussian chain, freely jointed chain, beadrod chain, worm like chain); Flory model of excluded volume, interaction with solvent; Langevin dynamics, Rouse model, Zimm model; scaling properties (semidilute solutions, confinement, weak adsorption); electrophoresis.
 Membranes:physical properties, elastic models; Monge representation, thermal fluctuations, surface tension; membrane tubes; membrane adhesion; interaction with the cytoskeleton.
 Introduction, definitions: spatial and/or temporal patterns in systems far from equilibrium; homogeneous, ordered (periodic) and chaotic states.
 Theoretical description: methods, dissipative dynamics, stability and bifurcations, linear stability analysis and nonlinear basic states. model equations.
 Nonlinear behavior in classical mechanics.
 Nonlinear behavior in chemistry (BjelousovZhabotinsky and Turing instabilities)
 Shear induced (flow) instabilities: TaylorCouette, Rayleigh, RayleighTaylor, KelvinHelmholtz, BenardMarangoni instabilities.
 Thermally driven convection: RayleighBenard instability. Role of anisotropy; thermal convection in liquid crystals.
 Electroconvection.
 Interfacial patterns: viscous fingering, linear stability analysis.
 Nonequilibrium solidification: dynamics of a solidliquid interface.
 Nonlinear optics.
 Computer simulation methods: DLA, phasefield model.
 Experimental techniques: shadow graph, image processing.
Disordered systems
This course is an introduction to the statistical mechanics of disordered systems, focused on spin glasses and related subjects.
 The required background: statistical mechanics, and, possibly, phase transitions.
 Topics covered:
 Basic phenomena: history dependence of susceptibilities, nonlinear susceptibility, ageing.
 EdwardsAnderson model and SherringtonKirkpatrick model, complex combinatorial optimization problems.
 Annealed and quenched averages, frustration. Mattis model.
 Energy barriers, the problem of the lower critical dimension, characteristic times.
 The order parameter. The replica trick. Replica symmetric solution of the SherringtonKirkpatrick model. The entropy paradox. AlmeidaThouless instability. Replica symmetry breaking.
 The Parisi solution. Physical interpretation. Ultrametricity, lack of selfaveraging. The stability of the Parisi solution.
 A hint at the rigorous solution of the SherringtonKirkpatrick model.
 Other spinglasslike systems: complex combinatorial optimization, Hopfield model and elements of the theory of neural networks. Algorithmic phase transitions.
 Literature: M. Mezard, G. Parisi. M.A. Virasoro: Spin glasses and beyond (World Scientific, Singapore, 1987) ISBN: 9971501155
Disordered Networks III (Fall and Spring semesters)
Special seminar for IVV year and PhD students
 These lectures treat the by now classic subjects of long range interaction spin glasses and neural networks from the viewpoint of equilibrium statistical mechanics. It is meant for students with a strong theoretical interest. I. As an exercise we describe the thermodynamical properties in the solvable case of pspin interaction spin systems. Then we turn to random systems, discuss Derrida's Random Energy Model, the "simplest spin glass", give a picture of pure and mixed thermodynamical states, and finally treat the random exchange pspin system by the replica method. We analyze why the replica symmetric solution is untenable for low T, show how to break replica symmetry and present Parisi's solution. Some feeling is given of experimental properties of spin glasses. II. After a sketchy introduction to biological neural systems, we present basics of artificial neural networks like the Hopfield model, the simple perceptron and multilayer feedforward networks. The storage problem of the perceptron is discussed by combinatorics, and adaptive methods like the perceptron and backpropagation algorithms are presented. The last part of the semester deals with the statistical mechanical approach of Gardner, where the replica method borrowed from spin glass theory is used to describe storage and prediction abilities of the perceptron.
Classical radiation theory (Fall semester)
Special seminar for III year students
 The first half of the semester is an introduction into classical field theory, then electrodynamics is treated from the field theoretical viewpoint, and in the end some salient problems of radiation theory are discussed. The title derives from a course running for decades, but since experience showed that students were mostly ignorant about elements of classical field theory, emphasis was shifted towards the latter. As an introduction the connection of the Maxwell equations with XIXth century experimental results is discussed. Then the general framework of classical field theory, variational approach, equations of motion, Lagrange and Hamiltonian formalism, the energymomentum tensor together with conservation laws follows. A short reminder to the basics of the special theory of relativity is included. Classical field theory is exemplified on ideal fluid dynamics, both nonrelativistic and relativistic, in Euclidean and curved coordinate systems, ending up with the general relativistic hydrodynamical equations of motion. Then the electromagnetic field interacting with a continuum of charges is treated by a variational approach. Subsequently discussed are the energy, momentum, and angular momentum of a wave field, the radiative Green function, the LienardWiechert potentials, radiated power both for small velocities and relativistically, elementary estimates about radiative loss in accelerators, natural spectral line broadening, the AbrahamLorentz electron, Dirac's relativistic classical equation of motion for a charged particle, the simplest picture of Cherenkov radiation, interaction of charged particles and the calculation of the first relativistic correction to the Coulomb potential.
Elements of classical field theory (Fall semester)
Student seminar for III year students
 This goes in parallel to and is meant for the participants of the previous course. Here lectures are given by students on introduction to Riemann geometry to be able to handle curvilinear coordinates, on problems from continuum mechanics like elasticity by variational principles, on the variational approach to Einstein's equations for general relativity and Hilbert's energymomentum tensor, surface effects in field theory, and other problems possibly by the speakers' choice.
Extreme value statistics and its physical applications (Spring semester)
Special seminar for IIIV year and PhD students
 The problem of extremal value fluctuations is introduced through empirical statistical problems like water level or appliance failure records. Then the classical basic extremal "universal" limit classes, Gumbel, Frechet, and Weibull are introduced. They are thoroughly, albeit nonrigorously, analyzed with regard to finite size effects, namely, the dependence of the empirical average, the variance, and the correction to the universal asymptote on the number of variables N. Treated are also the distribution of the kth maximum, and the joint statistics of the first k maxima. The emergence of extreme value statistics in surface fluctuations, like the width (roughness) statistics and extremal excursions of Brownian and more general random walks are discussed, in the light of most recent results.
Student seminars in statistical physics (Spring semester)
For IVV year physics students
 Fundamental issues and methods in statistical physics, like the treatment of stochastic processes by path integrals, random walks, Langevin and FokkerPlanck equations, master equations, birthanddeath processes, and other problems possibly by the students' choice, are worked out and presented by the students. The aim is also to have students to gain experience with creating Power Point or Latex slide presentations.
Physics of environmental fluid flows
In this introductory course we summarize the basic physics of the largest scale flow phenomena in the atmosphere and oceans.
 Necessary background: classical hydrodynamics.
 Subjects: Rotating homogeneous fluids, Coriolis force, Rossby number, NavierStokes equation in rotating reference frame, dimensionless representation, Froude number, dynamic pressure, geostrophic equilibrium, TaylorProudman theorem linearized equations, inertial oscillation, inertial waves, dispersion, phase and group velocities, shallow water equations, potential vorticity conservation, free surface Rossby waves, Kelvin waves at closed boundaries, surface curvature: fplane and betaplane approximations, planetary Rossby waves, finite viscosity: Ekman number, Ekman spiral, Ekman transport, stratification, BruntVaisala frequency, adiabatic atmosphere, potential temperature, potential density, Boussinesq approximation, internal waves at continuous stratification, equations for two layer fluids, geostrophic solutions, Margules formula, thermal wind, baroclinic instability.
 Literature: 1) B. CushmanRoisin: Introduction to Geophysical Fluid Dynamics (PrenticeHall, London, 1994) ISBN: 0133533018 2) J. Pedlosky: Geophysical Fluid Dynamics (Springer, NewYork, 1987) ISBN: 0387963871
Application of chaos theory: Nonlinear time series analysis
We provide a concise summary of nonlinear methods developed from theories of dynamical systems. Emphasize on computer exercises.
 Necessary background: introductory courses on chaos and nonlinear dynamics.
 Subject:  Linear tools, testing for stationarity, linear filters, linear predictions, phase space methods, delay reconstruction, false neighborhood, Poincare surface of section, recurrence plots, simple nonlinear prediction, nonlinear noise reduction, measuring Lyapunov exponent, attractor geometry and fractals, correlation dimension, interpretation and pitfalls, temporal correlations, scaling laws, detrended fluctuation analysis, testing nonlinearity with surrogate data, nonlinear statistics, transients, intermittency, quasiperiodicity.
 Literature: H. Kantz, T. Schreiber: Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 2004) ISBN 0521529026
Theory of quantum phenomena
 The density matrix and its representations
 Complementarity and environmentinduced decoherence
 The master equation and its solutions
 The measurement problem and the quantumclassical border
 Quantum Zeno effect
 Quantum jumps
 Quantum nondemolition
 Berry phases
 A quick introduction to quantum information
Recent experiments in quantum mechanics
 Neutron interferometry
 Ion and atom traps, laser cooling
 BoseEinstein condensation
 Micromasers
 Atom optics
 Schrödinger cats
 Photon detectors, twophoton interference
 Entanglement, EPR correlations, Bell inequalities
 Vibrating mirrors
Experimental methods in Biophysics
 Xray crystallography
 structure factors
 convolution
 Patterson function
 Phase refinement
 NMR spectroscopy
 Semiclassical theory
 Quantummechanical foundations
 Bloch equations
 chemical shift
 spinspin coupling
 2D (pulse) NMR
 Solomon equations and Overhauser relaxation
 Mass spectroscopy
 analysators: Magnetic sector, quadrupole, ion trap and time of flight (TOF)
 ion sources: ESI and MALDI
 Optical spectroscopy
 absorption
 fluorescence
 dichroism
 IR and Raman
 Chromatography
 gel filtration
 ion exchange
 affinity
 HPLC
?  Electrophoresis
 DebyeHuckel theory
 electroosmosis
 zeta potential and pH
 SDSPAGE, blotting, 2D electrophoresis and differential protein display
 Sedimentation and Centrifugation
 diffusion
 Svedberg equation
 zonal and densitygradient ultracentrifugation
 Optical waveguides
 electromagnetic theory
 applications
 Tomography
 Radon transformation
 CT
 PET
 MRI
Fullerenes and Carbon Nanotubes
 Discovery of C60, historical survay, isolated cagelike molecules
 Properties of C60 in gas liquid and solid phases
 Doped fullerenes, fullerites; fullerene polymers
?  Carbon nanotubes: geometrical, vibrational and electronic properties
 Applications
Theoretical Studies on Biopolymers

 structure calculations of polysaccharides
 studies on mechanical properties of DNA
 molecular mechanics and molecular dynamics studies on proteins
 statistical approach to study protein structure elements
 studies on transmembrane proteins
 studies on intrinsically unstructured proteins
Topics:
Physics of Semiconductors
In this course fundamentals of semiconductor materials and device physics are introduced  differences between general solid state physics and specific semiconductor properties are emphasized. Most recent applications are treated in some more details.
 Background: Elements of solid state physics and basic knowledge of quantum mechanics.

 Crystal physics  structure, structure of thin layers, interfaces, epitaxy, organic and amorphous semiconductors.
 Electron states  band structure, role of bonding, k.p perturbation, hole states.
 Motion of electrons  effective Hamiltonian, effective mass tensor, valence band, impurity states, shallow and deep impurities, scattering of electrons and holes.
 Statistics of semiconductors  intrinsic, extrinsic semiconductors, degeneracy, compensation, semiinsulators.
 Basic transport  phenomenology, Onsager relation, microscopic kinetic model, Boltzmann equation, conductivity, Hall effect, magnetoresistivity.
 Advanced electron transport  high field, instability, Gunn effect.
 a.c. transport  microwave, propagation of light below bandgap, cyclotron resonance.
 Thermal transport  thermal conductivity of electrons, bipolar (heat) conductivity, Peltier effect, thermoelectric heating and cooling.
 Quantum transport  reduced dimensionality, spacecharge layers, quantum hall effect (integer, fractional).
 Inhomogeneous semiconductors  diffusion, lifetime, injection, pn junction, MOS structure.
 Fundamental experimental techniques for characterization of semiconductor materials and device structures.
 Basic devices  pn junction diode, transistor, tunnel diode, MOS device, Zener diode.
 Light and semiconductors: optoelectronics  LED, laser diode, light detectors, MOS imaging, CCD physics.
 Light and semiconductors: solar cells  basics, theoretical limits, practical limits, future.
 Highlights of Hungarian pure and applied semiconductor research.
Subjects:
Specific literature is given at the end of each Section.
Káosz kialakulása mechanikai rendszerekben
This is an introductory course to the emergence and properties of chaotic motion in simple dissipative and conservative mechanical systems.

 Basic concepts and simple motion in dynamical systems: phase space, trajectory, fixed point, limit cycle, Poincaré map, PoincaréBendixson theorem
 Chaotic behavior in general: main features of chaos, Lyapunov exponents, examples: periodically kicked rotator, Lorenz model
 Dissipative systems:
 onedimensional maps: logistic map, period doubling bifurcations, chaotic bands, universality, Feigenbaum constants, fully developed chaos, tent map, Bernoulli shift, Lyapunov exponents, probability distributions, symbolic dynamics
 two dimensional maps: Hénon model, baker map, strange attractor, fractal dimension period doubling bifurcations and classification of strange attractors in systems of differential equations, intermittency, quasiperiodic transition to chaos, transient chaos, review of experiments
 Conservative systems: structure of the phase space in integrable and nonintegrable systems with examples, KolmogorovArnoldMoser theorem, PoincaréBirkhoff theorem, standard map, breakup of the last torus, ergodicity, mixing, KolmogorovSinai entropy, Arnold diffusion, billiards (e.g. Sinai, Bunimovich), chaotic scattering
Subject:
Literature: A káosz (szerk. Szépfalusy P., Tél T., Akadémiai Kiadó, 1982) H.G. Schuster, Deterministic Chaos: An Introduction (VCH, Weinheim, 1995) Tél TamásGruiz Márton, Kaotikus dinamika (Nemzeti Tankönyvkiadó Rt., 2002)
?
Mesosopic Systems I.
In this introductory course we summarize the basic physics of mesoscopic systems.

 Twodimensional electron gas  nanoscale wires and quantum dots
 Electronic transport  Landauer approach
 Scattering matrix and transfer matrix method
 Green's function method (FisherLee relation)
 Resonant tunneling
 AharonovBohm effect
 Weak localizations
 Universal conductance fluctuations
Subjects:
Literature: S. Datta: Electronic Transport in Mesoscopic Systems, (Cambridge University Press, Cambridge, 1995) C. W. J. Beenakker and H. van Houten in Quantum Transport in Semiconductor Nanostructures, Solid State Physics, Vol. 44, pp. 1228, edited by H. Ehrenreich and D. Turnbull, (Academic Press, Inc., Boston, 1991) Y. Imry: Introduction to Mesoscopic Physics, (Oxford University Press, Oxford, England, 1997) D. K. Ferry and S. M. Goodnick: Transport in Nanostructures, (Cambridge University Press, Cambridge, 1997) T. Heinzel: Mesoscopic Electronics in Solid State Nanostructures,(WileyVCH GmbH & Co. KGaA, Weinheim, 2003) HJ. Stöckmann: Quantum Chaos, An Introduction,(Cambridge University Press, Cambridge, 2000) ?
Mesosopic Systems II.
In this course we give a review about the most relevant experiments and theories related to mesoscopic systems. The course is based on the course of Mesosopic Systems I.

 Integer quantum Hall effect
 Fractional quantum Hall effect
 Quantum point contact
 Coulomb blockade
 Persistent current
 Quantum dots, artificial atoms
 Antidot lattice, classical and quantum chaos
 Lateral magnetic super lattice (magnetically modulated mesoscopic systems)
 Photonic crystals
 Shot noise
 Spintronics
Subjects:

 Supriyo Datta: Electronic Transport in Mesoscopic Systems (Cambridge Studies in Semiconductor Physics and Microelectronic Engineering) (Paperback)
 C. W. J. Beenakker and H. van Houten in Quantum Transport in Semiconductor Nanostructures, Solid State Physics, Vol. 44, pp. 1228, edited by H. Ehrenreich and D. Turnbull, (Academic Press, Inc., Boston, 1991)
 Y. Imry: Introduction to Mesoscopic Physics, (Oxford University Press, Oxford, England, 1997)
 D. K. Ferry and S. M. Goodnick: Transport in Nanostructures, (Cambridge University Press, Cambridge, 1997)
 T. Heinzel: Mesoscopic Electronics in Solid State Nanostructures,(WileyVCH GmbH & Co. KGaA, Weinheim, 2003)
 HJ. Stöckmann: Quantum Chaos, An Introduction,(Cambridge University Press, Cambridge, 2000)
 C. W. J. Beenakker and C. Schönenberg: Quantum Shot Noise, Pysics Today May 2003, and References therein
 D. Weiss, G. Lütjering, and K. Richter: Chaotic Electron motion in Macroscopic and Mesoscopic Antidot Lattices, Chaos, Soliton, & Fractals, Vol. 8, pp. 13371357
 R. B. Laughlin: Noble Lecture: Fractional quantization, Review of Modern Physics, Vol. 71, 863 (1999) and References therein; H. L. Stromer: Noble Lecture: The fractional quantum Hall effect, Review of Modern Physics, Vol. 71, 875 (1999) and References therein
 Spintronics and Quantum Computation, edited by D. D. Awschalom, D. Loss, and N. Samarth (Springer, Berlin, 2002) and References therein ; S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova and D. M. Treger, Science Vol. 294, 1488 (2001) and References therein
Literature:
Mesosopic Superconductivity
In this course we give a review of the present status of the mesoscopic superconductivity.

 Bogoliubov  de Gennes equation
 Andreev reflection, proximity effect
 Currents in superconductors
 Scattering at normalsuperconducting interface
 Conductance of normalsuperconducting hybrid systems
 Superconductingnormalsuperconducting systems: mesoscopic Josephson junctions
 Gauge transformation of the Bogoliubov  de Gennes equation
 Excitation spectrum for Andreev billiards
Subjects:

 P. G. de Gennes: Superconductivity of Metals and Alloys (Benjamin, New York, 1996)
 F. Andreev, Zh. Eksp. Teor. Fiz. 46, 1823 (1964), [Sov. Phys. JETP, 19, 1228 (1964)]
 A. Abrikosov: Fundamental of the Theory of Metals, (Elsevier Science Publishers, Amsterdam, The Netherlands, 1988)
 M. Tinkham: Introduction to Superconductivity, (McGrawHill, Inc., New York, 1996)
 J. B. Ketterson and S. N. Song: Superconductivity, (Cambridge University Press, Cambridge, 1999)
 C. J. Lambert and R. Raimondi, J. Phys. Condens. Matter 10, 901 (1998)
 C. W. J. Beenakker, in Mesoscopic Physics, Les Houches Summer School, edited by E. Akkermans, G. Montambaux, J. L. Pichard, and J. ZinnJustin (Elsevier Science B. V., Amsterdam, 1995); C. W. J. Beenakker, Review of Modern Physics 69, 731 (1997)
 M. Brack and R. K. Bhaduri: Semiclassical Physics, (AddisonWesley Pub. Co., Inc., Amsterdam, 1997)
Literature:
Trapped atomic gases II.
In this special course we continue the topics started in Trapped Atomic Gases I. The main interest is put on the current experiments performed in ultracold trapped gases. During the course theoretical issues of a few selected experiments are reviewed.
Necessary backgrounds: Quantum Mechanics and Statistical Physics. Background on many body physics is beneficial.

 Field theoretical descriptions of weakly interacting particles in external trapping potential.
 A simple finite temperature approximation for the collective excitations: The Popov approximation for bosons.
 Experiments with rotating condensates with vortices.
 ThomasFermi approximation for a single vortex. Excitations of a stable single vortex ground state using the hydrodynamical approach. Sumrule approach.
 Experiments with trapped fermions, observations of different phenomena in the BECBCS transition.
 The meanfield description of the BECBCS transition: the Leggett model.
Subjects:

 BoseEinstein Condensation in Atomic Gases, Editors: M. Inguscio, S. Stringari and C. E. Wieman, (IOS Press, Amsterdam, 1999) ISBN: 0967335558
 F. Dalfovo, S. Giorgini, L. Pitaevskii and S. Stringari: Theory of BoseEinstein condensation in trapped gases, Rev. Mod. Phys. 71, 463512 (1999).
 Qijin Chen, Jelena Stajic, Shina Tan, Kathryn Levin: BCSBEC Crossover: From High Temperature Superconductors to Ultracold Superfluids, Physics Reports 412, 188 (2005).
Literature:
Magnetism III
(twoterms special course. Usually, Magnetism I is in the autumn term, Magnetism II in the spring term)

 Magnetic phenomena are considered as electron correlation effects. The Hubbard model is introduced and used to interpret the most basic correlation effect: the Mott metalinsulator transition. The first argument is qualitative, and later a more sophisticated variational theory is given which also allows the understanding of heavy fermion behavior.
 The antiferromagnetic Heisenberg model is introduced as the effective hamiltonian of the largeU Hubbard model at half filling. Other kinetic exchange processes, including ring exchange with application to the magnetism of solid He3, are discussed. A detailed treatment of the twosite Coulomb processes allows the introduction of direct exchange.
 The survey of various mean field theories of magnetic order begins with the Stoner theory. Weak itinerant ferromagnets like ZrZn2 and MnSi are discussed in some detail.
 Students attending the course are expected to solve 46 homework problems before taking oral exam.
Magnetism I

This is the direct continuation of Part I. The basic concepts and results from Magnetism I are assumed to be familiar.  The variety of magnetic ordering phenomena is surveyed, the conditions of ordering, and the nature of the excited states over ordered ground states, are discussed in various theoretical frameworks.
 The discussion of weak itinerant ferromagnets is continued with an introduction of the quantum critical point. The same concept is used for rare earth systems with nonfermiliquid behavior.
 The last example of itinerant mean field states is the spin density wave state, illustrated on chromium.
 Localizedspin order is considered next. Spin wave theory is described both for ferromagnets and antiferromagnets. A detailed discussion of quantum fluctuations in the ground state is given, including recent results on the possibility of spin liquid ground states.
 A central theme of Part II is the generalization of the previous considerations to systems with spin and orbital degrees of freedom. The discussion of the Mott transition in the orbitally degenerate Hubbard model is followed by the derivation of the spinorbital kinetic exchange interaction, and surveying the experimental evidence for orbital ordering in d and felectron systems.
 A particular kind of magnetic cooperative behavior gives rise to the integer and the fractional Quantum Hall Effect.
 Students attending the course are expected to solve 46 homework problems before taking oral exam.
 Much of the material covered in Magnetism III is described in P.F.: "Lecture Notes on Electron Correlation and Magnetism" (World Scientific, Singapore, 1999). However, illustrative examples are usually taken from more recent literature, and the arrangement and emphasis is different from that found in the book.
Magnetism II
Experimental Methods in Solid State Physics I

 Amplitude and intensity of the diffracted beam; reciprocal lattice, Bragg's law and the Ewald sphere; atomic scattering factor and the structure factor; systematic extinction, DebyeWaller temperature factor.
 Xray sources; detectors; absorption spectroscopy; radiography; single crystal diffraction; powder diffraction; phase identification; quantitative phase analysis; indexing and lattice parameter determination; Xray topography.
 The particularities of electron diffraction; deviation parameter; transmission electron microscopy; image formation in TEM and diffraction; Kikuchi lines; the basic equations of the twobeam kinematic and dynamic theory; rocking curve; images of dislocations and other crystal defects; highresolution electron microscopy. Scanning electron microscopy: priciples of SEM and imaging modes; analytical electron microscopy; electron energy loss spectroscopy.
 Neutron sources and detectors; absorption; nuclear scattering; magnetic scattering; basic properties of neutron diffraction; timeofflight method; applications: structure analysis; Rietveld refinement; hydrogen atom location; residual stresses; neutron inelastic scattering and its application.
 Positron sources; positron annihilation; positronium; positron in solid matter; measuring methods: angular correlation, timelife, Doppler broadening; meauring apparatuses; applications: fermiology; positron trapping at crystal defects; positron emission tomography.
 Low temperature calorimetry: low temperature measurement of specific heat; elemental excitations; critical parameters; phase transformations; low temperature measuring methods; instrumentation. High temperature calorimetry: classical DTA; Boersma DTA; differential scanning calorimeter (DSC); phase transformations; kinematical investigations.
Elements of kinematic diffraction theoryXray methodsElectron methodsNeutron methods Positron annihilation spectroscopyCalorimetry
Experimental Methods in Solid State Physics II

 Scanning tunneling microscopy (STM): theoretical background; onedimensional elastic tunneling; imaging and spectroscopy; STM design and instrumentation; basics of the work; applications: metals and semiconductors, layered materials. Scanning force microscopy (SFM): design and instrumentation; imaging in contact mode; noncontact force microscopy; applications.
 Physical background of the resonanceabsorption; recoil energy loss; Dopplerbroadening; recoilfree emission; MössbauerLamb factor; experimental techniques; sources and detectors; Doppler velocity drive; measuring possibilities; hyperfine interactions: isomer shift; quadrupole splitting; magnetic hyperfine structure; relativistic effects; application in solid state physics.
 The common characteristics of the high energy ion beam methods; Rutherford backscattering (RBS): kinematic factor and mass resolution; elastic scattering cross sections; energy loss in solids; applications: composition and stoichiometry of the sample; thickness measurement; depth profiling; heavy ion backscattering; nonRutherford backscattering. Channeling: channeling equipment; crystal alignment; defect analysis methods; surface relaxation. Elastic recoil detection (ERD): principles of ERD; experimental setup; applications. Proton induced Xray emission (PIXE). Charged particle activation analysis.
 Classical and quantum properties of the angular momentum; transformation in rotating coordinate system; Bloch equation; spinspin and spin lattice relaxation; experimental methods: continuouswave method; Fourier method; instrumentation; different method in pulsed NMR for measuring relaxation times; applications in solid state physics and chemistry: Knight shift; Korringa relation; chemical shift; NMR tomography.
 Infrared spectra; Raman spectra; atomic spectroscopy; laser spectroscopy.
Scanning probe microscopy and spectroscopyMössbauer spectroscopy Highenergy ion beam spectroscopy Nuclear magnetic resonance spectroscopyElectronic and vibrational spectroscopy
Introduction to Micro and Nanotechnology

 Size ranges and technologies; specific properties of nanosize particles; ancient nanotechnology; instinctive nanotechnology; natural nanotechnology; beginning of conscious nanotechnology; nanoscience and nanotechnologies; ways to the nanoworld.
 Microscopy: transmission electron microscopy; high resolution TEM; scanning electron microscopy; scanning probe microscopy (AFM, STM).
 Diffraction: Xray diffraction; electron diffraction;
 Spectroscopy: photoelectron spectroscopy; optical spectroscopy; infrared spectroscopy; Raman spectroscopy; nuclear magnetic spectroscopy; positron annihilation spectroscopy.
 Characterization of nanoparticles; synthesis of nanoparticles; structure; fluctuations; reactivity; conduction electrons and dimensionality; partial and total confinement.
 Disordered nanostructured materials: glasses containing metallic nanoclasters, porous silicon. Ordered nanomaterials: multilayers; giant magnetic resistance; nanostructured crystals; crystals of metal nanoparticles; arrays of nanoparticles in zeolites; photonic crystals.
 Nature of carbon bond; graphite, diamond; carbon nanoparticles; fullerenes; fullerene crystals; carbon nanotubes; geometrical structure; dispersion relation; vibrational properties; mechanical properties; fabrication of nanotubes; applications.
 Intermolecular interactions; molecular recognition; colloid systems, properties of amphypatic molecules; selfassemby in 3D: micelles; membranes; nanoporous systems; selfassembled polymers; dendrimers, applications.
 Selfassembled monolayers (SAMs), chemical composition, preparation and structure; application in surface chemistry, biosensors, nanolitography.
 Formation and properties of the Lagmuirfilm; LangmuirBlodgett technics; surface patterning, applications.
 Quantum wells, wires and dots; conduction electrons and dimensionality; electron transport in nanosytems; ballistic and quasiballistic transport; quantum coherency; weak localization; conductivity fluctuation; AharonovBohm effect; quantum Hall effect; Landauer formula; quantum resistance; single electron tunneling; Coulomb blockade; single electron transistor;
 Short history of microtechnology, tendencies and limitations of the development; photolithography; nanolithography: Xray lithography; electron lithography; ion beam lithography; the state of the art of nanolithography.
 Microelecromechanical systems (MEMS); fabrication technologies, integration of micromachining with microelectronics; micromechanical sensors; applications; tendencies in development; nanoelectromechanical systems (NEMS).
 Application of new materials and devices today and in the near future; survey of the main fields: informatics; computer techniques; medicine; energy and environment; military use; space research; shorttime and longtime risks of the new technology; ethics issues.
Basics of nanotechnologyMethods of measuring nanopropertiesProperties of individual nanoparticles Bulk nanostructured materials Carbon nanostructuresSelfassemblyOrganic nanolayersElectron transport through nanoobjectsMicro and nanolithographyIntegrative systemsApplications, risks and ethics issues
Electronic states in solids

 Basic formalism of the density functional theory
 ThomasFermi model
 Hartree model
 The HohenbergKohn theorem
 Ground state energy functional
 Exchangecorrelation energy functionals. Local density approximation. Generalized gradient approximation
 Space groups
 Irreducible representation of space groups
 Group of the wave vector. Stars of wave vectors. Compatibility relations
 Properties of the density of states. Van Hove singularities
 Wannier functions
 Tight binding method
 WignerSeitz method
 Pseudopotential method
 Muffintin orbitals. Linearized muffintin orbitals method
 Nearly free electron model
 Friedel model
 Cohesion in metals
 Stability of metal structures
 Spin paramagnetism
 Stoner model
 Spin polarized density functional theory
 Stability of magnetic structures
Description of the electronic statesSymmetry of the electronic states in crystalsSolutions of Schrödinger's equation in periodic potentialThe metallic bond. Total energy of metalsMagnetism in metals
Nonequlibrium Thermodynamics II
 Rational thermodynamics
 Extended irreversible thermodynamics
 Microscopic foundation  Onsager, Grad
 Nonlocal equilibrium equation of state
 Nonlocal equilibrium entropy
 Axiomatic formulation of EIT
Hyperbolic Heat conduction
Introductory course to quantum chaos with emphasis on random matrix theory for quantum eigenstates and transport, together with related experiments in mesoscopic systems

 introduction and related experiments
 the role of symmetries
 universality classes
 Gaussian ensembles (orthogonal, unitary and symplectic)
 joint probability distribution of eigenenergies
 determination of the density of states by the Coulomb gas method and by
 use of the Green function
 level spacing statistics
 numerical studies and theory
 experiments
 scattering and transfer matrix method
 weak localization and RMT
 universal conductance fluctuations
 HJ. Stöckmann, Quantum Chaos: an introduction (Cambridge, 1999)
 C.W.J. Beenakker, Randommatrix theory of quantum transport Rev. Mod. Phys. 69, 731808 (1997), (arxiv.org/abs/condmat/9612179)
 F. Haake, Quantum Signatures of Chaos (Springer, 1991)
 M.L. Mehta, Random Matrices (Academic Press San Diego, 1991 and earlier)
Random Matrix TheoryScarsQuantum transportLiterature:
Many body problem I.
Necessary background: Quantum mechanics, Statistical physics.
The course develops the quantum theory of many particle systems. The lectures of the first semester are devoted to normal systems using the temperature Green's function technique. The first part is devoted to the general formalism, while the second part concentrates on the electron gas.

 Occupation number representation: creation and annihilation operators.
 Definition of the temperature Green's function in grand canonical ensemble.
 Expression of equilibrium physical quantities in terms of them.
 Perturbation theory, Wick's theorem, Feynman diagrams.
 Selfenergy and the Dyson equation.
 HartreeFock approximation.
 Electron gas in homogeneous positive background.
 Calculation of the correlation energy.
 Spectral function, retarded Green's function, analytic properties, elementary excitations.
 Density propagator and its spectral function: perturbation theory and analytic properties.
 Collective excitations in the electron gas (the plasmon)
 The problem of stability of normal systems.
Subjects:

 E.M. Lifsic and L.P. Pitaevskii: Statistical Physics, Part 2 : Volume 9 (Pergamon, 1980)
 A.L. Fetter and J.D. Walecka: Quantum Theory of ManyParticle Systems (McGrawHill, 1971)
 P. Szépfalusy and G. Szirmai: Véges hõmérsékleti soktestprobléma (lecture notes available in Hungarian under http://www.complex.elte.hu/~szirmai/SP.pdf).
Literature:
Many body problem II.
Necessary background: MANY BODY PROBLEM I.
The second semester is devoted to superfluid Bose and Fermi systems. The applied techniques include canonical transformation, equation of motion method, perturbation theory.

 BoseEinstein condensation in interacting systems.
 Bogoliubov theory of the elementary excitations in the Bose gas. Discussion of the Landau spectrum of elementary excitations in superfluid He II.
 Developing the perturbation theory of Bose systems in the presence of a BoseEinstein condensate. Beliaev equations.
 HugenholtzPines theorem, phonon spectrum.
 BogoliubovHartree approximation at finite temperature.
 Treating twobody collisions by summing up ladder diagrams.
 Elementary excitations in terms of the exact swave scattering length.
 Application to Bose gas in traps.
 Cooper instability in the attracting Fermi gas. Pair correlations, elements of the BardeenCooperSchrieffer theory.
 Determination of normal and anomalous Green's functions by applying the method of equation of motion.
 Energy gap as order parameter: temperature dependence.
 Crossover from BCS to Bose condensation.
Subjects:

 E.M. Lifsic and L.P. Pitaevskii: Statistical Physics, Part 2 : Volume 9 (Pergamon, 1980)
 A.L. Fetter and J.D. Walecka: Quantum Theory of ManyParticle Systems (McGrawHill, 1971)
 L.P. Pitaevskii and S. Stringari: BoseEinstein Condensation (Clarendon Press, 2003)
Literature:
Superconductivity
 Thermodynamical properties of superconductors.
 Order parameter, Ginzburg Landau equations.
 Second kind superconductors, vortex state.
 Description of the condensed state, BCS theory.
 The selfconsistent field method, the Bogoljubov equations.
 Microscopic analysis of the GinzburgLandau equations, the BogoljubovdeGennes equations.
 Andreev scattering.
 Josephson tunneling.
Proposed literature: de Gennes: Superconductivity of metals and alloys, Tinkham: Introduction to superconductivity.
Traffic Modeling in Communication Networks
Goals: to study the statistical properties of traffic in modern communication networks
One semester, 2 hours per week

 Types of communication networks and their basic properties from the point of view of traffic
 Poisson modeling of classical telephone systems. Markovian models.
 Queuing models and Erlang's formula
 Traffic modeling in the Internet: heavy tailed distributions, Long Range Dependence, scaling and Hurst exponents
 Fractal traffic models, OnOff processes, file length distributions
 Measuring traffic in real and simulated networks
 Round Trip Time, Packet Delay and Packet Loss statistics, 1/f noise, congestednon congested phase transition
 Protocols and traffic
 TCP as a dynamical system, modeling small networks with stochastic maps
 Traffic modeling with network simulator
 Routing and traffic
 Adhoc networks and load on random graphs
Lectures:

 Kleinrock, L., Queueing Systems, Volume I: Theory, Wiley Interscience, New York, 1975
 Kocarev L., Vattay G., Complex Dynamics in Communication Networks, Springer Verlag, 2005
Recommended literature
Few publications of the Lecturer:
 A. Fekete, G. Vattay and A. Veres, Improving the 1/sqrt(p) law for single and parallel TCP flows In Teletraffic Engineering in the Internet Era, ed.: J.M. de Souza,N.L.S. da Fonseca, E.A.S. Silva, NorthHolland Amsterdam (2001)
 A. Veres, Zs. Kenesi, S. Molnar, and G. Vattay, On the Propagation of LongRange Dependence in the Internet ACM SIGCOMM 2000 and Computer Communication Review 30, No 4, 243254 (2000)
 A. Fekete and G. Vattay, SelfSimilarity in Bottleneck Buffers Proceedings of Globecom, (2001)