Fiches de cours 2017-2018

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Statistical physics IV

PHYS-436

Enseignant(s) :

Kippenberg Tobias

Langue:

English

Summary

his course covers non-equilibrium statistical processes in the classical regime and treats important historical developments by Einstein, Boltzmann and Kubo. The second part of this course covers modern Quantum Stochastic methods and their application in modern Quantum Optics and Condensed Matter

Content

I. Introduction to classical non-equilibrium thermodynamics
- Brownian Motion and Einstein relation
- Fokker Planck Equation
- Boltzmann Equation

- Anomalous Diffusion, Levy Flights
- Boltzmann Equation

II. Statistical Mechanics of Linear Response
- Kubo Formula
- Fluctuation Dissipation Theorem
- Markovian Processes

III. Open Quantum Systems: Quantum mechanical description of Dissipation

- The quantum Master equation and open quantum systems
- The damped quantum mechanical harmonic oscillator 
- Two level system in a heat bath, de-phasing processes.
- Quantum stochastic Langevin equations

- Examples: Dephasing of Josephson junction Qubits

 IV. Quantum Noise and Quantum Measurements

- Quantum Noise and basics of linear quantum measurements
- Classical versus Quantum mechanical spectral densities

IV. Special topics: stochastic quantum methods in Quantum Optics
- Applications of quantum statistical processes and simulation thereof using the "MATLAB" Quantum Optical Toolbox
- Input-output theory Gardiner and Collet
- Applications of stochastic quantum Langevin equations in Quantum Optics:Master equation, Fokker Planck equation for Optical Parametric Oscillator, Ito formalism, Phase diffusion in Lasers
- Thermodynamical noise in Physics and precision measurements 

 

Learning Prerequisites

Recommended courses

Statistical physics I, II

Learning Outcomes

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

Transversal skills

Expected student activities

Students are expected to give (as a Bonus) a final presentation about a published journal paper that is related to non-equilibrium stastistical Physics in Biology, Sociology or Quantum Optics of Condensed Matter.

Assessment methods

Final presentation

Oral (or written exam)

Homeworks

Resources

Ressources en bibliothèque
Moodle Link

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
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     
En construction
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand