Sommersemester 2025

Lehrinhalt

* Optical telescopes: optics and characteristic parameters, telescope types, diffraction, resolution, aberrations and corrections, applications
* Optical detectors: detector types, semiconductors and CCDs, quantum efficiency, readout, noise sources, multi-chip cameras, applications
* Imaging: techniques, photometry, data reduction and characterisation, signal-to-noise
* Atmospheric effects and corrections: extinction, turbulence, seeing, active and adaptive optics, laser guide stars, applications
* Spectroscopy: types of spectrographs and spectrometers, dispersive elements, integral field units, data reduction and characterisation, applications
* Infrared astronomy: detectors and techniques, sources, applications
* Radio astronomy: detectors and instrumentation, synthesis techniques, types of radiation and sources, applications
* Astronomical interferometry: wavelength regimes, instrumentation, applications
* X-ray and gamma-ray astronomy: detectors and instrumentation, types of radiation and sources, applications
* Astroparticle physics: neutrino and Cherenkov detectors, sources and acceleration mechanisms of neutrinos and cosmic rays, applications
* Gravitational-wave astronomy: detection, sources, applications.
* In-situ exploration and remote sensing.

Lehrziel

After completing this course, the students have firm insight into the concepts, technologies, and the underlying physical principles and limitations of modern observational techniques along with scientific applications. They have knowledge of basic detector designs for different types of radiation and particles. They understand the environmental influence on astronomical observations. They are able to select and judge the adequate observational technique for studying an astronomical object of interest.

Lehrinhalt

- Astronomical basics: astronomical observations, methods and instruments;
orientation at the celestial sphere; fundamental terms of electromagnetic
radiation; distance determination, Earth-Moon system; terrestrial and gas
planets, small bodies; extra-solar-planets
- Inner structure of stars: state variables, stellar atmospheres and line
spectra; Hertzsprung-Russell diagram; fundamental equations, energy
transfer and opacity; nuclear reaction rates and tunnelling; nuclear fusion
reactions
- Stellar evolution: Main sequence, giants and late phases; white dwarfs,
Chandrasekhar limit; supernovae, neutron stars, Pulsars and supernova
remnants; binaries and multiple systems; star clusters
- Interstellar medium: cold, warm, hot gas phases dust, cosmic rays,
magnetic fields; ionization and recombination, Stroemgren spheres; heating
and cooling; star formation, matter cycle, chemical enrichment
- Galaxies: Structure and properties of normal galaxies and the Milky Way;
scaling relations; integrated spectra, luminosity function; cosmological
evolution of star formation; Black Holes in galaxies, active galaxies and their
properties, unified models
- Galaxy clusters: optical properties and cluster gas; hydrostatic model;
scaling relations; number densities and evolution
- Gravitational lensing: Concepts, mass distribution in galaxies and galaxy
clusters; cosmological lensing effect
- Large scale distribution of galaxies and gas: Structure in the spatial galaxy
distribution; redshift effects; biasing; Lyman-α-forest; Gunn-Peterson effect
and cosmic reionization
- Cosmology: Friedmann-Lemaître models, cosmological standard model;
origin and evolution of structures; halos of Dark Matter; Formation of
galaxies

Lehrziel

The students have gained basic knowledge and understanding of astronomical objects, measuring units and methods, and the relevant astrophysical processes. They have a firm grasp of the fundamental interrelations of objects and processes on different scales. They are able to reproduce the basic features of the modern world view including the physical reasoning, and connect astronomical and astrophysical phenomena to previously acquired knowledge in physics.

Informationen zur Veranstaltung

Lehrinhalt

If there are any problems registering for this module, please sent an Email to jordan@ari.uni-heidelberg.de.

Lecture: Thursdays, 14:15-15:45
Location: 
Philosophenweg 12, Kleiner Hörsaal

Tutorial Group 1: Thursday, 15:45-17:15 (Kleiner Hörsaal)
Tutorial Group 2: Thursday, 15:45-17:15 (Übungsraum 61, Erdgeschoss, Philosophenweg 12)

Do not mind to which exercise group you register. We will ensure that both exercise groups are approximately equally large. At the beginning of the semester, we can make adjustments if you want to collaborate with a specific person in a different group.  

This module consists of the lecture, the tutorials and the seminar.  

Exercises will be submitted via the "Übungsgruppensystem" in groups of two or three.  

To excel in the module MVAstro2 "Stellar Astrophysics," it is essential to complete an adequate number of exercises and attend the tutorials. Merely submitting exercises through the Übungsgruppensystem is insufficient; you must also be prepared to present your solutions during the tutorial sessions.  

Credit points cannot be awarded solely based on participation in the written exam; attendance at the tutorials is also required to receive credit.

Preliminary Schedule:
17.4.25: Introduction (Stefan Jordan)
24.4.25: Stellar structure 1 (Stefan Jordan)
01.5.25: May 1, holiday
02.5.25: Stellar structure 2 (Stefan Jordan)
08.5.25: Stellar structure 2 (Stefan Jordan)
15.5.25: Stellar structure 3 (Stefan Jordan)
22.5.25: Energy transport (Stefan Jordan)
29.5.25: Himmelfahrt, holiday
05.6.25: Energy production (Stefan Jordan)
12.6.25: Main sequence (Stefan Jordan)
19.6.25: Fronleichnam, holiday
26.6.25: Stellar evolution to the AGB (Stefan Jordan)
03.7.25: Late stages of stellar evolution (Stefan Jordan)
10.7.25: Stellar pulsations, rotation, magnetic fields (Stefan Jordan)
17.7.25: Stellar spectra (Stefan Jordan)
24.7.25: Written exam (Stefan Jordan)

Seminar:
 2-3 full days between July 28 and  Aug 1, 2025

The communication will be performed via the Übungsgruppensystem. 
https://uebungen.physik.uni-heidelberg.de/v/1992

Lehrinhalt

Module Part 1: Lecture “Galactic and Extragalactic Astronomy” (4 CP)
- Galaxy types and classification, correlations with physical properties,
stellar populations, population synthesis, chemical evolution concepts and
models (2);
- Milky Way (3): halo, bulge / pseudo bulge, central black hole, thin and
thick disk, spiral structure, star clusters, star formation history and chemical
enrichment, formation scenarios (e.g., Eggen-Lynden-Bell-Sandage), multi-
phase interstellar medium, dust, Galactic fountain, satellites, substructure
problem, Local Group;
- Spiral and elliptical galaxies (4): Surface photometry, profiles, origin of
spiral structure, mass measurement methods, rotation / velocity dispersion,
Tully-Fisher / Faber-Jackson relation, fundamental plane, super massive
black holes, active galaxies;
- Groups and clusters (3): morphology-density relation etc., mass
measurements, gravitational lensing, luminosity functions, interactions;
intergalactic gas; dark matter;
- Growth of structure (3): Origin of matter and elements, large-scale-
structure formation, large-scale matter distribution, redshift surveys, weak
lensing, galaxy formation and evolution, red / blue sequence, downsizing,
scaling relations, Butcher-Oemler effect, cosmic star formation history,
Lyman alpha forest, high-redshift universe, reionization, problems in galaxy
formation.

Module Part 2: Seminar (2 CP)
- Presentations and discussions on selected topics in Galactic and
extragalactic astronomy

Lehrziel

When successfully completing this course, the students are able to report on the properties of the wide range of galaxy types, understand their origin and evolution, and can elucidate the physical factors governing their evolution. They understand the main physical processes that shape the appearance of galaxies and galaxy clusters. They know about the connection between cosmological structure formation and the populations of visible objects. They have gained experience in applying dimensional and scaling arguments to estimate the relative importance of different physical processes.

Lehrinhalt

- Friedmann-Lemaître-cosmologies: cosmological redshift, parameter
set, effects of curvature and of the cosmological constant, Hubble
expansion and Cepheid-measurements
- Age of the Universe: age from the cosmological model, radiometric
dating and nuclear cosmochronology, age of the oldest cosmic
objects
- Distance-redshift relation of standard candles: distance-redshift
relations, calibration of supernovae, acceleration and dimming,
determination of densities and equations of state, evidence for dark
energy
- Abundance of chemical elements: thermal evolution, big bang
nucleosynthesis, other modes of nucleosynthesis (stellar, spallation,
explosive), reaction chains, element abundances
- Cosmic microwave background: formation of atoms, simplified
description of temperature anisotropies, measurement results and
conclusions from them (in particular spatial flatness), secondary
anisotropies
- Cosmic structures: linear growth, need for (nonbaryonic) dark
matter, large-scale distribution of galaxies, cosmic web
- Formation of galaxies: gravitational collapse, flat rotation curves
and virial equilibria, need for dark matter, abundance of haloes
- Gravitational lensing: gravitational light deflection, lens equation,
weak and strong lensing, measurements of lensing effects and their
inversion

Lehrziel

In this course, students gain fundamental understanding of the cosmological standard model and the cosmological evolution, including the impact of the basic observations and the connection to the physical framework. They gain a solid overview of the empirical basis of modern cosmology.

Lehrinhalt

1. Systems of star clusters 
(e.g around the giant elliptical galaxy M87, https://apod.nasa.gov/apod/ap040616.html )
--cluster age and mass distributions, formation/evolution/observational-biases interplay

2. Cluster age and mass estimates from their integrated photometry
--introduction to stellar population synthesis models

3. Cluster dynamical evolution
Gas-free evolution: clusters lose stars and eventually dissolve.  How fast?

4. From gas-embedded clusters to gas-free ones: expulsion of the residual star-forming gas and consequences
(e.g. from the gas-embedded Orion Nebula Cluster to the Pleiades open cluster
https://apod.nasa.gov/apod/ap120715.html
https://apod.nasa.gov/apod/ap120903.html )

5. Formation of star clusters (https://academic.oup.com/mnras/article/413/4/2741/964588):
--Modelling of star cluster formation, concept of star formation efficiency per freefall time, gas density-probability distribution functions

6. Colour-magnitude diagrams (https://esahubble.org/videos/heic1017b/):
-- cluster age estimates for the resolved stellar-population case, kinematic-based "cleansing" of cluster CMDs

Lehrinhalt

Vorgestellt werden aktuelle Fragestellungen der Forschung und zur Zeit laufende 
oder in Planung befindliche Forschungsprojekte. 
Themen sind: Schwarze Löcher (stellar, intermediär, supermassiv), Gravitationslinsen, Gravitationswellen, Dunkle Materie, etc.

Termine und Themen sind auf folgender Webseite zu finden:
https://blog.mpifr-bonn.mpg.de/silkebritzen/vorlesung-universitat-heidelberg/

Die Veranstaltung findet online statt und beginnt am 25.04. um 14 Uhr.

Der zoom-link lautet:
https://eu02web.zoom-x.de/j/9084381833?pwd=YU1UdWJRa1BzajF4Tyt4YVlSdU1BUT09 
Meeting ID: 908 438 1833

Lehrziel

Mein Ziel ist es, Interesse an aktuellen Fragen der Forschung zu wecken und über  spannende Forschungsprojekte zu informieren. Des Weiteren möchte ich den  Studenten Informationen über den Alltag in der Forschung liefern und Möglichkeiten für Master- und Doktorarbeiten aufzeigen.

Informationen zur Veranstaltung

Lehrinhalt

Why do stars lose mass and what are the mechanisms behind it? This lecture will provide on overview of the different types of winds we find in stars and their physical origin. After exploring the different wind regimes (solar wind, hot stars, cool stars), the lecture will also cover the consequences of strong mass outflow on the evolution and environment of stars.

Lehrinhalt

This lecture is an introduction to molecular astrophysics and astrochemistry.

Lehrziel

The spectroscopic and continuum observations of simple inorganic and complex organic molecules in space are at the forefront of observational astronomy. Powerful new facilities such as the Atacama Large Millimeter/submillimeter Array and the James Webb Space Telescope have enabled us to probe the molecular composition of the Universe from the Big Bang to local interstellar space, and from the distant past to the present. The wealth of diagnostic data is driving extensive laboratory and theoretical studies aimed at extracting key information about the physics and chemistry of space from these data. Our understanding of the life cycle of matter in the Universe is also intertwined with such a fundamental question as the origin of life. In this course, you will learn how molecules can be detected in a variety of interstellar environments, from the interstellar medium to planetary atmospheres, and how they are formed and destroyed there. You will learn about the basic spectroscopic properties of molecules and solids, how molecular lines and solid-state bands are used to study the underlying physical and chemical properties of the matter. The major processes of molecule formation and destruction in space, and the interplay between the gas-phase and surface reactions will be discussed from both experimental and theoretical perspectives. You will learn about the formation of the first elements after the Big Bang and the main chemical processes in the early Universe. You will also learn about the formation of other elements in stars, and what happens to these elements after they are ejected into the interstellar space at the end of the star's life. Finally, you will learn about exoplanets, atmospheres, habitability, and the origin of life.

Lehrinhalt

In this lecture, we will discuss the principles of radio and millimeter astronomy. This field is progressing rapidly, thanks to new facilities that reach unprecedented sensitivities and resolutions, such as ALMA and MeerKat, and soon the ngVLA, DSA-2000 and the SKA.
We will discuss the physical processes that give rise to radio and millimeter wave emission, from star forming regions in the Milky Way to galaxies in the very young universe. A focus will also be the technology by which to capture radio and millimeter emission, including the concepts of radio and millimeter interferometry.

Lehrinhalt

Historic/current definitions of 'planet';
Discovery methods: radial velocity, transit, astrometry, gravitational microlensing, direct imaging; strengths/weaknesses/biases;
Formation and evolution of planets and planetary systems: simulations & observation

Lehrinhalt

We will treat the following topics:
• Spectroscopy and metrology
• Atom-light interactions
• Cavity Quantum Electrodynamics 
• Matter waves
• Cooling and trapping
• Mass measurements
• Quantum gases
• (Ultracold) Collisions
• Single atoms and molecules
• Quantum information
• Femto- and attosecond processes

Lehrziel

After completing this course the students will be able to ż describe modern aspects of experimental research in atomic, molecular and optical physics, ż analyse standard experimental approaches of atomic, molecular and optical physics, ż design simple experimental set-ups in atomic, molecular and optical physics, ż apply the methods to simple practical examples.

Informationen zur Veranstaltung

Lehrinhalt

This lecture will provide an introduction to the fundamentals and current work in the research area of Attosecond Physics.  The pioneers of this field were awarded the Physics Nobel Prize in 2023 for providing the ultrashort flashes of light (attosecond pulses), and current opportunities to employ their techniques for the understanding and steering of electron motion in matter are quickly expanding.

The lecture will be accompanied by a tutorial (right after the lecture) for praticing our understanding of key concepts and physics pictures, also including (computational) experiments.

Important Dates:
- 15 April 2025, 14:15: First Lecture and Tutorial intro

Lehrinhalt

Special lectures on the quantum electrodynamics of precision spectroscopic experiments, covering both theoretical and experimental aspects

Lehrinhalt

Subject: Magnetic Resonance Imaging (MRI) and Nuclear Medicine

See website:
https://medphysrad-teaching.dkfz.de/medphys2.html

Lehrinhalt

I. Imaging Systems
II. Light Scattering

Lehrinhalt

* Structure of solids in real and reciprocal space
* Lattice dynamics and phonon band structure
* Thermal properties of insulators
* Electronic properties of metals and semiconductors: band structure and transport
* Optical properties from microwaves to UV
* Magnetism
* Superconductivity
(each chapter includes experimental basics)

Lehrziel

After completing the course the students - have gained a thorough understanding of the fundamentals of condensed matter physics and can apply concepts of many-particle quantum mechanics to pose and solve relevant problems. - will be able to describe the priciples of formation of solids and can propose appropriate experimental methods to study structural properties. They are familiar with and can apply the concept of reciprocal space. - they can apply fundamental electronic models to explain and predict properties of crystalline materials as metals, semiconductors, and insulators. - they can ascribe optical, magnetic properties of matter to electronic and structure degrees of freedom. - they can describe and theoretically explain fundamental properties of superconductivity. - they are able to choose appropriate experimental methods for probing structural, optical, magnetic, and electronic properties of condensed matter and can analyse the experimental results.

Informationen zur Veranstaltung

Lehrinhalt

This lecture introduces all physical concepts of the fundamentals of Environmental Physics and it is accompanied by exercises and tutorials every week.
The content spans:
• The fundamentals about the Earth climate system and its compartments, flow, transport, and the global radiation balance.
• Geophysical fluid dynamics, i.e. the fundamental laws of free and forced fluid movement and vorticity, and a practical guide to the first principles of turbulence.
• Global circulation of atmosphere and ocean, boundary layer physics, and slow flow through porous media and of ice.
• Gas and heat exchange between ocean and atmosphere. Global fluxes and cycles (energy, water, carbon).
• Isotope fractionation and isotope methods to study the Earth environments, focus on water and carbon isotopes.
• Introduction to models of environmental systems, basic principles of numerical climate modelling.
• Basic principles of radiative transfer. Climate system radiative forcing and sensitivity. Global climate change past, present and future.

Lehrziel

Students achieve a fundamental understanding of the key physical processes and interactions in the Earth surface system and its compartments, as well as of the human impact on these systems and the related societal implications. They are able to solve basic problems of environmental physics and interpret the results in the context of fundamental questions regarding the physics of the earth surface environments and the methodologies to observe and study those.

Informationen zur Veranstaltung

Lehrinhalt

• Fundamentals of physical oceanography, limnology, and hydrogeology 
• Heat and mass transfer between water and atmosphere 
• Flow and transport in surface and ground water  
• Tracer methods in the hydrological cycle

Lehrziel

Students achieve an advanced understanding of the physical processes in aquatic systems, the methods to study them, and their role in the climate system. They are able to solve advanced problems and interpret the results in the context of current questions in research and application. They can assess and use current scientific literature to further develop their knowledge base, enabling them to conduct independent master research projects in physics of aquatic systems.

Lehrinhalt

Global climate system:
- Climate forcing and response
- Atmosphere-ocean circulation and dynamics
- Energy cycle
Processes and interactions:
- Aerosols and meso-scale dynamics
- Atmosphere-ocean interactions
- Atmosphere-land interactions
Tools for climate studies:
- Satellite data and reanalysis 
- Earth system models
- Climate scenarios and projections

Lehrziel

Students achieve a specialised understanding of Earth system dynamics and complex climate models to study it, with focus on modern climate change. They are able to review literature, perform a climate data analysis, and interpret the results in the context of their project questions. They gain skills in critically reflecting the state of knowledge about climate change, design and articulate their results with a poster, and present and defend results at a poster conference. They have deepened their knowledge to conduct a research project in climate physics, and broadened their technical skills for programming and poster design.

Lehrinhalt

1 week block lecture, language: English, Sep. 22-26, 2025, 9-18h, INF229, R108 (first floor), lecturer: Dr. Jochen Landgraf.

Lehrinhalt

Lecture Homepage

The course consists of a lecture and an accompanying journal club

Focus of the lecture is the physics, the design and the application 
of particle detectors used in modern particle physics experiments. 
Covered topics are

- Interaction of particles with matter
- Scintillators and ToF detectors
- Gas detectors
- Silicon detectors
- Calorimeters
- Detector for particle identification
- Large detector systems
- ...

 

Lehrziel

After completion of the course the student has gained basic knowledge  about interactions of particles with matter, the physics of particle detectors,  their working principles, and their applications in experiments. The course  consists of a lecture and an accompanying journal club  Lecture: Introduction into the physics and the technical realization  of particle detectors; 2 hours/week; Wednesday 9:15 to 11:00. Journal Club: Deepening of knowledge on the basis of recent  detector papers; discussion of particular detector research;  1 hour/week; Fridays 11:15. 

Lehrinhalt

* Manifolds
* Geodetics, curvature, Einstein-Hilbert action
* Einstein equations
* Cosmology
* Differential forms in General Relativity
* The Schwarzschild solution
* Schwarzschild black holes
* More on black holes (Penrose diagrams, charged and rotating black holes)
* Unruh effect and hawking radiation

Lehrziel

After completing the course the students * have a thorough knowledge and understanding of Einstein's theory of General Relativity including the necessary tools from differential geometry and applications such as black holes, gravitational radiation and cosmology,  * have acquired the necessary mathematical tools from differential geometry, are trained in their application to physical situations with strong gravity and are familiar with their interpretation, * have advanced competence in the fields of theoretical physics covered by this course, i.e. the ability to analyze physical phenomena using the acquired concepts and techniques, to formulate models and find solutions to specific problems, and to interpret the solutions physically and communicate them efficiently, * are able to broaden their knowledge and competence in this field of theoretical physics on their own by a systematical study of the literature.

Lehrinhalt

• Effective action
• Symmetries and conservation laws
• Gauge theories: QED, QCD, QFT, quantized
• Feynman rules in Lorentz covariant gauges
• Renormalization in Gauge theories
• One-loop QED
• Spontaneous symmetry breaking and Higgs mechanism
• Renormalization groups, Wilson renormalization, lattice gauge theory

Lehrziel

After completing the course the students ż have a thorough knowledge and understanding of the regularisation and renormalisation programme in ż4-theory, of renormalisation in QED and non-abelian gauge theories (1-loop order), of the effective action and the modern renormalisation group approach, ż have acquired the necessary mathematical knowledge and competence for an in-depth understanding of this research field, ż have advanced competence in the fields of theoretical physics covered by this course, i.e. the ability to analyze physical phenomena using the acquired concepts and techniques, to formulate models and find solutions to specific problems, and to interpret the solutions physically and communicate them efficiently, ż are able to broaden their knowledge and competence in this field of theoretical physics on their own by a systematical study of the literature.

Informationen zur Veranstaltung

Lehrinhalt

- Introductory materials: bosons, fermions and second quantisation
- Green's functions approach
- Exactly solvable problems: potential scattering, Luttinger liquids etc.
- Theory of quantum fluids, BCS theory of superconductivity
- Quantum impurity problems: Kondo effect, Anderson model, renormalisation group approach
Depending on the lecturer more weight will be given to solid state theories or to soft matter.

Lehrziel

After completing the course the students - have a thorough knowledge and understanding, of the nowadays 'traditional' diagrammatic technique and the problems solved by this technique, including Landau's theory of quantum liquids and BCS theory of superconductivity, - of advanced non-perturbative approaches such as renormalization group transformations, bosonisation and Bethe Ansatz and there application to examples of quantum impurity problems such as potential scattering in Luttinger liquids, inter-edge tunneling in fractional quantum Hall probes and Kondo effect in metals and mesoscopic quantum dots, - have acquired the necessary mathematical knowledge and competence for an in-depth understanding of this research field, - have advanced competence in the fields of theoretical physics covered by this course, i.e. the ability to analyze physical phenomena using the acquired concepts and techniques, to formulate models and find solutions to specific problems, and to interpret the solutions physically and communicate them efficiently, - are able to broaden their knowledge and competence in this field of theoretical physics on their own by a systematical study of the literature.

Lehrinhalt

Contents:
1) Relativistic quantum theory (Dirac equation, relativistic light-matter
interaction)
2) Quantum theory of light and matter (quantized fields, interaction with
atoms)
3) Open quantum systems (matter and radiation, decoherence, Lamb-shift, natural line width)
4) Dynamics, time evolution and response theory
5) Many electron atoms and lattice models

Lehrinhalt

The course will cover advanced topics in Cosmology.

More information on
http://www.thphys.uni-heidelberg.de/%7Eamendola/advcosm-ss2025.html

Informationen zur Veranstaltung

Lehrinhalt

This course is MVBP2 in the modul handbook and is addressed to physics master students with an interest in biophysics. Motivated bachelor or PhD-students are also most welcome, as are students from neighboring disciplines. There are two lectures each week, each for 90 minutes, plus weekly homework and exercises. Together you can earn 6 credit points from this course. This lecture can be used for the oral master examination if combined with e.g. the lecture on statistical physics or the lecture on simulation methods, or with two short specialized lectures (like non-linear or stochastic dynamics). The details for the tutorial will be discussed in the first lecture, which is on Thu April 18.

Informationen zur Veranstaltung

Lehrinhalt

Basics and applications of nonequilibrium quantum field theory to particle physics/early universe cosmology and experiments with ultracold quantum gases: path integral formulation, resummation techniques, renormalization, classical aspects of nonequilibrium quantum fields, nonequilibrium instabilities, far-from-equilibrium scaling phenomena, thermalization.

Lehrinhalt

The course is ONLINE only. It will provide an introduction to Mathematica with applications to physics and statistics. You need to have Mathematica installed on your computer. The course will start on May 20, and continues for 8 lectures, every Tuesday at 11:15-13:00. More info 
https://www.thphys.uni-heidelberg.de/%7Eamendola/intromath-ss2025.html
  

   - Basics of Mathematica: functions, graphics, input/output, modules, algebraic manipulations, arrays, numerical methods
   - Solving common mathematical, physical, and statistical problems

Lehrinhalt

Bauteile gegenwärtiger Computer erreichen die Größenordnung von Atomen. Da für atomare und subatomare Physik die Quantenmechanik die akzeptierte und bestens bestätigte Theorie ist, wurde der Vorschlag von Feynman aus dem Jahr 1982 immer aktueller: nämlich Computer zu bauen und Algorithmen zu implementieren, die nach den Prinzipien der Quantenmechanik funktionieren. 
Beim Bau universell programmierbarer Quantencomputer und ihrer Nutzung wurden große Fortschritte erzielt und es gibt Hinweise dafür, dass sie in Zukunft gewisse Aufgabenstellungen wesentlich effizienter lösen können als klassische Computer. Ein viel diskutiertes und beachtetes Beispiel ist die Entschlüsselung aktuell verwendeter, bisher als sicher geltender Verschlüsselungsverfahren.  
Es ist nicht überraschend, dass gerade die der Anschauung am stärksten widersprechenden und daher im Anfangsstadium der Theorie am heftigsten kritisierten Konzepte der Quantenmechanik, wie Superposition und Verschränkung von Zuständen in verschiedenen Anwendungen einen Quantencomputer einem klassischen Computer überlegen machen. 
In der Vorlesung wollen wir insbesondere auf die Verknüpfung von Physik und Informatik in der Quanteninformationstheorie eingehen. 
 - Wir beginnen mit einer Vorstellung aktueller Herausforderungen der Digitalisierung und bekannter Grenzen (klassischer) Computer und geben eine kurze Einführung in Berechenbarkeitstheorie, Rechenmodelle, Algorithmen und reversibles Rechnen. Danach werden das Quantenbit und Rechenschritte darauf definiert, Quantenregister und Quantenschaltkreise eingeführt, wichtige Algorithmen untersucht und gezeigt, wie diese implementiert werden können.
 - Im Zusammenhang mit der Quanteninformatik wird der formale Aufbau der Quantenmechanik noch einmal vorgestellt. Dabei werden die Aspekte, die für die Funktionsweise eines Quantencomputers wesentlich sind, besonders hervorgehoben, z.B. Messprozess, E. Schmidt´scher Formalismus, Quantenkanäle, Superoperatoren und die Quanten-Fouriertransformation.
 - In einem dritten Teil wird die klassische Komplexitätstheorie kurz vorgestellt, um mögliche entscheidende Vorteile eines Quantencomputers aufzeigen zu können.
 - Der nächste Teil der Vorlesung besteht in einer Beschreibung und Diskussion des Shore´schen Algorithmus. Er beruht auf Ergebnissen der Zahlentheorie und der Quanten-Fouriertransformation. Er ist nicht nur der Algorithmus, der aktuell für die größte Aufmerksamkeit sorgt, sondern an ihm lassen sich auch die wesentlichen Vorteile des Quantencomputers und Elemente der Quantenkomplexität sehr gut darstellen.
 - Ein weiterer essentieller Punkt für die Entwicklung der Quantencomputer war die Entdeckung von Verfahren zur Fehlerkorrektur, die wir in diesem Teil der Vorlesung betrachten werden.
 - Die Eigenschaften der Quantenmechanik erlauben die Implementierung abhörsicherer, verschlüsselter Kommunikation. Diese wurde bereits über viele 100 km erfolgreich getestet (Nobelpreis für Physik 2022) und ist wesentliche Voraussetzung für ein Quanteninternet.
 - Abschließend sollen verschiedene Ansätze zum Bau von Quantencomputern und zur Realisierung von Gates vorgestellt werden.

Informationen zur Veranstaltung

Lehrinhalt

1. Strongly interacting fermions: the BCS-BEC crossover
1.1. Scattering theory and Feshbach resonances
1.2. BCS theory of superconductivity
1.3. Bose-Einstein condensation and superfluidity
1.4. Unitary Fermi gas and scale invariance
1.5. Contact density and Tan relations
1.6. Fermi polarons and spectroscopy
2. Bosons in optical lattices: the Mott Insulator—Superfluid transition
2.1. Optical lattices and Bose-Hubbard model
2.2. Mott Insulator—Superfluid transition
2.3. Quantum Critical Point, excitations and Higgs mode
2.4. Fermi-Hubbard model
2.5. Quantum Simulation
3. Real-time dynamics and transport
3.1. Nonequilibrium dynamics and thermalization
3.2. Collective modes and transport

Lehrinhalt

We derive the thermal ground state for the deconfining phase of SU(2) Yang-Mills Thermodynamics, discuss its thermal quasiparticle excitations, and compute the polarization tensor of the effective massless gauge mode. Next, we use these results under the postulate that thermal photon gases of sufficiently large spatial volumes are described by an SU(2) rather than a U(1) gauge principle. For the CMB this gives rise to a modified temperture-redshift relation with an interesting link to 3D Ising criticality. Moreover, we argue that the CMB large-angle anomalies may be traced to SU(2) screening effects and that an axial anomaly with chiral symmetry breaking at the Planck scale yields an ultralight axion particle whose temperature dependent mass essentially is determined by the SU(2) thermal ground state. The super-horizon sized condensate of these particles is a candidate for dark energy. To test the above postulate
recents results of a terrestial blackbody-cavity experiment are discussed and interpreted in the context of SU(2) Yang-Mills thermodynamics.

 Objectives: instanton, Matsubara sum, caloron, thermal ground state, thermal quasiparticle dispersion law, critical exponent, cosmological model, Veneziano-Witten, emissivity, Dicke switch, difference of dBm of noise power

Lehrinhalt

History of the neutrino
Flavor physics
Neutrino Oscillations in Vacuum and Matter 
Neutrino Masses in the SM and beyond 
Dirac and Majorana neutrinos
Neutrinoless double beta decay
Neutrinos from the Sun and the atmosphere
Reactor and accelerator neutrinos 
Neutrinos in cosmology
High energy astrophysical neutrinos 
Coherent elastic neutrino-nucleus scattering

Informationen zur Veranstaltung

Informationen zur Veranstaltung

Lehrinhalt

Lecture time & place: Wed 2:00pm at großer Hörsaal, Philosophenweg 12

Motivation:
Nonlinear dynamics is an interdisciplinary part of mathematical physics, with applications in such diverse fields as mechanics, optics, chemistry, biology, ecology, to name but a few. Equations with nonlinearities show a much more diverse behavior than their linear counterparts, for instance self-sustained oscillations, nonlinear competition (as linear superposition does not hold anymore), chaotic dynamics and pattern formation.

Contents:
The lecture deals with nonlinear dynamics on the level of ordinary differential equations (ODEs), introducing concepts like phase space analysis, attractors, (in)stability of solutions and bifurcations, multiple scale analysis and nonlinear oscillations.

Lehrinhalt

Effective Field Theories (EFTs) furnish an elegant means to take the first step towards the next quantum field theory of nature, because they allow to include physics beyond the standard model (SM) in a model-independent way via higher dimensional operators.
Beyond that, they are useful to tackle problems with separated scales, that arise in many areas of fundamental physics. EFTs allow to describe the important physics conveniently in terms of degrees of freedom that are most relevant at a given length-scale. In particular, they allow to consistently re-sum large logarithms of ratios of scales, that would otherwise spoil the perturbative expansion, and provide a modern notion of renormalization.
This lecture provides a comprehensive introduction to the concept of EFTs and modern applications, including the bottom-up approach to physics beyond the SM as a guide to the next theory of nature.

The topics covered include:
- General concept of EFTs and resummation
- EFT of weak interactions: Fermi-Theory and Flavor Physics
- EFT of QCD: Chiral Perturbation Theory
- EFTs and Electroweak Symmetry Breaking: the non-linear Sigma Model
- EFT of Axions / Axion-like particles
- EFTs and neutrino physics
- Bottom-up approach to a more fundamental theory of nature: SM-EFT and its variants
- EFT for Dark Matter

Lehrinhalt

- Axioms of Probability Theory; random variables, important distributions
- Bayesian inference
- Linear regression, non-linear regression
- Regularized regression to fit high-dimensional data
- Hypothesis testing: fundamental concepts
- Parametric and non-parametric tests
- Classification
- Cluster analysis
- Model selection

Lehrziel

After completion of this module, the students understand fundamental concepts of stochastics, and are able to relate them to concrete problems. They understand and are alert of possible pitfalls such as overfitting, multiple comparisons, or susceptibility to outliers. They know and are able to apply basic countermeasures and they have access to more advanced literature on the subject. Students are familiar with relevant high-level languages and statistical programming libraries, and know how to apply them to real-world data provided in the exercises.

Lehrinhalt

This seminar is part of the master module MVAstro3 (Galactic and Extragalactic Astronomy).  It supplements the lecture contents.  It is usually being held as a block event on three or four afternoons chosen in the course; typically on Saturdays.

Lehrinhalt

Durchführung von mehreren astrophysikalischen Versuchen je nach Kenntnisstand innerhalb einer Woche. Diese decken grosse Gebiete in der Astronomie ab. Dauer pro Versuch 1-1.5 Tage. Kein separates Protokoll oder Hausarbeit notwendig.

Lehrziel

Selbstständige Bearbeitung experimenteller Fragestellungen. Kennenlernen und Vertiefung diverser astronomischer moderner Tools wie zB Datenreduktion, virtuelles Observatorium, Interpretation diagnostischer Diagramme.