Statistical physics IV
PHYS-436
This file is part of the content downloaded from Statistical physics IV.
- News Forum (Forum)
- Zoom link for the lecture (URL)
- Stat. Phys. IV: Non Equilibrium Statistical Physic... (Text and media area)
- Key References for the Course (Text and media area)
- Gardiner - Handbook of stochastic methods (2ed., Springer, 1997) (File)
- Gardiner, Zoller - Quantum Noise (3rd., Springer, 2004) (File)
- Risken - The Fokker-Planck equation methods of solution and applications (2ed., Springer, 1989) (File)
- Ito calculus, Black Shoels formula (Folder)
- Fokker-Planck eq, Kramers escape rate (Folder)
- Levy flights, laser cooling (Folder)
- Crooks fluctuation theorem and Jarzynski equality (Folder)
- Metropolis-Hastings algorithm, Bayesian statistics (Folder)
- Application of the quantum Langevin equation: detection of gravitational waves (Folder)
- Paper Presentations (Text and media area)
- Beamer template for presentations (File)
- Google sheet with the schedule of the presentations (URL)
- List of topics for presentations (URL)
Week 1:
Introduction to Non-Equilibrium and Stochastic Processes (Einstein and Langevin Approach)
- Introductory Lecture Slides (File)
- Presentation list (File)
- Lecture 1 video (URL)
- Lecture 1 Summary Slides (File)
- Smoluchowski Mathematica Worksheet (Click + Right click "save as") (File)
- Lecture notes (Text and media area)
- Lecture 1 - Handwritten Notes (File)
- Core Reading Material for the Lecture (Text and media area)
- Handbook of stochastic methods (Gardiner) (File)
- Introduction to Stochastic Processes (Chapter 1 "Stochastic Methods" Gardiner) (File)
- Scriptum P. Martin "Advanced Statistical Mechanics" - Chapter 1,2 (File)
- Polycopié Professor Martin: Mécanique Statistique Avancée (français) (File)
- Supplementary information (Text and media area)
- ONLY Page 16-18: Derivation of Einstein (from "The Langevin Equation"). (File)
- Langevin Original paper 1908 (File)
- Original Paper from Einstein 1905 (File)
- Homework (Text and media area)
- Homework 1 (File)
- Homework 1 - Solutions (File)
- Paper for presentation (Text and media area)
- Science - Measurement of the Instantaneous Velocity of a Brownian Particle (File)
- What Is the Einstein relation of diffusi... (Text and media area)
- Student presentation - Xiaoyi Cheng (File)
Week 2:
Smoluchowski Equation, Markov Processes and Ito calculus
- Lecture 2 video (URL)
- Summary slides 2 (File)
- Lecture notes (Text and media area)
- Lecture 2 - Handwritten Notes (File)
- Readings (Text and media area)
- Gillespie "Mathematics of Johnson Noise and Brownian Motion" (File)
- Prof. Martin "Advanced Statistical Mechanics" Chapter 1 and 2 (File)
- Supplementary information (Text and media area)
- Original paper from Nyquist (File)
- Original paper by Johnson on Electrical Noise (File)
- Review on quantum noise and measurement by Clerk et al. (File)
- Original Paper from Orstein and Uhlenbeck (File)
- Backtracking by single RNA polymerase molecules observed at near-base-pair resolution (File)
- Homework (Text and media area)
- Homework 2 (File)
- Homework 2 - Solutions (Folder)
- Simulation of Brownian motion (Mathematica) (File)
- Simulation of 1D and 2D Brownian motion (Mathematica) (File)
- 2D Brownian motion simulation (Jupyter notebook) (File)
- Paper for presentation (copy) (Text and media area)
- Direct observation of kinesin stepping by optical trapping interferometry (File)
- Why do they use kinesin to monitor the random moti... (Text and media area)
- Paper presentation 2 (File)
Week 3:
Ito calculus, Langevin Equation and Spectral densities
- Lecture 3 video (URL)
- Summary slides 3 (File)
- Lecture notes (Text and media area)
- Lecture 3 - Handwritten Notes (File)
- Readings (Text and media area)
- Stochastic Methods Gardiner Chapter4 - Ito Calculus and SDE (File)
- Gillespie "Fluct. and Dissipation in Brownian Motion" - Derivation of the two force hyphothesis (File)
- Fluctuation Dissipation Theorem Kubo (File)
- Supplementary information (Text and media area)
- Gardiner Chapter 3 (File)
- Dalibard and Cohen-Tannoudji: Laser cooling and trapping of neutral atoms (File)
- SUPPLEMENTARY INFORMATION: Ito Calculus Application - Nobel Lecture 1997 Economics Scholes (File)
- SUPPLEMENTARY INFORMATION: Low Temperature Thermal Noise Thermometer Shore Rev Sci Ins 1959 (File)
- SUPPLEMENTARY INFORMATION: "Irreversibility and Generalized Noise", Phys. Rev. Callen Walton (File)
- "Fluctuation and Dissipation in Brownian Motion" Gillespie, Am. J. Phys (File)
- SUPPLEMENTARY INFORMATION: Measurements of quantum noise in resistively shunted Josephson junctions, Koch, Phys. Rev. (File)
- SUPPLEMENTARY INFORMATION: Financial Applications of Ito Calculus (Stochastic Methods, Gardiner, Ch. 10) (File)
- SUPPLEMENTARY INFORMATION: Black, Scholes, “The Pricing of Options and Corporate Liabilities”, Journal of Political EconomyBlack, Scholes (File)
- Python 3 installation guide (URL)
- Jupiter installation guide (URL)
- Homework (Text and media area)
- Homework 3 (File)
- Homework 3 - Solutions (File)
- Brownian Motion Jupyter Notebook (Folder)
- Paper for presentation (copy) (copy) (Text and media area)
- Thermal Noise in Mechanical Experiments PRD Saulson (File)
- What is the langevin equation for a mechanical res... (Text and media area)
Week 4:
Fluctuation dissipation theorem, Fokker Planck Equation
- Lecture 4 video (URL)
- Recording of lecture 4 (2022) (URL)
- Summary slides 4 (File)
- Lecture notes (Text and media area)
- Lecture 4 - Handwritten notes (File)
- Readings (Text and media area)
- Chapter3 EN (File)
- Martin Scriptum Chapter 3: Markov Processes (File)
- Risken The Fokker Planck Equation Chapter 4 (File)
- Gillespie Markov Processes Chapter 2 ( read: 2.5. Kramers Moyal Expansion and 2.2 Chapman Kolmogorov Equation (File)
- Riehle F. Frequency Standards, section 3.4 (File)
- Supplementary information (Text and media area)
- R. Kubo "Statistical Physics II", Chapter 1 (suggested reading 1.5 and 1.6) (File)
- The multivariate Langevin and Fokker Planck Equations, Gillespie, Am. J. Phys. 1996 (File)
- Homework (Text and media area)
- Homework 4 (File)
- Solutions week4 (File)
- Paper for presentation (copy) (copy) (copy) (Text and media area)
- Internal thermal noise in the LIGO test masses - A direct approach (File)
- Paper presentation 4 (2022) (File)
- Paper presentation 4 (2025) (File)
- Explain briefly how LIGO is used to detect gravita... (Text and media area)
- Scientific Background on the Nobel Prize in Physics 2021 (File)
- Stochastic climate models (File)
Week 5:
Fokker-Planck Equation, Kramers escape rate. Kramers Escape problem (Diffusion over a Barrier)
- Lecture 5 video (URL)
- Recording of lecture 5 (2022) (URL)
- Summary slides 5 (File)
- Lecture notes (Text and media area)
- Lecture 5 (File)
- Readings (Text and media area)
- Gardiner Stochastic Mehods - Chapter 5 The Fokker Planck Equation (File)
- Gillespie_Markov_Processes (File)
- Risken The Fokker Planck Equation - Chapter 5 (File)
- Martin "Advanced Statistical Mechanics" Chapter 3 (English) (File)
- Supplementary information (Text and media area)
- SUPPLEMENTARY INFORMATION:Kramers Original Paper on Reaction Rates (File)
- Example use of optical tweezers (File)
- Thermally activated transitions in a bistable three-dimensional optical trap. Nature 1999 (File)
- The scaling law of human travel. Nature 2006 (File)
- Understanding individual human mobility patterns Nature (File)
- Optimizing the success of random search (File)
- Homework (Text and media area)
- Homework 5 (File)
- HW5 solutions (File)
- Paper for presentation (Text and media area)
- Quantum Mechanics of a Macroscopic Variable: The Phase Difference of a Josephson Junction (File)
- Student presentation - Lecture 5 (Emil Spasov) (File)
- What is a Josephson junction? What are the Josphso... (Text and media area)
Week 6:
Levy flights. The master equation for discrete-time systems.
- Lecture 6 video (URL)
- Recording of lecture 6 (2022) (URL)
- Summary slides 6 (File)
- Lecture notes (Text and media area)
- Lecture note 6 (File)
- Lecture note 6 - Supplementary (File)
- Readings (Text and media area)
- Levy Flights and continous time random walks (CTRW) (File)
- Lévy Statistics and Laser Cooling - Chapter 2 (File)
- Lévy Statistics and Laser Cooling - Chapter 3 (File)
- Levy Statistics and Laser Cooling Ch. 4.1 (File)
- Gardiner Chapter 3 Markov Processes (File)
- SI Notes levy flights The scaling laws of human travel Nature (File)
- Supplementary information (Text and media area)
- Lévy Statistics and Laser Cooling - Chapter 4 (File)
- Lévy Statistics and Laser Cooling - Chapter 6 (File)
- Arrhenius cascade and anomalous diffusion example: Diffusion in biological substances (File)
- Arrhenius cascade and anomalous diffusion example: Transport in porous media (File)
- Arrhenius cascade and anomalous diffusion example: An optical realization of the Arrhenius cascade (File)
- Arrhenius cascade and anomalous diffusion example: Anomalous transit-time dispersion in amorphous solids. (File)
- Cohen Tannoudji - Nobel lecture (see section 3.3) (File)
- Levy flight search patterns of wandering albatrosses (File)
- Homework (Text and media area)
- Homework 6 (File)
- Homework 6 - Solutions (File)
- Paper for presentation (copy) (Text and media area)
- SUBRECOIL LASER COOLING AND LEVY FLIGHTS PRL Cohen Tannoudji (File)
- Velocity-Selective Coherent Population Trapping PRL Cohen Tannoudji (File)
- Explain the basic principles of atomic laser cooli... (Text and media area)
Week 7:
The master equation for discrete state system.
- Lecture 7 video (URL)
- Summary lecture 7 (File)
- Bayesian fitting (File)
- Lecture notes (Text and media area)
- Lecture note 7 (File)
- Readings (Text and media area)
- Gardiner - Handbook of stochastic methods - Chapter 7 - Master equation (7.1 - 7.2) (File)
- Chapter 4, "The master equation", Polycopy Martin (File)
- Supplementary information (Text and media area)
- Metropolis Monte-Carlo algorithm (File)
- Gregory Bayesian analysis ch 3 (The how-to of Bayesian inference) (File)
- Georgy Bayesian analysis ch 12 (Markov chain Monte Carlo) (File)
- Stochastic Epidemic Models and Their Statistical Analysis (File)
- Stochastic Epidemic Models with Inference (File)
- Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study (File)
- Metropolis-Hastings algorithm, Bayesian statistics (Folder)
- Homework (Text and media area)
- Homework 7 (File)
- Homework 7 solution (File)
- Data for "Spectral line problem" exercise (File)
- Paper for presentation (copy) (copy) (Text and media area)
- Equation of State Calculations by Fast Computing Machines (File)
- Student presentation - lecture 7 (Dario Sergio) (File)
- What is the Monte Carlo method and how is it imple... (Text and media area)
Week 8:
Crooks fluctuation theorem and Jarzynski equality. Review of quantum mechanics
- Lecture 8 video (URL)
- Summary slides 8 (File)
- Bayesian fitting (File)
- Bayesian fitting example (File)
- Lecture notes (Text and media area)
- Lecture note 8 (File)
- Readings (Text and media area)
- Scientific Background on the Nobel Prize in Physics 2021 (File)
- Jarzynski's equation (Text and media area)
- 25 years of nanoscale thermodynamics (File)
- Nonequilibrium Equality for Free Energy Differences – original paper from Jarzynski (File)
- Jarzynski - review 2011 Fluctuations and the Second Law (File)
- Experimental test of Jarzynski equality with nanobeads (File)
- Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski Equality (File)
- Metropolis Monte-Carlo algorithm (File)
- Review of Quantum Mechanics (Text and media area)
- Gardiner Stochastic Methods - Chapter 10 Quantum Mechanical Markov Process (10.1/10.2 review density matrix) (File)
- Scully Quantum Optics Chapter 2 (File)
- Walls Quantum Optics Chapter 2 (File)
- Supplementary information (Text and media area)
- Scully Quantum Optics Chapter 6 (File)
- Quantum fluctuations in electric circuits (Devoret) (File)
- Homework (Text and media area)
- Homework 8 (File)
- Homework 8 solution (File)
- Paper for presentation (Text and media area)
- Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies nature (File)
- Review Crooks fluctuation theorem and Jarzynski's ... (Text and media area)
Week 9:
Quantum Langevin equations (harmonic oscillator and two level system coupled to a heat bath).
- Lecture 9 video (URL)
- Summary slides 9 (File)
- Lecture notes (Text and media area)
- Lecture note 9 (File)
- Readings (Text and media area)
- Review of Quantum Mechanics (Text and media area)
- Crispin Gardiner, Peter Zoller The Quantum World of Ultra-Cold Atoms and Light Book I Foundations of Quantum Optics Chapter 10.5 (File)
- Scully, "Quantum Optics", Chapter 9 Quantum Theory of Damping (File)
- Quantum Langevin Equation (Text and media area)
- Crispin Gardiner, Peter Zoller The Quantum World of Ultra-Cold Atoms and Light Book I Foundations of Quantum Optics Chapter 11 (File)
- Supplementary information (Text and media area)
- Review on cavity QED (Haroche) (File)
- Crispin Gardiner, Peter Zoller The Quantum World of Ultra-Cold Atoms and Light Book I Foundations of Quantum Optics Chapter 12 (File)
- Gregory Bayesian analysis ch 3 (The how-to of Bayesian inference) (File)
- Homework (Text and media area)
- Homework 9 (File)
- HW 9 Solution (File)
- Papers for presentation (Text and media area)
- Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion (File)
- Questions for the paper:Introduce the optomechanic... (Text and media area)
Week 10:
Application of the quantum Langevin equation: detection of gravitational waves
- Lecture 10 video (URL)
- Summary Slides 10 (File)
- Lecture notes (Text and media area)
- Lecture note 10 (File)
- Readings (Text and media area)
- "Statistical Methods in Quantum Optics 1" HJ Carrmichael Chapter 1 (File)
- Walls Chapter 7, Input-Output Formalism of Optical Cavities (File)
- Pace et al. - 1993 - Quantum limits in interferometric detection of gra (File)
- Gardiner, Collet, "Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation", PRA 1984 (File)
- Quantum Optics Walls Chapter 8.3 (File)
- Hanbury Brown & Twiss original paper (File)
- Hanbury Brown and Twiss - Experiment (File)
- Quantum Optics Walls Chapter 8: Applications of Squeezed light (File)
- Homework (Text and media area)
- Homework 10 (File)
- Solutions week10 (File)
- Paper for presentation (Text and media area)
- Questions for paper:What is the working principle ... (Text and media area)
- A New Method for the Detection of a Periodic Signal of Unknown Shape and Period (File)
9 May - 15 May
Week 11:
The quantum optical master equation
- Lecture 11 video (URL)
- Summary slides 11 (File)
- Lecture notes (Text and media area)
- Lecture note 11 (File)
- Readings (Text and media area)
- "Statistical Methods in Quantum Optics 1" HJ Carrmichael Chapter 1 (File)
- "Statistical Methods in Quantum Optics 1" HJ Carrmichael Chapter 2 (File)
- Scully Quantum Optics chapter 8 - Quantum master equation to Fokker-Planck equation (File)
- Gardiner, Stochastic Methods, "Quantum Master Equation" (File)
- Supplementary information (Text and media area)
- INFORMATION: Python QuTiP (Quantum Optics Toolbox) installation guide Windows (File)
- INFORMATION: Python QuTiP instllation guide for Mac (File)
- Cahill, Glauber - 1969 - P representation (File)
- Carmichael, Statistical Methods in Quantum Optics, 1.5 Quantum regression theorem (File)
- Homework (Text and media area)
- Homework 11 (File)
- Homework 11 solution (File)
- Papers for presentation (Text and media area)
- Decoherence Dynamics of Complex Photon States in a Superconducting Circuit - PRL - 2009 (File)
- Questions for paper:Review the structure of the de... (Text and media area)
16 May - 22 May
Week 12:
Quantum master equation, reservoir engineering
- Lecture 12 video (URL)
- Lecture 12 recording (2022) (URL)
- Review of lecture 12 (part 1) (URL)
- Summary slides 12 (File)
- Lecture notes (Text and media area)
- Lecture note 12 (File)
- Readings - Quantum reservoir engineering (Text and media area)
- Kienzler et al., Quantum harmonic oscillator state synthesis by reservoir engineering (File)
- Clerk et al. Introduction to quantum noise, measurement and amplification (File)
- Caves Quantum limits on noise in linear amplifiers (File)
- Supplementary information - Quantum trajectories (Text and media area)
- Wiseman, Milburn - Quantum measurement and control - chapter 4 (Quantum trajectories) (File)
- Scully Quantum Optics - Chapter 8 (Quantum theory of damping - density operator and wave function approach) (File)
- Shelved Optical Electron Amplifier: Observation of Quantum Jumps (File)
- Haroche, Quantum jumps of light recording the birth and death of a photon in a cavity (File)
- SUPPLEMENTARY INFORMATION: Scully, "Quantum Optics" Chapter 6.3 - Wigner Weiskopf Derivation (File)
- Zurek - Decoherence and the Transition from Quantum to Classical (2002) (File)
- Homework (Text and media area)
- Homework 12 (File)
- Papers for presentation (Text and media area)
- Poyatos, Cirac, Zoller, Quantum Reservoir Engineering with Laser Cooled Trapped Ions (File)
- Cavity-Assisted Quantum Bath Engineering - PRL - 2012 (File)
- Student presentation 2025 - Óscar Alves (File)
- Homework Solution (File)
Ascension Day (Holiday)
Final Exam
- Final exam (Text and media area)
- Sample Exam 2019 (File)
- Sample Exam 2021 (File)
- Sample Exam 2022 (File)
- Exam topics 2025 (File)