Module Handbook

  • Dynamischer Default-Fachbereich geändert auf PHY

Notes on the module handbook of the department Physics

Die hier dargestellten Studiengang-, Modul- und Kursdaten des Fachbereichs Physik [PHY] befinden sich noch in Entwicklung und sind nicht offiziell.

Die offiziellen Modulhandbücher finden Sie unter https://www.physik.uni-kl.de/studium/modulhandbuecher/ .

Module PHY-MB-M-6

Many-Body Quantum Systems (M, 20.0 LP)

Module Identification

Module Number Module Name CP (Effort)
PHY-MB-M-6 Many-Body Quantum Systems 20.0 CP (600 h)

Basedata

CP, Effort 20.0 CP = 600 h
Position of the semester 2 Sem. from WiSe/SuSe
Level [6] Master (General)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Physics
Area of study [PHY-AQP] Advanced Quantum Physics
Reference course of study [PHY-88.C16-SG] M.Sc. Advanced Quantum Physics
Livecycle-State [NORM] Active

Notice

At least 8 CP must be completed in the courses [PHY-WPFTP-036-K-7] Advanced Quantum Mechanics I+II, [PHY-WPFTP-164-K-7] Many-Body Quantum Theory I and/or [PHY-WPFTP-189-K-7] Many-Body Quantum Theory II.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V PHY-WPFTP-036-K-7
Advanced Quantum Mechanics I+II
WP 56 h 184 h
SL1
ja PL1 8.0 irreg.
2V PHY-WPFTP-164-K-7
Many-Body Quantum Theory I
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
2V PHY-WPFTP-189-K-7
Many-Body Quantum Theory II
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
2V PHY-WPFEP-202-K-7
Quantum Gases I
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
2V PHY-WPFEP-275-K-7
Quantum Gases II
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
2V PHY-WPFTP-172-K-7
Quantum Information
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
2V PHY-WPFEP-295-K-7
Quantum Information Technology
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
4V PHY-WPFTP-175-K-7
Quantum Field Theory I+II
WP 56 h 184 h
SL1
ja PL1 8.0 irreg.
4V PHY-WPFTP-116-K-7
Solid State Theory I+II
WP 56 h 184 h
SL1
ja PL1 8.0 irreg.
2V PHY-WPFEP-288-K-7
Quantum Technology
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
2V PHY-WPFTP-343-K-7
Superconductivity
WP 28 h 92 h
SL1
ja PL1 4.0 irreg.
  • About [PHY-WPFTP-036-K-7]: Title: "Advanced Quantum Mechanics I+II"; Presence-Time: 56 h; Self-Study: 184 h
  • About [PHY-WPFTP-036-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFTP-164-K-7]: Title: "Many-Body Quantum Theory I"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFTP-164-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFTP-189-K-7]: Title: "Many-Body Quantum Theory II"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFTP-189-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFEP-202-K-7]: Title: "Quantum Gases I"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFEP-202-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFEP-275-K-7]: Title: "Quantum Gases II"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFEP-275-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFTP-172-K-7]: Title: "Quantum Information"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFTP-172-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFEP-295-K-7]: Title: "Quantum Information Technology"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFEP-295-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFTP-175-K-7]: Title: "Quantum Field Theory I+II"; Presence-Time: 56 h; Self-Study: 184 h
  • About [PHY-WPFTP-175-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFTP-116-K-7]: Title: "Solid State Theory I+II"; Presence-Time: 56 h; Self-Study: 184 h
  • About [PHY-WPFTP-116-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFEP-288-K-7]: Title: "Quantum Technology"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFEP-288-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
  • About [PHY-WPFTP-343-K-7]: Title: "Superconductivity"; Presence-Time: 28 h; Self-Study: 92 h
  • About [PHY-WPFTP-343-K-7]: The study achievement must be obtained. It is a prerequisite for the examination for PL1 .
Some of the courses take place at irregular intervals. A current overview of the courses offered can be found in the campus management system of the TU Kaiserslautern (https://www.kis.uni-kl.de).

Study achievement SL1

  • Verification of study performance: continuous and active participation in the courses
  • Study achievement is a prerequisite for the examination.
    Proof of regular and active participation in course, the conditions for the regular and active participation are made public at the beginning of the course

Examination achievement PL1

  • Form of examination: oral examination (60 Min.)
  • Examination Frequency: irregular (by arrangement)

Evaluation of grades

The grade of the module examination is also the module grade.

In justified exceptional cases, a module examination can consist of partial examinations (sub-module examinations). This has to be approved by the chairperson of the examination board. In such cases, the grade of the module examination must be calculated as the arithmetic average of the grades for the individual test performances.

Contents

  • discrete groups, including application to eigenvalue spectra
  • continuous (Lie) groups, including application to electron spin and other elementary particle properties
  • quantum mechanics of open systems
  • scattering theory
  • relativistic quantum mechanics: Klein-Gordon and Dirac equations, nonrelativistic limit
  • many-body theory of quantum liquids
  • finite temperatures
  • elementary quantum field theory: quantization of the electromagnetic field.
introduction to many-body models (fermionic and bosonic systems, spin models); approximation methods (Hartree-Fock, Bogoliubov transformations); equation-of motion-methods; polarons; Green-functions-based methods; Feynman diagrams, including applications to excitations in many-fermion systems; introduction to non-equilibrium techniques.
introduction to many-body models (fermionic and bosonic systems, spin models); approximation methods (Hartree-Fock, Bogoliubov transformations); equation-of motion-methods; polarons; Green-functions-based methods; Feynman diagrams, including applications to excitations in many-fermion systems; introduction to non-equilibrium techniques.
  • Making and probing ultracold quantum gases
  • Bose-Einstein condensation
  • properties of Bose-Einstein condensates
  • solitons
  • vortices
  • ultracold Fermi gases
  • BEC-BCS crossover
  • Experimental techniques
  • laser cooling and trapping
  • evaporative cooling
  • Bose-Einstein condensation
  • degenerate Fermi gases
  • interaction between ultracold atoms
  • Gross-Pitaevskii equation
  • Thomas-Fermi approximation
  • Hartree-Fock theory
  • Bogoliubov theory
  • vortices and superfluidity
  • Landau-Khalatnikov two fluid modell
  • spinor gases
  • disorder
  • Feshbach resonances
  • BEC-BCS crossover
  • optical lattices
  • Bose-Hubbard model
  • Hubbard model
  • low-dimensional quantum gases
  • quantum states
  • entanglement and its measures
  • teleportation
  • qubits and diVincenzo criteria
  • single qubit gates and realizations
  • quantum correlations and two-qubit gates
  • quantum computation and simple algorithms
  • quantum cryptography and quantum communication
  • quantum error correction
  • experimental implementations of quantum computation
  • quantum repeaters
  • quantum algorithms:
    • Grover’s algorithm
    • Shor’s algorithm.
  • classical field theory
  • canonical field quantization
  • Noether theorem
  • Schrödinger field, Klein-Gordon field, Maxwell field, Dirac field
  • quantum electrodynamics
  • perturbation theory
  • Wick theorem, Feynman diagrams
  • scattering processes
  • renormalization
  • quantization of gauge fields
  • introduction to the standard model.
  • Drude model
  • failures of the free electron model
  • crystal lattices
  • band structure theory
  • phonons
  • Matsubara formalism
  • exactly solvable models
  • strong electronic correlations and magnetism
  • superconductivity.
  • introduction to quantum properties:
    • matter waves
    • quantum statistics
    • entanglement
  • matter wave applications and sub-wavelength microscopy
  • applications in time-keeping:
    • optical clocks
    • squeezed states
  • superconductivity and superfluidity, and their applications.
  • Phenomenology
    • Historical introduction
    • critical temperature
    • Meissner-Ochselfeld effect
    • type I and type II superconductor
    • thermodynamics of superconductors
    • London theory
    • flux quanta
  • Ginzburg-Landau theory:
    • Wave function of superconductivity
    • inhomogeneous superconductor
    • Ginzburg-Landau equations
    • London penetration depth and coherence length
    • critical magnetic fields
    • magnetization curve
    • interaction between flux quanta
    • critical current
  • Bardeen-Cooper-Schrieffer-Theorie:
    • Josephon effects
    • Feynman theory
    • SQUID
    • Cooper problem
    • Jellium model of electron gases
    • Coulomb interaction
    • lattice vibrations
    • electron-phonon interaction
    • BCS ground state
    • energy gap
    • excited states
    • Gorkov derivation of Ginzburg-Landau theory

Competencies / intended learning achievements

Successful completion of this module will develop the following skills, knowledge and expertise:
  • The student will know and understand the fundamental concepts, methods and approaches of many-body quantum systems.
  • The student will have acquired a structured specific knowledge on those sub-fields and topics of many-body quantum systems which are treated by the particular courses that the student has taken.
  • The student will understand essential aspects of interactions among large numbers of quantum particles, and their implications for technological applications.
  • The student will acquire an overview of current fundamental problems in many-body quantum systems.
  • The student will be able to understand and interpret discrepancies between theoretical predictions and experimental results.
  • The student will be aware of how modern quantum many-body theory and experimental techniques were developed historically.
  • The student will appreciate how progress on the quantum many-body problem has contributed to the development of the fundamental concepts of modern physics in general.
  • The student will be able to apply fundamental scientific methods, such as induction, model construction, and experimental testing, to solve scientific problems and develop new scientific insights, especially in the contexts of many-body quantum systems.
  • The student will also be able to apply the essential working strategies and paradigms that are specific to many-body quantum systems, in order to recognize and solve typical problems involving quantum systems of many interacting particles.
  • The student will conversely understand how the specific concepts and quantum many-body physics relate to the basic principles of physics in general.

Literature

  • Sakurai: Advanced Quantum Mechanics, Addison-Wesley.
  • Dyson: Advanced Quantum Mechanics, World Scientific Publishing
  • Schwabl: Quantenmechanik für Fortgeschrittene, Springer
  • Münster: Quantentheorie, de Gruyter
  • Gottfried, Yan: Quantum Mechanics: Fundamentals, Springer
  • Landau, Lifschitz: Course of Theoretical Physics Vol. 3, Quantum Mechanics: Non-Relativistic Theory, Pergamon Press
  • Landau, Lifschitz: Course of Theoretical Physics Vol. 4, Relativistic Quantum Theory, Butterworth-Heinemann
  • Roessler: Solid-State Theory, Springer
  • Lipparini: Modern Many-Particle Physics, World Scientific
  • Doniach, Sondheimer: Green’s Functions in Solid State Physics, Imperial College Press
  • Haug, Jauho: Quantum Kinetics in Transport and Optics of Semiconductors, Springer
  • Wen: Quantum Field Theory and Many-Body Systems
  • Roessler: Solid-State Theory, Springer
  • Lipparini: Modern Many-Particle Physics, World Scientific
  • Doniach, Sondheimer: Green’s Functions in Solid State Physics, Imperial College Press
  • Haug, Jauho: Quantum Kinetics in Transport and Optics of Semiconductors, Springer
  • Wen: Quantum Field Theory and Many-Body Systems
  • Metcalf, van der Straten: Laser Cooling and Trapping, Springer
  • Pethick, Smith: Bose-Einstein Condensation in Dilute Gases, Cambridge University Press
  • Salomon, Shlyapnikov, Cugliandolo: Many-Body Physics with Ultracold Gases, Les Houches Lecutre Notes 2010, Oxford University Press
  • Zwerger: The BEC-BCS Crossover and the Unitary Fermi Gas, Springer Lecture Notes 836, Springer
  • Pitaevskii and Stringari, Bose-Einstein condensation, Clarendon Press
  • Cohen-Tannoudji and Guery-Odelin, Advances in atomic physics, World Scientific Publishing
  • Metcalf, van der Straten: Laser Cooling and Trapping, Springer
  • Pethick, Smith: Bose-Einstein Condensation in Dilute Gases, Cambridge University Press
  • Salomon, Shlyapnikov, Cugliandolo: Many-Body Physics with Ultracold Gases, Les Houches Lecutre Notes 2010, Oxford University Press
  • Zwerger: The BEC-BCS Crossover and the Unitary Fermi Gas, Springer Lecture Notes 836, Springer
  • Barenghi, Parker: A Primer on Quantum Fluids, Springer
  • Griffin, Nikuni, Zarembar: Bose-Condensed Gases at Finite Temperatures, Cambridge University Press
  • Lewenstein, Sanpera, Ahufinger: Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems, Oxford University Press
  • Pelster: Bose-Einstein-Kondensation, Vorlesungsmanuskript 2004
  • Pitaevskii, Stringari: Bose-Einstein Condensation and Superfluidity, Oxford University Press
  • Stoof, Dickerscheid, Gubbels: Ultracold Quantum Fields, Springer
  • Ueda: Fundamentals and New Frontiers of Bose-Einstein Condensation, World Scientific
  • Pethick, Smith: Bose-Einstein Condensation in Dilute Gases, Cambridge University Press
  • Buckel, Kleiner: Superconductivity: Fundamentals and Applications, Wiley-VCH
  • Gerry, Knight: Introductory Quantum Optics, Cambridge University Press
References will be announced in the course or on the website of the course.
  • Peskin, Schroeder: An Introduction to Quantum Field Theory, Westview Press
  • Dyson: Advanced Quantum Mechanics, World Scientific Publishing
  • Gross: Relativistic Quantum Mechanics and Field Theory, Wiley
  • Mandl, Shaw: Quantum Field Theory, Wiley
  • Dyson: Quantenfeldtheorie, Springer
  • Greiner: Relativistic Quantum Mechanics - Wave Equations, Springer
  • Greiner, Reinhardt: Quantum Electrodynamics, Springer
  • Greiner, Reinhardt: Field Quantization, Springer
  • Schweber: QED and the men who made it - Feynman, Schwinger, and Tomonaga, Princeton University Press
  • Veltman: Diagrammatica - The Path to Feynman Diagrams, Cambridge University Press
  • Lancaster, Blundell: Quantum Field Theory for the Gifted Amateur, Oxford University Press
  • Ashcroft, Mermin: Solid state physics, Cengage Learning
  • Mahan: Many-Particle Physics, Springer
  • Czycholl: Theoretische Festkörperphysik, Springer
  • Kittel: Quantum Theory of Solids, Wiley
  • Pethick, Smith: Bose-Einstein Condensation in Dilute Gases, Cambridge University Press
  • Buckel, Kleiner: Superconductivity: Fundamentals and Applications, Wiley-VCH
  • Gerry, Knight: Introductory Quantum Optics, Cambridge University Press
  • Bransden, Joachain: Physics of Atoms and Molecules, Prentiss Hall
  • Haroche, Raimond: Exploring the Quantum, Oxford University Press
  • Tinkham: Introduction to Superconductivity, Dover Publications
  • Nielsen, Chuang: Quantum Computation and Quantum Information, Cambridge University Press
  • Annett: Superconductivity, Superfluids, and Condensates, Oxford University Press
  • Bennemann, Ketterson (Eds.): The Physics of Superconductors: Vol. I Conventional and Unconventional Superconductors, Springer
  • Bennemann, Ketterson (Eds.): The Physics of Superconductors: Vol. II Novel Superconductors, Springer
  • Blundell: Superconductivity - a Very Short Introduction, Oxford
  • Kleiner, Buckel: Superconductivity - Fundamentals and Application, Viley VCH
  • De Gennes: Superconductivity of Metals and Alloys, Taylor & Francis
  • Tinkham: Introduction to Superconductivity, Dover

Materials

depending on choice, see respective course description

Registration

depending on choice, see respective course description

Requirements for attendance (informal)

depending on choice, see respective course description

Requirements for attendance (formal)

None

References to Module / Module Number [PHY-MB-M-6]

Course of Study Section Choice/Obligation
[PHY-88.C16-SG] M.Sc. Advanced Quantum Physics Many-Body Quantum Systems [WP] Compulsory Elective