Homepage  Vivien Lecomte, LPMA
Lecture at Master 2  Erasmus Mundus Masters in Complex Systems
Theoretical analysis of complex systems
(1st semester, 2013)
Homepage of the Master
Date and place
Prerequisites and Recommended reading

Prerequisites  mathematical tools

Recommended reading  Physical background

Going further
Outline of the lecture
To ask questions on the lectures between classes, you can use the following [Wiki website].

Lecture 1 (Wednesday, August 28th, 2013) Room PC 21
[Pdf of handwritten notes for Part I – pages 16]

Lecture 2 (Wednesday, September 4th, 2013) Room PC 21
[Pdf of handwritten notes for Part I – pages 610]
[Pdf of handwritten notes for Part Ib – pages 1013]
[Pdf on functional derivatives]

Miniproject (Due date: Friday, September 20th, 2013)
[Miniproject]
[Directory with the pdf of references]
[Wiki website for asking questions]

Lecture 3 (Friday, September 20th, 2013, 9:0012:00)
Room PC 9
[Correction of the Miniproject]
[Pdf of handwritten notes for Part Ib – pages 1316]
[Directory with references on the Itō vs Stratonovitch dilemma]

Lecture 4 (Wednesday, September 25th, 2013) Room PC 6
[Mathematica file for the numerics of the Miniproject]
[Pdf of handwritten notes for Part Ib – pages 1620]
[Pdf on Gaussian integrals (in french)]

Lecture 5 (Wednesday, October 2nd, 2013) Room PC 6
[Pdf of handwritten notes for Part IIa – pages 14]
[Wiki website for asking questions on Homework 4]

Lecture 6 (Friday, October 11th, 2013, 9:0012:30)
Room PC 7
[Pdf of handwritten notes for Part IIa – pages 45]
[Mathematica file for the discrete Brownian walk of Homework 4]

Lecture 7 (Friday, October 18th, 2013, 9:1512:45)
Room PC 6
[Pdf of handwritten notes for Part IIa – pages 69]
[Python solution for Homework 5, with heap queues]
[Python program to illustrate the scaling of P(K,t)]

Partial Exam (Wednesday, October 23th, 2013, 10:0012:00)
Room 67 (couloir des langues)
[Pdf of the partial exam]

Lecture 8 (Wednesday, November 6th, 2013) Room PC 6
[Pdf of handwritten notes for Part IIb]
[Miniproject 2: cloning algorithm]
[Wiki website for asking questions]
[Miniproject 2: a Python algorithm using heap queues]

Lecture 9 (Wednesday, November 13th, 2013) Room PC 6
[Cloning with time mixing, stopped by maximum time]
[pdf]
[Cloning, stopped by maximum population]
[pdf]
[Cloning, constant population]
[pdf]

Lecture 10 (Wednesday, November 20th, 2013) Room PC 6
[Cloning for bosonic BaD process.]
[pdf]
[Mathematica file for Legendre transforms]
[Pdf of handwritten notes for Part III]

Lecture 11 (Wednesday, November 27th, 2013) Room PC 6
[Pdf of handwritten notes for Part IV]

Lecture 12 (Wednesday, December 4th, 2013) Room PC 6
[Pdf of handwritten notes for Part V]
[Mathematica file for the dynamical phase transition in the KCM]

Exam (Wednesday, December 11th, 2013) Room PC 6
[Pdf of the exam]
[Pdf of the correction]

Project Presentations (Wednesday, December 18th, and Thursday, December 19th, 2013)
Projects (Presentation on December 18th19th, 2013)

Place: LPMA, Bâtiment Sophie Germain, avenue de France, 75013 Paris.

Type of presentation:

You can either choose a subject on your own, in which you study the large deviation function of a dynamical observable using the cloning algorithm discussed during the lectures, or chose among those possible subjects and references (see also the last lecture):
 Mapping between equilibrium and nonequilibrium current fluctuation in the SSEP in contact with reservoirs:
 Dynamical phase transition between clustered and nonclustered profiles in the periodic SSEP on a ring:

Inactive dynamical phase of a symmetric exclusion process on a ring
Vivien Lecomte, Juan P. Garrahan, Frédéric van Wijland, J. Phys. A 45 175001 (2012)
[arXiv:1203.1600],
link,
paper

Universal cumulants of the current in diffusive systems on a ring
Cécile AppertRolland,
Bernard Derrida,
Vivien Lecomte and
Frédéric van Wijland,
Phys. Rev. E 78 021122 (2008)
[arXiv:0804.2590],
link,
paper
 Dynamical coexistence of phase between active and inactive regions in a KCM:

Firstorder dynamical phase transition in models of glasses: an approach based on ensembles of histories
Juan P. Garrahan, Robert L. Jack, Vivien Lecomte, Estelle Pitard, Kristina van Duijvendijk and Frédéric van Wijland,
J. Phys. A 42 075007 (2009)
[arXiv:0810.5298],
link,
paper

Finite size scaling of the dynamical freeenergy in a kinetically constrained model
Thierry Bodineau, Vivien Lecomte and Cristina Toninelli, J. Stat. Phys. 147 1 (2012)
[arXiv:1111.6394],
link,
paper

Note that you are allowed to start from the Python programs for the population algorithms we will discuss during the exercises.
References