Universität Wien

520015 VU Stochastic processes in physics (2021S)

5.00 ECTS (3.00 SWS), SPL 52 - Doktoratsstudium Physik
Continuous assessment of course work
VDS-PH
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 15 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 09.03. 11:00 - 12:10 Digital
  • Thursday 11.03. 11:00 - 12:10 Digital
  • Tuesday 16.03. 11:00 - 12:10 Digital
  • Thursday 18.03. 11:00 - 12:10 Digital
  • Tuesday 23.03. 11:00 - 12:10 Digital
  • Thursday 25.03. 11:00 - 12:10 Digital
  • Tuesday 13.04. 11:00 - 12:10 Digital
  • Thursday 15.04. 11:00 - 12:10 Digital
  • Tuesday 20.04. 11:00 - 12:10 Digital
  • Thursday 22.04. 11:00 - 12:10 Digital
  • Tuesday 27.04. 11:00 - 12:10 Digital
  • Thursday 29.04. 11:00 - 12:10 Digital
  • Tuesday 04.05. 11:00 - 12:10 Digital
  • Thursday 06.05. 11:00 - 12:10 Digital
  • Tuesday 11.05. 11:00 - 12:10 Digital
  • Tuesday 18.05. 11:00 - 12:10 Digital
  • Thursday 20.05. 11:00 - 12:10 Digital
  • Thursday 27.05. 11:00 - 12:10 Digital
  • Tuesday 01.06. 11:00 - 12:10 Digital
  • Tuesday 08.06. 11:00 - 12:10 Digital
  • Thursday 10.06. 11:00 - 12:10 Digital
  • Tuesday 15.06. 11:00 - 12:10 Digital
  • Thursday 17.06. 11:00 - 12:10 Digital
  • Tuesday 22.06. 11:00 - 12:10 Digital
  • Thursday 24.06. 11:00 - 12:10 Digital

Information

Aims, contents and method of the course

This course is an introduction into the theory and simulation of stochastic processes with applications in physics as well as in related areas such as chemistry and biology.

Course subjects include: dynamics of many-particle systems, randomness and noise, random variables, stochastic processes, Markov processes, master equation, Fokker Planck equation, stochastic differential equations, Langevin equation, fluctuation dissipation theorem, diffusion, Kramers problem, non-equilibrium fluctuations, stochastic engines, quantum measurement, open quantum systems and decoherence.

The lectures will be accompanied by practical exercises in which the concepts discussed in the lectures will be used, mainly with the help of computer simulations, to solve specific problems. For selected topics we make the connection to their application in concrete experiments.

Prerequisites: basic knowledge of statistical physics, command of a higher programming language (e.g., C, C++, Python).

Assessment and permitted materials

Continuous participation in the exercises, test at the end of the semester.

Minimum requirements and assessment criteria

Contributions to the exercise classes as well as a final exercise will be evaluated.

An overall positive evaluation requires a positive evaluation of exercise classes and exam.

The weighting between exercise classes and exam for the final grade is 50% each.

The date for the final written exam is 24.06. 11:00 - 12:10

Grading written exam:

1: 87-100%
2: 75-86%
3: 63-74%
4: 50-62%
5: 0-49%

For evaluation of the exercises your electronically submitted solutions will be used as well as the presentation during the exercise class. 2 points are given for each part of the solution.
The grade is evaluated based on the total number of points until end of the semester, with grading based on the following key (rounded to the better grade):

1: 87-100%
2: 75-86%
3: 63-74%
4: 50-62%
5: 0-49%

Examination topics

Topics of the lecture and the exercises.

Reading list

- R. Mahnke, J. Kaupuzs and I. Lubashevsky, “Physics of Stochastic Processes”, (Wiley-VCH, Weinheim, 2009).

- N. G. Van Kampen, “Stochastic Processes in Physics and Chemistry”, (North Holland, 1992).

- C. W. Gardiner, “Handbook of stochastic methods”, (Springer, 2004),

- A. Papoulis , “Probability, random variables, and stochastic processes”, (McGraw-Hill, 1984).

- W. Feller, “An introduction to probability theory and its applications”, Vol. 1 & 2 (Wiley, 1971)

- W. A. Gardner, “Introduction to random processes with applications to signals and systems”, (McGraw-Hill, 1990).

- H. Risken , “The Fokker-Planck Equation: Methods of Solutions and Applications”, (Springer, 1996).

- D. T. Gillespie, “Markov Processes”, (Academic Press, 1992).

- M. Kac “Random walk and the theory of Brownian motion”, The American Mathematical Monthly 54: 369–391 (1947).

- S. Chandrasekhar “Stochastic problems in physics and astronomy”, Review of Modern Physics 15: 1–89 (1943).

- S. Redner, “A Guide to First-Passage Processes”, (Cambridge University Press, 2001).

- N. G. van Kampen, “Ito versus Stratonovich,” Journal of Statistical Physics 24: 175–187 (1981).

Association in the course directory

M-VAF A 2, M-VAF B

Last modified: Fr 12.05.2023 00:27