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Levitov, Leonid, 8.514 Strongly Correlated Systems in Condensed Matter Physics, Fall 2003. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA
Strongly Correlated Systems in Condensed Matter Physics
Fall 2003
Quasiparticles and Green's functions in BCS theory. (Image courtesy of Professor Leonid Levitov, from the course materials.)
Course Highlights
This course includes lecture notes, problem sets, and a term paper project.
Course Description
In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation. The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group.
*Some translations represent previous versions of courses.
Syllabus
Aim of the Course
The aim of the course is two-fold. First, we shall discuss topics of interest for both condensed matter and atomic physics, focussing on the effects of quantum statistics, interactions, and correlations in many-particle systems. Our second goal will be to provide a gentle introduction to the methods of quantized fields and their applications in many-body physics. We shall try to emphasize the physical and visualizable aspects of the subject. While the course is intended for students with a wide range of interests, many examples will be drawn from condensed matter physics.
Prerequisites
Statistical Mechanics and Quantum Mechanics, introductory level courses, such as 8.044 (Statistical Physics I), 8.08 (Statistical Physics II), and 8.04 (Quantum Physics I).
Course Topics
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Bose Condensates (Quasiparticles, Collective Modes, Superfluidity, Vortices)
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Fermi Gases and Liquids, Collective Excitations
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Cooper Pairing (BCS Theory, Off-diagonal Long-range Order, Superconductivity)
-
Atom Interacting with an Optical Field
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Lamb Shift, Casimir Effect
-
Dicke Superradiance
-
Quantum Transport and Wave Scattering in Disordered Media, Localization
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Tunneling and Instantons
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Macroscopic Quantum Systems, Coupling to a Thermal Bath
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Spin-boson Model, Tunneling and Localization
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Kondo Effect
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Spin Dynamics and Transport in Gases and Solids
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Cold Atoms in Optical Lattices
-
Quantum Theory of Photodetection and Electric Noise
Recommended Text
Stone, Michael. The Physics of Quantum Fields. Springer, 2000.
Problem Sets
Weekly, 13 problem sets in total, due the first session of the week, in class (at the beginning of the lecture).
Term Paper
A list of term paper topics will be provided and discussed in class.
Grade
| ACTIVITY |
PERCENTAGE |
| Problem Sets |
60% |
| Term Paper |
40% |
Calendar
|
SES #
|
TOPICS
|
KEY DATES
|
|
1
|
Coherent States
|
PS 1 out
|
|
2
|
Squeezed States
|
PS 2 out
|
|
3
|
Second Quantization Bosons
|
|
|
4
|
Bose Condensation Quasiparticles
|
PS 3 out PS 1 due
|
|
5
|
Bose condensation (continued); Superfluidity, Vortices
|
|
|
6
|
Fermi Gases Second Quantization
|
PS 4 out PS 2 due
|
|
7
|
Fermi Liquids Collective Modes
|
|
|
8
|
BCS Pairing Quasiparticles
|
PS 5 out PS 3 due
|
|
9
|
Bogoliubov-de Gennes Equation
|
|
|
10
|
Quantized Electromagnetic Field
Photons E & M Vacuum
|
PS 6 out PS 4 due
|
|
11
|
Atoms interacting with an Optical Field Lamb Shift
|
|
|
12
|
Casimir Effect
|
PS 7 out PS 5 due
|
|
13
|
Dicke Superradiance
|
|
|
14
|
Feynman path intregral
|
PS 8 out PS 6 due
|
|
15
|
Tunneling as dynamics in imaginary time
|
PS 9 out
|
|
16
|
Dissipative tunneling (Caldeira-Leggett theory)
|
PS 10 out PS 7, 8 due
|
|
17
|
Particle coupled to environment (tunneling suppression & decoherence)
|
PS 11 out
|
|
18
|
Field integral (bosons)
|
PS 9 due
|
|
19
|
Field integral (fermions)
|
PS 10 due
|
|
20
|
Mean field theory (BCS superconductivity revisited)
|
PS 11 due
|
|
|
|