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Welcome to the 8.513 webpage,

Fall 2008,
Coherent and collective phenomena in quantum transport

#### Problem set 11
pdf
due Dec 4 in lecture; solutions:
pdf

#### Reading on one-dimensional localization: Density of states
pdf ; Lyapunov exponent, localization length
pdf

#### Lecture 23 (Nov 25) One-dimensional models of disordered systems:
lecture notes , photos

#### Lecture 22 (Nov 20) Scattering and transfer matrices; statistics of transmissions
photos

#### Lecture 21 (Nov 18) Thouless energy and its relation to conductance; level correlation in a mesoscopic conductor
photos

#### Lecture 20 (Nov 13)
Hermitian and circular ensembles, spectral rigidity, pair correlation function
photos

#### Problem set 10
pdf
due Nov 13 in lecture; solutions:
pdf

#### Lecture 19 (Nov 6)
Spectral statistics of random matrices
photos

Topics in random matrix theory:
course by Jacobus Verbaarschot

Relation between random matrices, quantum chaos and Anderson localization:
Lecture 3 by Boris Altshuler;
Lecture by Oriol Bohigas and Marie-Joya Giannonni

#### Lecture 18 (Nov 4)
Wigner-Dyson random matrix theory.
photos

#### Problem set 9
pdf
due Nov 6 in lecture; solutions:
pdf

Reading on weak localization, weak antilocalization, and universal conductance fluctauation: Jorgen Rammer "Quantum Transport Theory"
Chap. 9 , Chap. 11
#### Experimental data discussed in Lectures 14-17 can be found here:
pdf

#### Lecture 17 (Oct 30)
Mesoscopic Aharonov-Bohm effect. Universal conductance fluctuations. Weak antilocalization with SO scattering.
photos

#### Lecture 16 (Oct 28) Weak localization and Anderson localization; Magnetoresistance in a strip geometry
photos

#### Problem set 8
pdf
due Oct 30 in lecture; solutions:
pdf

#### Lecture 15 (Oct 23) Weak localization, dephasing length, megnetoresistance
photos

#### Lecture 14 (Oct 21) Coherent backscattering; Weak localization;
Aharonov-Bohm effect
pdf photos

#### Problem set 7
pdf
due Oct 23 in lecture; solutions:
pdf

#### Lecture 13 (Oct 16) Drude formula; Ward identity for j-A response; weak localization
photos

#### Lecture 12 (Oct 14) Averaging the Greens functions over disorder; the non-crossing approximation, Drude conductivity
photos

Reading on Greens functions and disordered systems: Jorgen Rammer "Quantum Transport Theory"
Chap. 2 , Chap. 3
#### Lecture 11 (Oct 9) Kubo formula, Matsubara Greens functions, and analytic continuation
photos

#### Problem set 6
pdf
due Oct 16 in lecture; solutions:
pdf

#### Lecture 10 (Oct 7) Retarded and advanced Greens functions, perturbation theory
photos

#### Problem set 5
pdf
due Oct 9 in lecture; solutions:
pdf

paper on boundary scattering: H. Sondheimer, Adv. Phys. 1, 1 (1952) pdf
#### Lecture 9 (Oct 2)
pdf

#### Problem set 4
pdf
due Oct 2 in lecture; solutions:
pdf

#### Lectures 5, 6, 7
pdf

#### Problem set 3
pdf
due Sep 25 in lecture; solutions:
pdf

#### Lecture 4
pdf

Properties of S-matrix (from Baz, Zeldovich and Perelomov "Scattering, reactions and decays in quantum mechanics")
#### Lecture 3
pdf

#### Lecture 2
pdf

#### Problem set 2
pdf
due Sep 18 in lecture; solutions:
pdf

#### Lecture 1
pdf

#### Problem set 1
pdf
due Sep 11 in lecture; solutions:
pdf

** Lectures: ** Tu, Thr, 1:00-2:30,
in Rm. 2-151
by Prof Leonid Levitov,

Office 6C-345,
Telephone: x3-6817,
levitov@mit.edu,

Office hours: Tu, 2:30-3:30 in 6C-345

** Problem sets: **
weekly, 13 in total, due Thursday in class (at the beginning of the lecture);

** Term paper: **

A list of term paper topics
will be provided and discussed in class;

** Grade: **
problem sets 60%, grading 10%, term paper 30%

#### Course syllabus
pdf
and weekly schedule
pdf

Please tell us what you expect to learn in 8.513
and provide information on your background by answering these
questions:
pdf

##### Return to the TOP of this page

Last modified: September 5, 2006
levitov@mit.edu