Theory of Stochastic Processes
Module PH1006
Module version of SS 2019
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
available module versions  

SS 2021  SS 2019  WS 2015/6 
Basic Information
PH1006 is a semester module in German 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.
 Theory courses for condensed matter physics
 Theory courses for Biophysics
 Complementary catalogue of special courses for nuclear, particle, and astrophysics
 Complementary catalogue of special courses for Applied and Engineering Physics
 Specialization Modules in EliteMaster Program Theoretical and Mathematical Physics (TMP)
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) 

300 h  90 h  10 CP 
Responsible coordinator of the module PH1006 in the version of SS 2019 was Ulrich Gerland.
Content, Learning Outcome and Preconditions
Content
The module develops the theory of stochastic processes and the methods for their analysis. Examples to practice the acquired methods will be chosen primarily from the area of biophysics, but the major teaching and learning content (see below) is relevant for all areas of physics.
Table of Content:
 Probability Theory
 Stochastic Processes
 Master Equation
 Stochastic Thermodynamics
 Observables on Trajectories
 FockerPlanck Equations
 Langevin Equations
 Approximation Methods and Limits
Learning Outcome
At the end of the module students know the basic methods to handle physical systems that can be described by stochastic processes as well as the basic assumptions necessary to apply them. They are able to
 set up and solve Master equations, stochastic differential equations and Fokker Planck equations and know simple simulation methods.
 understand and apply the basic principles of stochastic thermodynamics.
 apply and adapt approximation methods for the analysis of complex stochastic processes
Preconditions
A solid basis in statistical physics (e.g. PH0008) is assumed.
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Type  SWS  Title  Lecturer(s)  Dates  Links 

VO  4  Theory of Stochastic Processes  Gerland, U. 
Mon, 08:30–10:00, PH HS3 Wed, 12:00–14:00, PH HS3 

UE  2  Exercise to Theory of Stochastic Processes 
Kremser, S.
Responsible/Coordination: Gerland, U. 
dates in groups 
Learning and Teaching Methods
The modul consists of a lecture and exercise classes.
In the thematically structured lecture the theoretical contents are presented and discussed. The theoretical models for the description of stochastic processes are developed on the blackboard together with the students. Concrete physical examples are studied indepth and compared to experimental results.
In the exercises additional understanding questions are answered together with the students. Furthermore, specific topics of the lecture are discussed indepth and relevant aspects are reviewed in regular intervals. Questions of students are given a large space.
In the homeworks the students have the opportunity to apply the presented techniques to concrete problem examples and to analyze the results. In the course of this analytic calculation exercises, simple numerical simulations and conceptual questions with answers in the form of continuous text are chosen as task form. The solution proposals of the students are corrected to give the students feedback for their modeling and solution abilities and to detect and correct misconceptions as early as possible.
Media
Lecture notes, problem sheets (containing homework problems and questions for exercises), web page
Literature
 Crispin Gardiner: "Stochastic Methods: A Handbook for the Natural and Social Sciences" (Springer)
 N.G. van Kampen: "Stochastic Processes in Physics and Chemistry" (NorthHolland)
Module Exam
Description of exams and course work
There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.
For example an assignment in the exam might be:
 Modelling of a concrete example with a Master equation and solving the equation
 Approximation of a given Master equation through a FokkerPlanck equation with the KramersMoyal or Van Kampen Expansion, Solution of the FokkerPlanck equation
 Transformation of a Langevin Equation into a FokkerPlanck equation
 Calculating the entropy production of a system obeying a Master equation
Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.
There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the midterm of At least 70% of the problems in the homeworks and the mock exam need to be worked on. A problem counts as worked on if at least an ansatz leading to the solution is found.
Exam Repetition
The exam may be repeated at the end of the semester.