Welcome to the 8.514 webpage,
Fall 2003, Many-body phenomena in condensed matter and atomic physics

Course Structure and Description:

Lectures: Tu, Thr, 9:30-11:00, in Rm. 12-134 by Prof Leonid Levitov,
Office 12-112, Telephone: x3-6817, levitov@mit.edu,
Office hours: by appointment
Problem sets: weekly, 13 in total, due Tuesday in class (at the beginning of the lecture);
Recommended text:
Michael Stone, The Physics of Quantum Fields, (Science Library and Physics Reading Room have copies)
Term paper:
A list of term paper topics will be provided and discussed in class;
Grade: problem sets 60%, term paper 40%

Course syllabus postscript pdf and weekly schedule postscript pdf
(Note: the schedule is tentative and probably will be revised as we go on).

Please tell us what you expect to learn in 8.514 and provide information on your background by filling this questionnaire: postscript pdf
Selected lecture notes are available

Term paper topics suggestions are HERE

Problem Sets:

Problem Set #1: postscript pdf
Problem Set #2, due 09/23/03: postscript pdf
Problem Set #3, due 09/30/03: postscript pdf (09/18/03, few typoes corrected)
Problem Set #4, due 10/07/03: postscript pdf
Problem Set #5, due 10/14/03: postscript pdf
Problem Set #6, due 10/14/03: postscript pdf
Problem Sets #7,8, due 11/04/03: postscript pdf
References on bosonization (the oscillator picture of a Fermi liquid):
K. Sawada, Phys. Rev. v.106, p.372 (1957); Sawada et al. Phys. Rev. v.108, p.507 (1957); G. Wentzel, Phys. Rev. v.108, p.1593 (1957).
References on Bogoliubov-deGennes equation and Andreev scattering:
I read about it in the books by deGennes, Tinkham, and Abrikosov. Also, the original paper by Andreev is reasonably well-written.
Problem Set #9, due 11/20/03: postscript pdf
Problem Set #10, due 12/02/03: postscript pdf 11/26/03, edited and restructured
Problem Set #11, due 11/09/03: postscript pdf NEW

Lecture notes:

Lecture 1: Coherent states postscript pdf
Lecture 2: Squeezed states postscript pdf
Lecture 3: Second quantization postscript pdf
Lectures 4, 5: Bose condensation postscript pdf
Lecture 6: Superfluidity, vortices, finite temperature effects postscript pdf new

Vortices moving


Smoke ring fountain

vortex lattice

Bose condensation of trapped gas


Vortex lattice in trapped BEC condensate

vortex lattice

Hydrogen atom in a coherent state

Hydrogen atom

Second quantization, artist's image

Hartree-Fock wavefunction

Selected articles and lectures for 8.514 reading:

Phys Rev, 130, 2529 (1963) The Quantum Theory of Optical Coherence, by R J Glauber
1 2 3 4 Animation: Wave packet dynamics of coherent (displaced) and squeezed states, by Franco Nori
quant-ph/9708012 The Discovery of Squeezed States, by M M Nieto
cond-mat/0307004 Many Body Physics: Unfinished Revolution, by P. Coleman

Other links:

quant-ph/9612050 Displaced and Squeezed Number States, by M M Nieto
Second Quantization , by K. Ingersent
Second Quantization , Problems
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Last modified: September 2, 2003
Leonid Levitov