SCP7081763 - PHYSICS OF COMPLEX SYSTEMS 2020-2021

Dear students,

    below you will find a preliminary list of "projects" among which you
need to choose the one you will present at the exam, and general
guidelines for exams and project choice. I will upload related papers
on Moodle later on today. Please consider carefully the rules on
project choice; in brief: there will be a first deadline next Monday
to assign projects, restricted to those of you willing to take the
exam within February 2021 (but you can always choose a project after
the deadline and take the exam anyway in January/February).

I wish you all and your dearest ones a Merry Christmas and a happy 2021.

Kind regards


Antonio Trovato


---------- EXAM ORGANIZATION --------------------------------------

- As I already told you, I will be flexible concerning exam dates; we
can agree on different dates with respect to the official one, even
separately with each of you.

- During the exam I may make questions about topics covered in the
course, only if related to the subject of your presentation.

- The presentation should last at least 30 minutes and not more
than 1 h (the upper bound can be flexible).

- The presentation will be given (and slides will be written) in
English.

- The presentation itself can take any form. In the winter session we
will have online exams, so you may prepare slides or write on a tablet
(as I do for teaching) or write on a piece of paper properly kept in a
webcam frame. If in May/June we are back to the pre-Covid life, and
therefore to exams in physical presence, you may also choose to
deliver your presentation on the blackboard.

- Aside from the replies to my possible questions, I will evaluate the
way you organize your presentation (for example on which parts of the
source material you focus and which ones you leave out of the
presentation) and how you are in control of the subject.

- In the (hopefully most unlikely) case the exam grade is not accepted
by the student, she/he will need to select a different project (among
the available ones) when retaking the exam; the first selected project
will remain not available to other students.

---------------------- PROJECT CHOICE -------------------------------------

- The same project cannot be chosen by more than one student. This
rule is supposed to be maintained for the whole 2021; an already
assigned project will not be available for the rest of the year
(except in the case described below).

- You can e-mail to me the project you wish to select. I will set a
(first) deadline on next Monday, December 28th (say at midnight).
On Tuesday 29th, I will deal with possible double requests for the
same project, but I hope you can organize yourselves to avoid this.

- ONLY students willing to take the exam within the end of the winter
session (February 27th, 2021) are allowed to select a project within
next Monday; in case the exam is not taken within that date, the
selected project will then become available to other students.

- The projects yet to be assigned after next Monday deadline could be
selected later on at any time; I will provide other deadlines with the
only purpose of avoiding debates on choice priority.

- The projects are roughly divided into 3 classes (although in a
couple of cases they are a mixture): book sections/chapters to read
and report on, scientific papers to read and report on, numerical
simulations to perform and report on. You are welcome to propose a
specific project you are interested in, or to propose a generic
subject (I will try to find a relevant paper).

- One paper corresponds to one project (with the exception of the
Hinrichsen paper, to be used only as a reference in the simulation
projects, see below), even when they are grouped under one item in the
list. I refer to paper by last author's name.

- The project description is very brief: you are in general expected
to be mature enough to "digest" and organize the source material by
yourself; yet, you are welcome to discuss with me in case of any major
doubt.

- The list is preliminary, because it lacks the topics of the January
lectures. I will add later on related projects.  The topics of the
last 3 lectures should be: large deviation theory, Jarzynski equality
and fluctuation theorem; generalized ensemble methods in Monte Carlo
simulations (in particular Wang-Landau method).



------------- PROJECT LIST ----------------------------------------------

BOOK SECTIONS

-- Livi-Politi book

1) Random Walk with Absorbing Barriers (1.5.2) + Stationary Diffusion
with Absorbing Barriers (1.6.3) + Isotropic and Anisotropic Random
Walk in a Trap (D.5,D.6) with application to Compact Directed
Percolation (4.2.1) + numerical simulations of lattice random walk
with absorbing trap (the general idea is to verify with a simulation
the analytical results: we can discuss the details)

2) Generalized Random Walks + Anomalous Diffusion (chapter 1.7) +
Sokolov Paper

3) Details of the Mean Field solution of the TASEP Model + BRIDGE
model: mean field general solution and exact solution of the BRIDGE
model for beta << 1 (4.4.2, 4.5, appendix K)

4) Thermoelectric effects (quick recap of Seebeck, Peltier + Thomson
Joule) + thermo-magnetic and galvano-metric effects (2.8.2)

5) Linear Response in Quantum Systems (2.9 and 2.10)

6) Interface Roughness: scaling, exponents, self-affinity; general
derivation of WE,KPZ equations (5.2, 5.3, 5.4, 5.5)

7) Edwards-Wilkinson equation (5.6)

8) Kardar-Parisi-Zhang equation (5.7)

-- Mezard-Montanari book

9) Introduction to Combinatorial Optimization and Complexity classes
(P vs NP): (chapter 3)

10) Proof of the "direct part" of channel coding theorem for a generic
channel (6.4,6.8) and of the "converse part" for BST (6.5)

11) Number partitioning (chapter 7)

COMPUTATIONAL PROJECTS

(in case you are interested we need to discuss the details - projects
12-16 refer to the technique used to get Fig. 20 of the Hinrichsen
paper)

12) Domany-Kinzel model (d=1+1), evaluation of rho(t,p) -> quenched
average (q fixed), omogeneous initial conditions: find p_c and
critical exponent using phenomenological scaling -> fig. 20 Hinrichsen
2001

13) Contact processes (1+1) DP vs. DyP (p2 = 0; p2>0): find transition
point and critical exponents for Dyp

14) Parity conserving model (1+1): PC vs DP; find transition point and
critical exponents

15) More inactive states: DP2 vs. DP: find transition point and
critical exponents

16) TASEP model with open boundary conditions: (random or zero initial
conditions) find asymptotic stationary density profiles in the
different phases

17) BRIDGE model: (random or zero initial conditions) find asymptotic
stationary density profiles in the different phases

SCIENTIFIC PAPERS

20) Review percolation: Sabari

21) Review Maximum entropy methods to study protein sequences: Weigt

22) Review KPZ: Corwin

23) Review of Reaction-Diffusion models: Voit, Frey, Galic, Luthey-Schulten

24) Non equilibrium statistical physics: Attard, Van den Broek