TE2: Stochastic Dynamics of Particles and Fields – Materials

Lecture Notes

• You can find the preliminary lecture notes here (to receive the password, write a mail to m.striebel@physik.lmu.de)
• Current Lecture Notes (updated on 27.01.2022)

The Lecture Notes are still a work in progress and any kind of feedback is appreciated (questions, typos, etc.)!

Handwritten Notes

• Perturbation Theory for Models with Relaxational Dynamics

Lecture Slides

• Introductory Lecture (28.10.2021)
• Elementary Processes (updated on 04.11.2021)
• Fundamentals Markov Processes (updated on 12.11.2021)
• Master Equations (25.11.2021)
• Langevin Equation (updated on 10.12.2021)
• Path Integral Formalism (20.01.2022)
• Critical Dynamics Close to Thermal Equilibrium (21.01.2022)

Jupyter Notebooks 

• Simple Random Walk in 1D
• Poisson Process (Gillespie vs. fixed-timestep)
• Random Walk (Gillespie vs. fixed-timestep)
• Stochastic Cell Growth

Papers and Other Material

• "Statistical Physics and biology", 1993 Phys. World 6 (9) 42, feature article by Giorgio Parisi (2021 Nobel laureate in physics),
• Nextstrain (Real-time tracking of pathogen evolution),
• Article in Physics Today about the 2021 Nobel laureates in Physics,
• "Brownian motion: a paradigm of soft matter and biological physics", Frey, E., & Kroy, K. (2005), Annalen der Physik, 14(1-3), 20–50,
• "Statistical Fluctuations in Autocatalytic Reactions", M. Delbrück, J. Chem. Phys. 8, 120 (1940).
  Delbrück was one of the first to introduce Master equations (without using the term) in this paper on autocatalytic reactions (linear birth),
• "The Perron-Frobenius Theorem and the Ranking of Football Teams", James P. Keener, SIAM Review 35 (1) (1993),
• "Method of Characteristics", an extensive overview of a method to solve a certain kind of partial differential equations,
• "Kinetic Proofreading", J. J. Hopfield, PNAS 71 (1974),
• "Stochastic Problems in Physics and Astronomy", S. Chandrasekhar, Rev. Mod. Phys. 15 (1943),
• "Sedimentation of Brownian Particles in a Gravitational Potential", B. U. Felderhof, Journal of Statistical Physics 109 (2002),
• R. Phillips et al.: Physical Biology of the Cell, now available online,
• "Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model", T. Reichenbach, M. Mobilia, E. Frey, Physical Review E 74 (2016), through analytical methods supported by numerical simulations, this paper studies the properties of a paradigmatic non-spatial three-species stochastic system, namely, the “rock-paper-scissors” or cyclic Lotka-Volterra model,
• "Phase transitions in virology", R. Solé, J. Sardanyés, S. F. Elena, Reports on Progress in Physics 84 (2021),
• "Langevin equation for the density of a system of interacting Langevin processes", D. S. Dean, J. Phys. A: Math. Gen. 29 (1996),
• "Non-equilibrium phase transitions", H. Hinrichsen, Phys. A: Stat. Mech. App. (2006),
• "Phase Transitions and Scaling in Systems Far from Equilibrium", U. C. Täuber, Annu. Rev. Condens. Matter Phys. (2017), 
• "Renormalization group theory and critical phenomena", E. Frey, Lecture Notes (2013). 

How to Access Online Articles

Many scientific articles can be accessed through the university library and your personal account. The different options (e.g. using the bookmarklet for quick access) are explained here:

https://www.en.ub.uni-muenchen.de/borrowing/digital-access/e-media-login/index.html

Topics

The main themes discussed in the lecture will be:

• Elementary Stochastic Processes 
• Theory of Markov Processes 
• Master Equations & Path Integrals 
• Stochastic Dynamics of Particles 
• Stochastic Dynamics of Fields 
• Non-equilibrium Field Theories