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Dr. Johnson
works in computational quantum mechanics mostly in applications to
nuclear physics and astrophysics.
I have
projects for senior (B.S.) thesis, M.S., in computational physics, or Ph.D in
computational science.
Theoretical
physics at SDSU is heavily computational. I expect students to be fluent in
some computing language; although I will help with algorithmic design, I
won't be responsible for teaching you to program. I work mostly in FORTRAN
and strongly encourage you to learn that. C/C++ is acceptable, but be aware
you have be self-sufficient (that is, I won't bail you out if you run into
trouble). For some projects MATLAB or MATHEMATICA would also be acceptable,
but again you must be self-sufficient.
You must
have received an "A" in quantum mechanics to work on these projects
as a minimum.
Research
in theoretical/computational physics is difficult and time-consuming. A
research project requires a minimum of 300 hours of work. That is 10
hrs a week over TWO semesters. (You cannot complete a resarch project in one
semester.) Some projects may require even more time. (If you do not
bring significant programming ability to the table it will require at least
an additional semester to bring your skills up to the necessary level.)
In
addition to carrying out the research, you must write up your results (senior
thesis, at least 25-40 pages, or master's thesis, around 70-100 pages), and
you must make a presentation of your work. These are departmental
requirements.
The following
are a sample of the types of projects students may engage in.
Scattering with non-local
potential
If you
enjoyed learning quantum mechanics, here is a chance to apply your learning.
You will write a computer program to solve for the scattering of the
Schrodinger equation, but using a non-local potential, and compare the
results to local potentials (I would guess about 500 lines of code). I will
provide much of the original code, in Fortran, but you will be require to
make changes and to run the programs. Must be comfortable with Fortran and
with the Linux computing environment.
Quantum chaos
I have
several projects where students can compare classical and quantum chaos. You will write your own computer codes. Must
be comfortable with Fortran and with the Linux computing environment. Requires
knowledge of quantum mechanics and classical mechanics.
Nuclear
Reactions in strong magnetic fields
Nuclear
reactions that occur on the surface of a white dwarf or neutron star can be
in the presence of very strong magnetic fields. These fields may be strong
enough to change nuclear reactions rates. This project will be to compute
such changes.
Dependence
of weak decays on interactions
An
important topic in nuclear astrophysics are "weak decays" (as in
the weak nuclear force), essentially beta decays and electron capture. In the
pf-shell nuclei, between calcium and copper, there are a large number
of competing phenomenological interactions. In this project you will run
codes to compute the strength of the Gamow-Teller nuclear matrix element and
compare for different interactions. You will not need to write any code, but
you must be comfortable in Linux and running Fortran code. A good project to
improve your knowledge of nuclear physics.
Coulomb interaction and weak
decays
The nuclear
interaction does not distinguish between protons and neutrons (this is known
as "isospin invariance") but the Coulomb interaction, which is
about 100 times weaker than the nuclear force, does (this is called
"isospin breaking"). As one goes farther and farther from the
line of stability, this effect should become apparent.
Most of the
codes exist, as do the files for the nuclear interaction. Your job would be
to program up the Coulomb interaction (about 200 lines of code) and to
compare isospin-conserving and isospin-breaking interactions. Must be done in
Fortran.
Nuclear Reaction Networks
You will set up codes to simulate nuclear reaction
networks in stellar environments, downloading the basis information from the
internet. Requires a basic understanding of solving differential
equations, but does not require quantum mechanics (a bit of knowledge about
thermodynamics and, hopefully, nuclear physics would be useful but not
absolutely necessary). You must know how to program in Fortran, C, or
possibly MatLab. You will also prepare on-line tutorials for other students.
See Dr. Johnson for more information.
Time-dependent reaction
networks
Reaction
networks occur in nucleosynthesis of heavy elements, particularly in
supernova. The competition between neutron capture and beta-decay describe
isotopic abundances....mostly.
In
calculations of reaction networks the neutron flux can vary smoothly in time.
What happens if the neutron flux varies rapidly in flux and/or temperature?
In particular, is the system ergodic (does the ensemble average give the same
result as the time average)?
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