Quantum ManyBody Physics in NonEquilibrium
Module PH7012
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Basic Information
PH7012 is a semester module in English language at Master’s level which is offered in summer semester.
This Module is included in the following catalogues within the study programs in physics.
 Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
If not stated otherwise for export to a nonphysics program the student workload is given in the following table.
Total workload  Contact hours  Credits (ECTS) 

270 h  90 h  9 CP 
Responsible coordinator of the module PH7012 is Ulrich Schollwöck.
Content, Learning Outcome and Preconditions
Content
This module provides an introduction to the nonequilibrium manybody theory of quantum systems, required for the description of transport phenomena in quantum systems and their response to external perturbations, and of modern nonequilibrium measurements in condensed matter systems. The fundamental theoretical concepts to be taught are nonequilibrium Green’s functions and the Keldysh formalism. The module starts with a short repetition of second quantization and important models of condensed matter physics. It proceeds to formulating the nonequilibrium evolution of quantum systems and the evaluation of timedependent averages and correlations based on contour integration (Keldysh formalism). After introducing the hierarchy of manyparticle Green’s functions, the module elucidates the physical content of (nonequilibrium) singleparticle and twoparticle Green’s functions. In order to actually evaluate Green’s functions, the module will then move through several of the key approximations made, meanfield approximations, KadanoffBaym conserving approximation, and manybody perturbation theory. The formalisms will then be applied to important problems of nonequilibrium many body theory, namely linearresponse theory and transport phenomena. The use of the formalisms will be illustrated by their use for the understanding of actual experiments.
Learning Outcome
After completing the Module the student is able to:

Explain and use the main models of interacting condensedmatter systems

Understand the physical meaning and use of singleparticle and twoparticle Green’s functions out of equilibrium

Set up calculations of physical observables and correlations in nonequilibrium quantum systems using the Keldysh contour formalism

Understand and use the main approximations required to actually evaluate the formal expressions of 2 and 3.

Derive and use key results from quantum linear response and transport theory.
Preconditions
In addition to the requirements for the Master’s program in Quantum Science and Technology, the completion of a module in (equilibrium) quantum manybody physics is advisable.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Please keep in mind that course announcements are regularly only completed in the semester before.
Type  SWS  Title  Lecturer(s)  Dates  Links 

Learning and Teaching Methods
The module consists of a lecture series (4 SWS) and exercise classes (2 SWS), comprising two lecture sessions and one exercise session per week.
The main teaching material will be presented on the blackboard. This will be supplemented by power point / keynote presentations to summarize / illustrate stateoftheart applications of the methods taught in the module. Weekly problem sets are offered to obtain a better comprehension of the lecture content and to improve their familiarity with them. The solutions to the problem sets are discussed in weekly exercise classes.
Participation in the exercise classes is strongly recommended, since the exercises are aids for acquiring a deeper understanding of the core tools of nonequilibrium manybody physics and for practicing to solve typical exam problems.
Media
Power point /keynote and One Note presentation, blackboard.
Literature
Standard textbooks of quantum manybody theory that also treat nonequilibrium, e.g.:

Gianluca Stefanucci, Robert van Leeuwen, Nonequilibrium ManyBody Theory of Quantum Systems, Cambridge University Press 2013: Comprehensive textbook on nonequilibrium theory in a unified presentation

Jorgen Rammer, Quantum Transport Theory, Perseus Books, 1998: Nonequilibrium quantum theory with special interest in transport phenomena

Henrik Bruus, Karsten Flensberg, ManyBody Quantum Theory in Condensed Matter Physics, Oxford University Press, 2004: Popular introduction to equilibrium quantum manybody theory with an introduction to nonequilibrium phenomena, laying the ground for more advanced nonequilibrium problems

Leonid Keldysh, Progress in Nonequilibrium Green’s functions II, ed. M. Bonitz and D. Semkat, World Scientific 2003: Perspective on the field by its leading inventor
Module Exam
Description of exams and course work
There will be a written exam of 120 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using conceptual questions and computational tasks.
For example an assignment in the exam might be:
 Derive the formal solution of a nonequilibrium quantum problem in the Keldysh contour formalism.
 Discuss the physical content of a nonequilibrium Green’s function.
 Explain the LuttingerWard theorem.
 What is the linked cluster theorem?
 Calculate timedependent screening in an electron gas.
 Applications of the LandauerBüttiker formula
Exam Repetition
The exam may be repeated at the end of the semester.