Research Labworks for MSc

Information

Im Projektpraktikum Physikalisches Experimentieren im 1. und 2. Mastersemester werden Themen bearbeitet, die in der Regel verschiedene Experimente und komplexe Untersuchungen erfordern. Dafür stehen in den Räumen des Fortgeschrittenenpraktikums zahlreiche Techniken und Versuchsplätze zur Verfügung. Darüber hinaus können zur Lösung der Aufgaben geeignete Experimentierplätze in den Forschungslabors der Fakultät einbezogen werden.

Ein Projektthema soll über ein Semester (4 CP) an einem Nachmittag pro Woche bearbeitet werden. Die Studierenden können sich im Rahmen der Wahlfreiheit für ein Thema aus den Gebieten Astronomie, Festkörperphysik, Optik, Theorie/Computational Physics bewerben. Abhängig von den konkreten technischen und organisatorischen Bedingungen gibt es Themen/Komplexe für einzelne oder mehrere Bearbeiterinnen und Bearbeiter mit sich ergänzenden Aufgaben.

Seminar: Am Ende des Wintersemesters stellen die Studierenden die von Ihnen bearbeiteten Themen in einem Seminarvortrag vor.

Die Organisation des Projektpraktikums erfolgt zentral durch die Leitung des F-Praktikums.

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The Research Labwork in Physics in the 1. and 2. Master semester serves the purpose of training in a specific physical issue as well as project planning in order to improve experimental skills.

One Project should be completed during the semester at one afternoon per week (4 CP). The experiments can be chosen from one of the following topics: optics, solid state physics, astronomy, computational physics. Depending on the specific conditions, one project can be done by either on or more students, in the latter case, with complementary tasks.

Seminar: At the end of the winter semester students present their results in form of a scientific talk or a poster.

The Organization of the research labwork is managed by the F-Praktikum.

Laserphysics/Optics

Nd:YLF Shortpulsed - Laser Inhalt einblenden

Flash lamp pumped Nd:YAG (also Nd:glass or Nd:YLF as used for this experiment) lasers are still the work horses used for laser material processing, i.e. cutting, drilling, welding, soldering, or forming of workpieces. Additionally, they are often used as a pump source for optical-parametric or femtosecond laser amplifiers in science or for instance as a driver for inertial confinement nuclear fusion. The latter applicationcomprises the world’s largest lasers generating up to some MJ pulse energy in only some ns in time. Because of the acceptable efficiency, low cost of ownership, and flexibility of flash lamp pumped solid state lasers for the generation of high pulse energies, they are still widely used today. This kind of lasers have the capability to generate microsecond, nanosecond and even picoseconds pulses by techniques that are universal for short pulse lasers. The underlying basics for these techniques are taught within this experiment together with pulse characterization using auto-correlation and basics of nonlinear optics as well as laser pulse amplification. Since with the rare-earth element neodymium an almost ideally four-level laser schem can be realized, it perfectly serves as a model to understand laser dynamics in more depth.    

Teaching Goals and Content 

  • working principle and properties of solid-state lasers (Nd:YLF)
  • spiking in free-running mode
  • dependence of output power on pump power
  • working principle of a Pockels cell
  • generation of short pulses by Q-switching
  • non-linear optics: second harmonic generation (SHG) and phase matching principle
  • generation of picosecond pulses by ‘non-linaer mirror’ mode-locking
  • measurement of pulse width by intensity auto-correlation with SHG
  • optical amplification of short pulses in flash lamp pumped rod amplifiers

Experimental Techniques and Equipment

 

  • flash lamp pumped Nd:YLF-laser with four laser heads
  • cavity with SHG for mode-locking
  • cavity with Pockels-cellfor q-switching
  • motorized SHG auto-correlator for ps-pulses
  • energymeter, photodiodes, oscilloscope

Supervisor:   Dr. J. Hein (phone number 47209)

Place:            F-Praktikum

For this experiment two students are recommended.

 

Femtosecond - Laser Inhalt einblenden

Nowadays the generation of ultra-short laser pulses with a duration down to some femto seconds is state of the art. Such pulses find their application not only in the field of scientific research to investigate ultra-fast processes, to perform ultra-precise spectroscopy, or to generate extreme electrical and magnetic fields through ultra-high light intensities, but they are also applied in material processing, medicine, especially in ophthalmology. Nevertheless, the generation and metrology of ultra-short pulses require complex measurement techniques. The basics to understand the underlying effects of pulse generation, stretching and compression as well as their measurement will be taught here. Some of these effects are based on non-linear optics and frequency conversion, that requires phase matching to get reasonable efficiencies. Second harmonic generation and two-photon absorption are used for pulse characterization by auto-correlation here. The limitations of the auto-correlation for the reconstruction of the temporal behavior of the laser field will be investigated in more detail.   

Teaching Goals and Content 

  • Working principle and properties of solid-state lasers (Ti:sapphire)
  • Cavity stability and longitudinal cavity modes
  • Dependence of output power on pump power
  • Generation of femtosecond pulses by Kerr-lens mode-locking
  • Compensation of group velocity dispersion in optical cavities
  • Impact of spectral phase on pulse duration and temporal pulse shape
  • Measurement of band-width and duration of laser pulses
  • Application of Fourier-Transform to explain pulse stretching and compression
  • Interferometric and intensity auto-correlation and their limitations for pulse characterization
  • Measurement of group velocity dispersion (GVD) of several materials

Experimental Techniques and Equipment

 

  • diode-pumped, frequency-doubled 5W Nd:YV04-laser as pump source
  • homemade Ti:sapphire femtosecond laser with prism GVD compensation
  • external prism pulse compressor
  • optical spectrometer
  • second harmonic generating auto-correlator
  • photodiodes, powermeter and oscilloscope

Supervisor:   Dr. J. Hein (phone number 47209)

Place:            F-Praktikum

For this experiment two students are recommended.

 

Semiconductor nanowires in strong laser fields Inhalt einblenden

Interaction of high intensity ultrashort laser pulses in near- or mid-infrared spectral range with semiconductor nanowires results in charge carrier excitation from the valence to the conduction band via highly nonlinear processes of multiphoton absorption or tunneling. One of the consequences of this excitation are highly nonlinear currents driven by the laser electric field in the bands that lead to generation of high-order harmonics (HHG) of the driving optical field. This regime of nonlinear optical interaction is way beyond the weak perturbation regime responsible for low order second or third harmonic generation forming a foundation of conventinal nonlinear optics. Another possible consequence of strong field excitation in semiconductor materials is population inversion between the valence and conduction band.

Together with the geometry of nanowires naturally forming a cavity due to reflection from end facets and providing high spatial localization of the field inside the wire, this paws the way to realization of nanoscale semiconductor lasers that are considered as a next frontier in laser research revolutionizing development of optoelectronics, on-chip photonic devices and untrasensitive sensors.

Since both HHG and strong field pumped nanolasers originate from highly nonlinear process of excitation in intense field of ultrashort laser pulses with photon energy much lower than the material bandgap, these phenomena should be very sensitive to effects of local field enhancement that occur in the vicinity of dielectric or metallic structures with a size small in comparison to the excitation wavelength. The goal of the suggested project is experimental investigation of the efficiency, spectral characteristics and the threshold in lasing and HHG in semiconductor nanowires made of ZnO or CdS on polarization and intensity in ultrashort mid-infrared laser pulses tunable in a broad range from 1.3 to 4 µm.

Goals and Context

  • Impact of nanostructuring on the nonlinear absorption of light
  • Ultrashort laser pulses and nonlinear optics

Methods

  • High power lasers
  • Setting up optical experiments with modern components
  • (time-resolved) Optical spectroscopy
  • Logging, analyzing and interpretation of measured data, comparison to literature results

Prerequisites

  • Basic knowledge about laser and solid state physics
  • (nonlinear) optics, experimental skills, good knowledge of English

Organization

Person in charge: Prof. Dr. Christian Spielmann

Supervision: Daniil Kartashov ( daniil.kartashov@uni-jena.de)

Place: Labs of the IOQ/QE at Max-Wien-Platz 1

Per term, two students may work on the topic

Modelling of Nanooptical Structures with Rigorous Numerical Methods Inhalt einblenden

Goals and Context

Computer simulatios are an essential part of Nanophotonics since the fabrication of the nanoscopic devices is challenging and the experimental characterization of optical fields with nanometer resolution is equally complicated. Therefore, reliable methods are required to calculate the electromagnetic response of nanostructured matter in advance. Since we are dealing with structures in the sub-wavelangth range, "rigorous" methods are required, which solve Maxwell´s equations without any approximation. Different approaches have become popular and important for certain classes of nanooptical structures (waveguides, gratings, metasurfaces, nanoantennas).

Methods

The students can optional choose one numerical method (FMM, FDTD, FEM, BPM), which they will get to know in detail, and implement it in a programming language suitable for high-performance computing. Afterwards the method will be used to simulate the behavior of a nanooptical structure and to optimize the design.

Programming can be done in any language preferred by the students, but Python and Mathlab in some extent are supported by existing implementations.

Prerequisites

  • Basic knowledge of partial differential equations
  • Basic knowledge of optics
  • Basic knowledge of numerical methods
  • Familiar with at least one programming language supporting numerical simulations (preferred Python or Mathlab)

Organization

Person in charge: Prof. Dr. Thomas Pertsch (thomas.pertsch@uni-jena.de)

phone: 947560

Place: Abbe Center of Photonics, Computer Pools

Per term, one or two students may work on the topic.

 

Three-dimensional imaging with Optical Coherence Tomography Inhalt einblenden

Optical coherence tomography (OTC), also known as low-coherence tomography, is an imaging technique, that is mainly established in medicine but is also used for a range of nondestructive testing applications in industry. While for many applications, OCT is performed using infrared light, the method has been successfully applied in a wide range of spectral regions. OCT is an interferometric method, which in its simplest realization strongly resembles a Michelson interferometer. Consequently, the axial resolution of an OCT measurement is only limited by the coherence length of the light source, i.e.its spectral bandwith. This enables axial resolutions well below of those that can be achieved with other imaging schemes. To obtain a 3D image, however, the axial imaging has to be combined with appropriate lateral imaging techniques, e.g. conventional microscopy or lateral scanning.

The aim of this project is the construction "from scratch" of the OCT imaging setup with visible light, including data acquisition and sample positioning amongst other things. This new OCT setup will not only be build for educational purposes but will later serve as a test facility for new methods. Students will be asked to design appropriate test samples and use them to characterize their setup.

Teaching Goals and Content

  • Planning and setup of an optical experiment
  • Principles of Optical Coherence Tomography and related methods
  • Characterization of an Imaging setup
  • Design and production of test samples

Prerequisites

  • Knowledge and interests in optics, especially imaging
  • Good experimental skills
  • Basic programming skills

Organization

Supervisor: Felix Wiesner (felix.wiesner@uni-jena.de);  phone: 947629

Place: F-Praktikum

For this experiment two students are recommended

 

Solid State Physics

Investigation of thin Layers with X-Rays Inhalt einblenden

Learning target and topics:

 Students will learn in these experiments methods on surface characterization, thin film analysis as well as x-ray diffraction analysis on nanoparticles. Therefore grazing incidence reflectometry data as well as wide angle scattering of nanosized particle will be recorded. Surface- and interface roughness, layer thickness as well as electron density will be determined from the data analysis. For crystalline thin layers the crystal phases, particle sizes and deformation can be treated from the diffraction profile analysis (Williamson-Hall analysis). For crystalline layers a preferred orientation and an angular distribution of the crystallites can be obtained by a pole-figure measurement. The experimental data will be compared with simulation.

  •  x-ray diffraction theory (wide angle x-ray scattering)
  •  x-ray optics (grazing angle x-ray scattering)
  •  Williamson-Hall analysis
  •  Scherrer-formula
  •  crystal phase analysis
  •  kinematical and dynamical diffraction
  •  temperature vibration

Experimental equipment:

For the laboratory work an x-ray diffractometer with Bragg-Brentano focusing combined to a graphite monochromator will be used. For instance polycrystalline material can be measured with this diffractometer (pole-figure measurement). A second high resolution diffractometer can be used for grazing incidence reflectometry and wide angle x-ray scattering of epitaxially grown thin films to determine particle sizes and crystalline deformation. For multilayer mirrors the layer thickness, surface- and interface roughness can be measured.

  •  x-ray diffractometry
  •  x-ray reflectometry
  •  detection of x-rays

Supervisor:      Dr. I. Uschmann (phonenumber 47264)

Place:              Institut für Optik und Quantenelektronik, X-ray-laboratories Max-Wien-Platz 1

The topic can be worked out by one or two students.

Investigation of Multilayer Mirrors for X-Rays Inhalt einblenden

Learning target and topics:

  • Thin metal layers: deposition, characterization of the layer properties and structure
  • High vacuum technology
  • Introduction and application of various analysis methods
    • Scanning Electron Microscopy (SEM) and Energy Dispersive X-Ray Analysis (EDX)
    • Scanning Tunneling or Atomic Force Microscopy (STM, AFM)
    • AugerElectronSpectroscopy (AES)
    • X-ray diffractometry

Experimental equipment

  • Sputter coating system from Oxford Instruments
  • Thermal evaporation system (self-made)
  • Mass Spectrometer for residual gas analysis
  • Scanning Electron Microscope
  • Atomic Force Microscope
  • Scanning Tunneling Microscope
  • Auger Electron Spectrometer

Supervisor:   Dr. Frank Schrempel (Phone 47807), Dr. Ingo Uschmann (Phone 47264)
Venue:           F-Praktikum, IFK and IOQ

The topic is suitable for one or two students.

 

Carbon-Nanotubes Inhalt einblenden

Hardly any other topic inspires the intellectual curiosity in the past decades such as nanotechnology. In addition to the enormous range of applications in the semiconductor, textile and automobile industry, mechanical engineering, architecture, aerospace engineering, medical and energy technology, it also provides an interesting insight into the physical and chemical processes and properties at the atomic and subatomic level. In this field the so-called carbon nanotubes are of particular importance. Since their discovery in 1991 by SumioIjima and his research group as well as the experimental studies of Bethune et al., different research groups largely succeeded to understand the production mechanism of these nanoscopic structures and their wide potential for applications. Beside to their high tensile strength and elasticity they have extraordinary good conduction properties. In the field of research they are therefore used as electronic components such as field effect transistors and electrical sensors and as probes for scanning force and scanning tunneling microscopes. In the industry they are used, among others, as conducting composites.

In the internship, CNTs are grown by means of the chemical vapor deposition (CVD) technique. First, the substrates needed shall be prepared by the student itself and, especially, the for the CVD process required catalyst (cobalt or iron) shall be grown structured by means of the thermal deposition method. The characterization of the substrates and CNTs shall be done by means of atomic force microscopy (AFM) and Auger electron spectroscopy (AES) as well as scanning electron microscopy (SEM) and Raman spectroscopy, respectively. The letter is a widely-used optical analysis tool, which is perfectly suited to gain information about the quality of the CNTs as well as their structures to a certain extent. After optimizing the process parameters of the CVD, self-made CNT networks shall be tested in terms of their performance as gas sensors (FET setup). For this purpose, I-V curves are measured computer-aided in dependence of different environmental parameters (partial pressure of the gas to be detected, temperature, …).

Objectives

  • Nanotechnology / Nanostructures
  • Carbon nanotubes - structure, properties, preparation, growth, use, characterization
  • Coating processes (in particular chemical and physical gas-phase deposition)
  • Sample preparation
  • Vacuum technology
  • Learn about chemical vapor deposition (CVD) systems
  • Using the scanning electron microscope (STM) or atomic force microscope (AFM)
  • Application of Raman spectroscopy
  • Electrical characterization: I-U, sensor properties

Experimental techniques

  • CVD equipment, medium vacuum
  • Samples: single crystalline silicon with oxidic passivation and quartz with catalyst coating of both substrates
  • Vacuum coating, thermal evaporation
  • Raman spectrometer
  • Scanning electron microscope (SEM)
  • Atomic Force Microscope (AFM)
  • Auger electron spectrometer (AES)
  • Computer-aided measurements of I-V curves

Supervisor:               Dr. Marco Grünewald (Phone 47454)

Venue:                      F-Praktikum and labs of the IFK

The topic is suitable for one or more students. 

 

Vacuum Coating of thin Metal Layers Inhalt einblenden

Thin layers are layers with thicknesses in the micrometer and nanometer range. Their physical parameters such as electrical conductivity often deviates from that of the bulk material, allowing for altered, tailored properties and new functionalities. In addition, the material savings are often of great economic importance. Well known is the application in the field of protection against environmental conditions, e.g. against corrosion or oxidation. However, thin layers are most important in microelectronics, where almost all components are manufactured using thin-film technology. In optics, thin layers and layer stacks are used to influence the reflection and transmission behavior, but also the polarization. In particular, layer systems play a prominent role in X-ray optics.

In the internship, metallic layers are usually deposited and characterized by different methods. Concrete topics and goals, amongst others taken from current research projects, are proposed by the supervisor at the beginning of the internship, but can be discussed and adapted depending on the interests.

Learning goals and content

  • Deposition of thin metal layers by means of various coating methods (sputter coating, thermal evaporation)
  • Characterization of the layer properties (e.g., composition, roughness, crystalline properties) depending on substrate properties and coating parameters (e.g. chamber pressure, residual gas composition, process times, substrate heating)
  • Introduction and application of various analysis methods
    • Scanning Electron Microscopy (SEM) and Energy Dispersive X-Ray Analysis (EDX)
    • Scanning Tunneling or Atomic Force Microscopy (STM, AFM)
    • Auger Electron Spectroscopy (AES)
    • X-ray diffractometry (in cooperation with the X-ray group)

Experimental equipment

  • Sputter coating system from Oxford Instruments
  • Thermal evaporation system (self-made)
  • Mass Spectrometer for residual gas analysis
  • Quartz layerthickness monitor
  • Scanning Electron Microscope
  • Atomic Force Microscope
  • Scanning Tunneling Microscope
  • Auger Electron Spectrometer

Supervisor:   Dr. Frank Schrempel (Phone 47807)
Venue:           F-Praktikum

The topic is suitable for one or two students.

Mass Spectroscopy Inhalt einblenden

Under vacuum conditions, many physical and thermodynamic properties change, wherefore they are used in industry and research in a variety of processes and for a variety of reasons. Thus, one makes use of the reduced heat flow and conduction properties for heat isolation in order to produce particularly low or high temperatures. The industry uses vacuum for preservation or the fact that moisture can be removed from food or biological samples by freeze drying at low temperatures in vacuum by sublimation. The high energy technology uses vacuum to increase the dielectric strength. The large mean free path of atoms and molecules in vacua is fundamental to the operation of particle accelerators, electron microscopes and coating equipment, which are often already operated under ultrahigh-vacuum (UHV) conditions. An important method of modern analytics is the analysis of gas compositions by means of mass spectrometers, which is used in both structure determination and substance identification as well as quantitative analysis, especially in the trace range with detection limits down to the femtogram range (10-15 g).

In the internship, principles of vacuum generation, its measurement and characterization are introduced and investigated, which the physicist meets in almost all areas. Mass spectra are measured and interpreted under different conditions. The aim is to use the UHV chamber to characterize surfaces using desorption spectroscopy.

Learning goals and content

  • Vacuum: Basics, Generation, Measurement
  • Handling ofvacuumtechnology
  • Special features of the ultra-high vacuum
  • Introduction of the basic principle and the technique of mass spectrometry, substance identification and interpretation of mass spectra
  • Adsorption and desorption on surfaces, physisorption, chemisorption
  • Thermal Desorption Spectroscopy (TDS)

Experimental equipment

  • Ultra high vacuum system
  • Turbomolecular pump, rotary vane pump
  • Ion getter pump, titanium sublimation pump
  • Vacuum measurement: dependent on gas type and independent
  • Vacuum gauges: Pirani, Penning, ionization gauge, capacitive
  • Quadrupole mass spectrometer, residual gas analysis
  • gas inlet system, gas valves

Supervisor:   Dr. Frank Schrempel (Phone 47807)
Venue:          F-Praktikum

The topic is suitable for one or two students.

Electron Diffraction Inhalt einblenden

According to de Broglie matter has not only particle but also wave character. It was shown that electrons, due to their rest mass, already exhibit wavelengths of around 1 angstrom at acceleration voltages of about 150 V, which is in the range of atomic distances in solids. Crystals therefore represent natural diffraction gratings for accelerated electrons, just as they do for x-rays of similar wavelengths. However, due to the strong inelastic interaction between electrons and atoms, the electrons in solids ranges from less than 1 to several 100 nm which is thus considerably smaller than for x-rays. This makes electron diffraction especially suited for the investigation of crystalline surfaces and thin layers.

The aim of this projects is to understand principles of electron diffraction, especially reflection high energy electron diffraction (RHEED), which is a widely used characterization method for inorganic compounds with the ability of in situ growth monitoring of thin films. Students prepare their own samples, starting from cleaning single-crystal surfaces, followed by the deposition of films via molecular beam epitaxy as well as their structural characterization by means of RHEED. All preparation and analyzing steps are performed under ultrahigh vacuum (UHV) conditions.

Learning goals and content

  • principles and application of electron diffraction in two dimensions (2D)
  • concept of reciprocal space
  • preparation of atomically clean single crystals
  • highly-ordered ultrathin layers by molecular beam epitaxy
  • vacuum technology (pumps, gauges, rest gas analysis etc.)

Experimental equipment

  • UHV chamber with:
    • RHEED device (electron gun, phosphor screen, camera)
    • sputter gun and sample heater
    • vacuum pumps (roughing, turbo, ion getter, and titanium pump)
  • metal single crystals as sample substrates
  • effusion cells for deposition of salts (NaCl, KCl) and organic materials
  • quadrupole mass spectrometer

Supervisor:        Dr. Marco Grünewald (marco.gruenewald@uni-jena.de)
                            Maximilian Schaal (maximilian.schaal@uni-jena.de)

Venue:                F-Praktikum

The topic is suitable for one or more students. 

Computational Physics

N-Body-Simulation of Planet Dynamics Inhalt einblenden

Goals and context:

In this project, mutual gravitational perturbations in systems containing stars, planets, and minor bodies are studied. Depending on the scenario and configuration, these perturbations can lead to different types of short and long-term phenomena: resonances and chaotic behavior as well as secular effects. Possible examples for specific scenarios include: capture in and release from orbital resonances; long-term stability of planetary systems; Lyapunov exponent and chaotic motion; influence of small perturbers on chaotic systems; secular perihelion drift in multi-planet systems; Kozai mechanism. For each specific problem, analytic approximations are available and can be used for comparison with the numerical results.

Methods:

 A handful of numerical integrators is available, covering a set of different algorithms (Bulirsch­-Stoer, Runge-Kutta, Everhart, (hybrid) symplectic) and scenarios. The integrators can be compared with respect to their precision and speed. Simulation results can then be visualized and statistically examined with self-made programs/scripts.

Instructor:      Dr. Torsten Löhne (phone number 47531)

Venue:          Astrophys. Inst. and Unisternwarte, Haus 2 (Schillergässchen 3)

The complex topic can be worked on by one or multiple students. The actual tasks will be adapted.

Navier-Stokes-Equations Inhalt einblenden

Goals and Context

Computational Fluid Dynamics (CFD) is a central part of computational physics and has been a driver for the development of modern numerical methods. It involves solving flow mechanical problems that cannot be solved analytically and are expensive to study experimentally by integrating generally nonlinear, partial differential  equations.

In this project, the students will apply numerical methods to solve the Navier-Stokes-Equations for the case of an incompressible fluid to study flow within a cavity and flow around obstacles.

Methods

Timestepping schemes for integration of hyperbolic equations as well as a relaxation scheme for solving elliptic equations will be employed to solve the Navier-Stokes-Equations numerically on a staggered grid in two dimensions. The stability and convergence behavior of these schemes will be examinated.

The students will use C/C++, Python or Matlab to implement these methods.

Prerequisites

  • Basic knowledge of partial differential equations
  • Basic knowledge of numerical methods
  • Familiarity with at least one of the suggested programming languages

Organisation

Person in charge: Prof. Dr. Bernd Brügmann

Supervision: Sarah Renkhoff (sarah.renkhoff@gmail.com)

Place:  Abbeanum, Fröbelstieg 1 or PAF Computerpool

Per term, one or two students may work on the topic

Bootstraping Conformal Field Theories Inhalt einblenden

Quantum field theory (QFT) is the modern language of particle and condensed matter physics. A guiding principle in the study of QFTs is symmetry, which is used to constrain the dynamics of a theory. An especially interesting, and currently vigorously studied, subset of quantum field thoeries are the so called conformal field theories (CFTs). In addition to the usual Poincare transformations, CFTs are also invariant under angle-preserving mappings, which are referred to as conformal transformations. Conformal field theories have many applications, for example in condensed matter physics; as well as in gravitational physics, in context of the holographic duality. The main benefit of conformal symmetry is that it constrains any CFT to be determined by a set of real numbers, collectively called CFT data. The CFT data is constrained by the bootstep equation (also called the crossing equation), which is an equation that stems from the crossing symmetry of four-point correlation functions. In principle, solving the bootstrap equation provides one with all of the information contained in a conformal theory. However, this task is easier said than done. Unfortunately, the bootstrap equation containes infinite sums, and is thus not easy to handle. Nevertheless, the bootstrap community made breakthrough progress in 2008 when it was discovered that the bootstrap equation has a geometric interpretation, which allowes for an effective numerical treatment. Famously, the numerical bootstrap was applied to the three-dimensional Ising model, yielding results which far-exceeded those obtained from other methods, such as Monte-Carlo simulations. Since then, conformal bootstrap methods have received a large amount of attention, both in terms of numerical studies as well as the development of novel analytical techniques, and it is considered to be a promising field of research nowadays.

In this project one of the aims is to implement the numerical conformal bootstrap method, applied to the three-dimensional Ising model.

Aimes and Scopes

  • Acquiring the basics of conformal field theories
  • Deriving consistency contraints for CFTs using the conformal bootstrap approach
  • Exploring varous implementations of the bootstrap equations, ranging from numerical SDPT for the three dimensional Ising Model to novel analytical methods for conformal field theories

Prerequisites

  • Basic knowledge of quantum field theory is required
  • Programming skills (Phython, C++) are highly recommended

Contact

Martin Ammon (phone 47145) or Sean Gray (phone 47141)

Venue: Theoretisch-Physikalisches Institut, Fröbelstieg 1 (Abbeanum)

One or two students may work on this topic per term.

 

 

Wave Equation Inhalt einblenden

Goals and Context

  • Basic concept of hyperbolic partial differential equations (PDEs) and the initial-boundary value problem (IVBP)
  • Finite differencing methods for derivative approximation
  • Method-of-line for time-domain PDEs with Runge-Kutta timesteps
  • Numerical implementation of methods to solve multi-D PDEs
  • Concepts of numerical stability and convergence

Methods

The students will solve the IBVP with the wave equation in 1+1 and 2+1 dimensions (one time dimension and one and two spatial dimensions) numerically. The project has different sequential steps:

  • Wave equation and reduction to first order system
  • Characteristic analysis and well-posedness
  • Finite differencing approximation of derivatives and convergence
  • Runge-Kutta time integrators
  • Solution of IBVP withthe 1+1 wave equation and periodic boundaries using the method of lines
  • Stability and convergence
  • IBVP with open boundaries and Sommerfeld boundary conditions
  • Wave equation with a potential: the Regge-Wheeler equation, scattering of graviational waves off a black hole and quasi-normal modes
  • More spatial dimensions: the 2+1 wave equation

Students can code in their preferred language, although Python is strongly recommended (open sources, simple and optimal for visualizations).

Prerequisites

  • Basic knowledge of partial differential equations
  • Basic programming skills

Organisation

Person of charge: Prof. Dr. S. Bernuzzi

Supervision: Vsevolod Nedora (vsevolod.nedora@uni-jena.de)

Place: Abbeanum, Fröbelstieg 1 or PAF Computerpool

Per term, one or two students may work on the topic.

 

 

 

Strong interactions on the computer: Gauge theory on the lattice Inhalt einblenden

The strong interaction that binds the elementary particles in nuclear matter is responsible for most the mass of visible matter. The mass is generated due to the interaction strength and it is hence essential for the formation of our universe. Nevertheless its charges can not be observed at the scales of our everyday live due to confinement: at low energies, a free charge of the theory can not exist and only bound states of fundamental particles are observed. At high enough energies, on the other hand, the theory is rather simple due to a phenomenon called asymptotic freedom. This simple fundamental theory is specified by the guiding principle of local gauge invariance, a generalization of the gauge principle of electrodynamics.

The confinement is an essential property of the theory, but it is not accessible by analytic perturbative methods. Some decades ago, the numerical techniques of Monte Carlo simulations on a space-time lattice have been developed. They are by now the most important methods to investigate the theory especially in the confined regime. This low temperature regime of bound state particles is separated by a deconfinement transition form a high temperature regime at which the fundamental constituents, the quarks and gluons, become relevant degrees of freedom.

The aim of this project is to understand the theoretical foundations of gauge theories and explore properties of the theory in numerical simulations.

Goals of the project

  • obtain understanding of theoretical foundations of gauge theories and strong interactions
  • understand the basics of lattice Monte Carlo simulations in quantum field theory
  • derive a program code for the simulation of SU(2) pure gauge theory (some skeleton code and examples are provided)
  • investigate the deconfinement transition
  • optional extensions: improved algorithms, static quark-antiquark potential and further observables

Prerequisites:

  • basic knowledge of quantum field theory
  • programming skills (C++, C, Fortran)

Contact:

Dr. Georg Bergner, Theoretisch-Physikalisches Institut; Phone 9-47139

e-mail: georg.bergner@uni-jena.de

Where: Theoretisch-PhysikalischesInstitut, Fröbelstieg 1 (Abbeanum)

Per term, one or two students may work on the project.

Astronomy

Historical Novae Inhalt einblenden

Problem:

In the last two millennia, astronomers (as well as citizen scientists) from Far East (China, Korea, Japan), Arabia and Europe have observed some 100 new objects on sky ("new stars" or "guest stars"). These objects could be novae or supernovae, if neither a tail nor motion relative to the stars is reported (which would be typical for comets). Novae (non-final explosions) and supernovae (final explosions) were visible for several days to some months and their date and position, as well as brightness and colors were recorded. Nine of them were identified as Galactic supernovae. Among the remaining "guest stars", there could be more supernovae, but also several novae. Historical novae and supernovae are important for modern astrophysics: (a) Since in those historical cases, the date of the explosion is known, the age of the products are precisely known and not as uncertain as astrophysical measurements would allow to determine - the latter have large error bars for gaseous shells, the (super-)nova remnants as well as for white dwarfs and neutron stars. (b) The historical light curve can be used to determine the type of the supernova (e.g. core-collapse or thermo-nuclear). (c) If a runaway star is found (from a supernova in a binary stellar system), its parallax gives an accurate distance for the (super-)nova remnants (e.g. neutron star), more precise than otherwise possible.

Tasks (e.g.):

  • identification of nova candidates from historical texts,
  • follow-up observations at the AIU Jena telescope,
  • compilation of a light curve and best fit solution to typical light curves of different supernova types, or
  • search for runaway stars in the database of the Gaia satellite.

The project can contain the analysis of historical texts (Terra-Astronomy), possibly own astronomical observations, data reduction, statistics (best fit solution etc.) and astronomical interpretation.

Supervision: Prof. Dr. Ralph Neuhäuser (Tel. 947500) or Dr. Dr. Susanne Hoffmann, AIU (Tel. 947527)

Location: Astrophysikalical Institute, Schillergäßchen 2

The project can be undertaken by 1 to 2 students (or several teams).

Special language knowledge can be an advantage (like Chinese, Arabic, Latin, etc.), but is not required.

 

Observation of Exoplanets Inhalt einblenden

Contents and learning objectives:

Since the discovery of the first planet outside our solar system some 20 years ago, more than 1000 of these exoplanets have been detected around distant stars. Several dozens of planets could be imaged directly next to their host star, using modern observing techniques on large telescopes of the 8 to 10m class. The vast majority of exoplanets, however, were detected indirectly by accurate spectrophoto-metric measurement of the light of their host stars. The transit method is today the most successfully used method for the planet search.

In the transit method, the occultation of the host star by its exoplanet is observed. By means of precise photometric measurements, the light curve of the star is measured during the transit of the planet, which allows the determination of the orbital period, the inclination of the planetary orbital plane and the planetary radius.

From the combination of the obtained results with available spectroscopic measurements (msin (i), minimum mass of the planet), the mean density of the exoplanet can be determined, which allows conclusions about its internal structure.

In this project, the students should use the observing method described above for the detection of planets in order to determine the properties of exoplanets, as well as their actual orbital parameters. The students learn the important basics for the reduction and analysis of photometric data of stars, which they themselves have recorded with the modern instruments, operated at the University Observatory in Großschwabhausen (see Fig. 1 & 2). Each exoplanet can be processed by 1 up to 3 students. The specific task will be adjusted depending on the observed exoplanet.

Technology:

The photometric observations are carried out by the students at night at the University Observatory in Großschwabhausen (see Fig. 2) with the CCD-cameras, which are operated at the individual telescopes of the observatory.

Supervisor: Dr. Markus Mugrauer (phone number: 47514)

Location (night observation): University Observatory in Großschwabhausen

Location (data reduction and analysis): Astrophysical Institute, Schillergäßchen 2, Jena

Observation of Binary Stars Inhalt einblenden

Contents and learning objectives:

Since the discovery of the first binaries, visual, photometric and spectrometric observations have shown that most stars observable in the night sky are indeed stellar systems of two or even more stars. These binary or multiple star systems, which are bound together by their gravitational force, follow the laws of celestial mechanics, which were first empirically described by Kepler and then later astrophysically explained by Newton. Thanks to the classical mechanics, it is possible with observations to precisely determine the properties of the stars in these stellar systems, in particular their masses.

Since the mass of stars determines their evolution significantly, the observation and characterization of binary star systems is astrophysically very important. While wide binaries can still be observed directly with a telescope, more closer systems can be investigated spectroscopically by means of the Doppler effect. The movement of the components around their center of gravity reveals itself as a shift of the spectral lines in the common spectrum of the stellar system. The precise analysis of the radial velocities of the stars yields an exact characterization of the orbital parameters of the stellar system (e.g. period and orbital eccentricity) as well as its mass function or the mass ratio of its components.

In this project the students use the observing method described above for the detection and characterization of spectroscopic binary stars in order to determine the properties of these systems, as well as their actual orbital parameters. The students learn the important basics for the reduction and analysis of spectroscopic data of stars, which they themselves have taken with the modern instruments, operated at the University Observatory in Großschwabhausen (see Figs. 1 & 2).

Each spectroscopic binary system can be processed by 1 up to 3 students. The specific task will be adjusted depending on the observed stellar system.

Technology:

The spectroscopic observations are carried out by the students at night at the University Observatory in Großschwabhausen (see Fig.2) with the Échelle spectrograph FLECHAS, which is operated at the 90cm reflector telescope of the observatory.

Supervisor: Dr. Markus Mugrauer (47514)

Location (night observation): University Observatory in Großschwabhausen

Location (data reduction and analysis): Astrophysical Institute, Schillergäßchen 2, Jena

 

Observation of Asteroids Inhalt einblenden

Contents and learning objectives:

With Johannes Kepler's discovery of the laws of planetary motion, the true dimension of our solar system was revealed for the first time. Since the orbital periods of the known planets were already very well known at that time from celestial observations, with the 3rd Kepler's law also the semi-major axes of the orbits of the planets around the Sun could be described relative to the Earth's orbit. It showed that the then outermost planet of the solar system Saturn is about ten times farther from the Sun than the Earth. Furthermore, already Kepler noticed a remarkably large gap between Mars and Jupiter in the solar system, in which another planet was suspected.

After the by chance discovery of the planet Uranus in 1781 by Wilhelm Herschel, the Titius Bode series, which was already developed in the mid of the 18th century, appeared as a law to describe the semi-major axes of the planets in the solar system. This series also predicts a planet located in the large gap between Mars and Jupiter at a = 2.8au. At the end of the 18th century numerous astronomers then went in search for this unknown planet. On New Year's Eve in 1801, Giuseppe Piazzi discovered a point-like object in the sky that he could observe for several nights until mid-February and measure its movement. Further observations of the planet, named after the Roman goddess of agriculture Ceres, were no longer possible and so the newly found planet was lost again. Only thanks to the method of orbit determination based on celestial observations, developed by Carl Friedrich Gauss, the orbit of Ceres could be determined from the observations of Piazzi and so the position of the planet in the sky became predictable. Thus succeeded in December 1801 the rediscovery of Ceres.

Since many other celestial bodies in Ceres-like orbits around the Sun were soon discovered and all appeared point- or star-like in the sky as Ceres, these objects were henceforth referred to as asteroids (Greek for star-like) and also as minor planets or as planetoids. Ceres is the largest body in the asteroid belt between Mars and Jupiter in which more than 690000 asteroids are currently known. Because of its size and round shape, Ceres is nowadays called a dwarf planet.

In this project, the students will first observe asteroids, whose orbits are not sufficiently well known, using the CCD cameras installed at the telescopes of the University Observatory in Großschwabhausen. In the taken imaging data, the positions and magnitudes of the asteroids are then precisely measured. By means of modern orbit determination methods, the orbits of the asteroids and their absolute brightnesses are determined, which also enables an estimate of their sizes.

In this practical course, the students learn the important basics of the reduction and analysis of astrometric and photometric data, which they themselves have recorded with the modern instruments, operated at the University Observatory in Großschwabhausen (see Fig. 1 & 2). One asteroid each can be processed by 1 up to 3 students. The specific task will be adjusted depending on the observed asteroid.

Technology:

The observations are carried out by thestudents at night at the University Observatory in Großschwabhausen (see Fig.2).

Supervisor: Dr. Markus Mugrauer(47514)

Atmospheric Influence on Observations Inhalt einblenden

Atmospherical Influence on Astronomical Observations

Problem: Observational targets close to the horizon are are strongly influenced by atmospherical conditions. Refractions and Opacity depend on the air pressure, temperature, humidity and amount of dust in the atmosphere (smog). Although modern astrophysics avoids these problems by observing only at big height above the horizon, there are several astronomical computations which need to make use these parameters – especially in navigation, computational history of science, skyscape astronomy etc. There is a huge amount of thumb rule equations and estimates for the parameters to fill in there, e.g. when calculating heliacal risings or any naked eye observation.

There are only a few and unsystematic trials for testing the estimated parameters empirically (e.g. Schlosser, 1996, Schaefer, 1993, Bennet, 1982). The parameters for air pressure and humidity can be testes by experiments but the diversity of human eyes and their effects is not. It requires a long-term study with as many different people as possible which has never been done. Therefore, we started to develop a software application for a citizen science experiment which will collect the atmospherical data automatically (from weather stations) and give humans everywhere in the world (every climate, every ethnic group) the ability to participate in our broad study on human’s vision and the visibility of stars.

variant A

observation and

lab experiment

  • Development of a measurement station for installtion at different places which registers:
    • weather information and daily images of the sky for simultaneous sky photos at different climates (e.g. here, Central Europe and Indonesia) and comparison of the data.
    • measurements of sky brightness and comparison with humans input of estimated limiting stellar magnitude (systematic measurements at different conditions of weather and lunar phase)
  • Systematic observation of the young and old lunar crescent as often as possible: What is the thinnest sickle seen and how high was it above the horizon? (with naked eye, binoculars)
  • Systematic observations of (heliacal) risings and settings (and simultaneous measurement of temperature, pressure, humidity etc.)

variant B

programming

Further development of a software application with which many observers all over the worlds are enabled to participate in the observations described above.

Supervisor:         Dr. Susanne M. Hoffmann (Telefon 47527)

Location:             Astrophysikalisches Institut, Schillergässchen 2

1 to 3 students can work on the topic simultaneously.

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