\documentstyle[12pt]{article}
\textwidth=6.0in
\textheight=8.5in
\hoffset -.5in
\voffset -.75in
\parindent 0in
\pagestyle{empty}
\begin{document}
\begin{center}{\bf Course Description: Computational Physics (509) }
\vskip .2in
\end{center}
\begin{center}{\bf Instructor: Gabriel Kotliar}
\vskip .2in
\end{center}

\begin{center}
Brief Description
\end{center}

Many body physics, 621, will  be an introduction
to the  study non relativistic systems  containing
a large number of degrees of freedom.
There will be equal emphasis on: a) concepts, b)
general results, c) techniques.


It is an essential  course
for  those students intending to 
study condensed matter physics.  
621  will be a second semester continuation
of 620 (Many Body I).


Will meet in SEC 217, on Tuesdays and Thursdays,
$9:50-11:10 $, {\large starting Tuesday January 19th.
 but there will be no lecture on Thursday
21}.

\vskip 1cm
Many body physics provides the right {\it language}
to describe the results of experimental investigations.
This conceptual part will be stressed throughout the
course and makes it very suitable for students interested
in experimental physics. 


Topics to be covered are:

\begin{itemize}
\item
Review of  the basic green functions and   approximation techniques. 
Hartree Fock, RPA, density functional.
\item 
Bosonization:
One and zero dimensional systems.
Impurity models
\item
Renormalization Group and 
Fermi Liquid Theory.
Quasi-particles and Collective Excitations.
\item
Dynamical  Mean  Field Methods. Theories of   the Mott transition. 
\end{itemize}

The only prerequisite for this course is 
620 or equivalent.
There will be no final examination.
Assessment will be based on 
take-home assignments


{\center Additional Information}
Information about the course will be posted
at the web site http://www.physics.rutgers.edu/~kotliar/course/course.html 
 


\end{document}

A partial list of topics is described below
\begin{itemize]
\item

\item
One dimensional systems.
After an introduction,  to the many body physics
we will start with  one dimensional systems.
Physical realizations of these are manifold, ranging from
one dimensional wires, organic compounds, and edge states
in quantum hall systems.


The one dimensional many body problem is much simpler than
its two and three dimensional counterpart and it will allow us
to build  our confidence in the concepts and techniques learned
in the previous semester.

Along the way we will introduce, bosonization techniques and
the functional integral language with bosonic and fermionic
variables which is very  useful  in  providing new ways
of thinking about and solving  many body problems.




We will then introduce the  mean field approach  to the many body
problem. This approach  is the basis of our understanding of
many complex systems.






\item
 





1) Introduction to strongly correlated systems.
Electrons in Solids.

2) What do we want to know.
a)Building model Hamiltonian
b) Unraveling the low energy physics.
c) Effective action point of view.
d) Calculating total energies.
\item


3) Fermi liquid theory.
PATH INTEGRAL APPROACH.

1) The old fashion diagrammatic approach.
2) An effective action point of view.
Applications: He3 Nuclei.
\item

4) One dimensional systems.
a) Bethe anzats
b) Bosonization
c) Luttinger liquids

5)
theory of transport
Projection operators.

\item

6) Mean Field Theories
Bethe lattice

7) 0 dimensional models impurity models

8)large d example of MFT

\item
9) Disordered electrons. Anderson Localization problem
\item
10 ) Superfluid Helium3.

11) Numerical methods.



\item
Electrons in magnetic fields.
Quantum Hall effect.
Vortex lattice analytic functions.



Bose systems.
:wq


Density functional theory.

Berry Phase, Wess Zumino, Chern Simons and effective actions.

Superconductivity and pair breaking.

Superradiance+ Laser pysics.

Quantum Criticality.

Kinetic equations, superconductivity and pair breaking.

Understanding of He3 as a lab for quantum field theory.

Super-symmetry and Anderson Localization.
Integration of Grassman Variables and Functional Integrals.


Mean Field theory and the Bethe Lattice.

Quantum Hall physics.

\end{itemize}


