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EPFLx: Advanced statistical physics

We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications.

Advanced statistical physics
10 weeks
3–5 hours per week
Self-paced
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Starts Apr 19
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Advanced statistical physics

About this course

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This 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, etc will be treated in detail. Prior knowledge of statistical physics is highly recommended but not required.

At a glance

  • Institution: EPFLx
  • Subject: Physics
  • Level: Advanced
  • Prerequisites:

    Graduate level knowledge of mathematics and physics

  • Language: English
  • Video Transcript: English

What you'll learn

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  • Formulate statistical processes mathematically
  • Solve 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

Syllabus

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  • Lecture 1: Brownian motion and 3 derivations
  • Lecture 2: Continuous stochastic process
  • Lecture 3: Stochastic differential equations
  • Lecture 4: Fluctuation dissipation theorem
  • Lecture 5: Fokker Planck equation
  • Lecture 6: Lévy flights
  • Lecture 7: Master equations
  • Lecture 8: The Crook and Jarzynski equality
  • Lecture 9+10: Quantum optics and quantum Langevin equation
  • Lecture 11+12: Quantum regression theorem

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