Homepage  Vivien Lecomte, LPMA
Lecture at Master 2  Erasmus Mundus Masters in Complex Systems
Theoretical analysis of complex systems
Homepage of the Master
Date and place
Recommended reading
Outline of the lecture

Lecture 1 (Tuesday, October 2nd, 2012)
[Pdf of handwritten notes for Part I – pages 17]
Homework for next lecture: reread carefully the notes (pages 17 of the pdf) and familiarize yourself with the remaining pages (710).
Have a look to the notes (see link below) on functional derivatives (a close look on pages 13; the rest is mainly illustrative).

Lecture 2 (Tuesday, October 9th, 2012) Morning
[Pdf of handwritten notes for Part I – page 720]
[Pdf on functional derivatives.]
[Pdf on Gaussian integrals (in french).]

Lecture 3 (Tuesday, October 9th, 2012) Afternoon
 1:30pm to 5pm  Salle n°52, couloir des langues
[Pdf of handwritten notes for Part II – pages 13]
[Pdf of the exercice for October 16th]
[Directory with the pdf of references.]

Lecture 4 (Tuesday, October 16th, 2012)
[Pdf of handwritten notes for Part II – pages 46]
[Pdf of the correction of homework 1]
[Mathematica file for the correction.]

Lecture 5 (Tuesday, October 23rd, 2012)
[Pdf of handwritten notes for Part II – pages 612]
[Pdf version of the Mathematica file.]
[Python program for the TASEP in open boundary conditions.]

Lecture 6 (Tuesday, October 30th, 2012) [Room : Petite Classe 20]
[Pdf of handwritten notes for Part II – pages 1317]

Lecture 7 (Tuesday, November 6th, 2012)
[Pdf of handwritten notes for Part III]
[Correction of homework 2a: Python program for the cloning of the fermionic deathandbirth process (nonconstant population).]

Lecture 8 (Tuesday, November 13th, 2012)
[Pdf of handwritten notes for Part III]
[Correction of homework 2b: Python program for the cloning of fermionic deathandbirth process, now at constant population.]

Lecture 9 (Tuesday, November 20th, 2012)
[Pdf of handwritten notes for Part III]
[Pdf of handwritten notes for Part IV]
[Correction of homework 3: Python program for the cloning of bosonic deathandbirth process, at constant population.]

Lecture 10 (Tuesday, November 27th, 2012)
[Pdf of handwritten notes for Part IV]
[Pdf of handwritten notes for Part V]
Exam, January 15th, 2012

Please chose a timeslot on this Doodle page.

Place: room 0D7, 175 rue du Chevaleret, 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
(As discussed during the lecture, it is easier here to study a SSEP not on a ring but on an isolated segment.)
 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
(As discussed during the lecture, you can start from the meanfield study of the model on a complete graph.)

Note that you are allowed to start from the Python programs for the population algorithms we have discussed during the exercises (see links above).
References