PHYS-436 / 5 credits

Teacher: Kippenberg Tobias

Language: English

## Summary

This first part of the course covers non-equilibrium statistical processes and the treatment of fluctuation dissipation relations by Einstein, Boltzmann and Kubo. Moreover, the fundamentals of Markov processes, stochastic differential and Fokker Planck equations, mesoscopic master equation, noise s

## Recommended courses

Statistical physics I, II, III

Quantum Optics

## Learning Outcomes

By the end of the course, the student must be able to:

• Formulate correct mathematical models of statistical processes
• Solve succesfully the quantum master equation using QuTip in Python
• Apply numerical simulation tools to non-equilibrium systems
• Explore the quantum optical numerical Toolbox (MATLAB)
• Visualize non-equilibrium processes numerically using Jupyter Notebooks
• Elaborate modern examples from Literature of Non-Equilibrium Processes
• Apply EMCEE Python package to Bayesian statistical data analysis

## Transversal skills

• Make an oral presentation.
• Summarize an article or a technical report.
• Take feedback (critique) and respond in an appropriate manner.
• Use both general and domain specific IT resources and tools

## Teaching methods

Blackboard, summary slides and homeworks.

## Expected student activities

Weekly graded homeworks for an extra point.

## Assessment methods

Written exam (plus extra points via weekly homeworks)

## Supervision

 Assistants Yes

## Bibliography

• Primary references:
• Scientific Papers  (e.g. Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems, and many more)
• Other references. Selected chapters of the books:
• Risken H. The Fokker-Planck equation.. methods of solution and applications (2ed., Springer, 1989)(T)(485s)
• Gardiner - Handbook of stochastic methods (2ed., Springer, 1997)
• Markov Processes, Gillespie
• Statistical Methods in Quantum Optics 1 HJ Carrmichael
• Lévy statistics and laser cooling—Cambridge University Press
• Quantum Noise, Gardiner Zoller, Springer

## Notes/Handbook

Moodle with Notes, papers, and bookchapters

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Statistical physics IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Statistical physics IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Statistical physics IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Statistical physics IV
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

## Reference week

 Mo Tu We Th Fr 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22