Some Possible Thesis projects:

The first two of these involve programming in C or C++, which can be learned
on-the-job.

(1) Lattice calculation soliton masses in simple quantum field theories


Chris Bednarzyk '01 started a calculation of the mass
of objects called solitons which exist in simple quantum field
theories, and I'm looking for someone to continue that
work. Solitons are nontrivial solutions to field theories
that are stable in time and are often characterized by
certain topological features. They exist in many sorts
of field theories, and I'm trying to understand their
features in simple quantum field theories with the
eventual hope of moving to more complicated gauge theories
that are of more phenomenologically interesting. The project
will involve programming and running Monte Carlo simulations
using C or C++ (which you can learn on-the-job) and learning
some stat mech and quantum field theory.

(2) Persistence

In nonequilibrium statistical mechanics we often look for
simple diagnostics to characterize complicated behaviors.
One diagnostic that's been of interest lately is called
the sign-time distribution (which is a generalization of a related
quantity called persistence). The idea in its simplest form is:
on a lattice of spins which can be either spin-up or spin-down,
place a little clock, which runs if the spin is up and doesn't
if the spin is down. Now let the spin configuration evolve
according to some dynamics you've decided upon, and after
a long time check to see what the distribution of times on the
clocks is. My collaborators and I have done this simulation for
the case in which the dynamics is given by the diffusion equation,
and we've found some surprising features. We'd like to do simulations
for other statistical models and perhaps eventually in quantum
field theories. The project would involve programming in C or C++
and learning some statistical mechanics.

(3) Quantum Carpets

The probability density in simple one-dimensional quantum mechanical
systems, plotted as a function of space and time, shows beautiful
interference patterns full of ridges and valleys. The features
of these "quantum carpets" have evaded description that is
both simple and complete. Ross O'Connell '02 has spent this year
working to disentangle the roles of the energy levels, the potential,
and the initial wavepacket in determining the features of the
carpet, but there's plenty more to be done. If the one-dimensional
case is understood, extensions to more complicated systems (e.g.
two- or three-dimensional cases) or to "wavepacket engineering",
(learning how to choose potentials and construct wavepackets that
are ideal for certain applications in chemistry, etc.), would be
interesting. This project requires quantum mechanics at the level
of Physics 48 and will probably make considerable use of Mathematica.

(4) Particle Physics

Topcolor models

Topcolor models are a class of extensions to the Standard Model
which introduce new QCD-like interactions in place of the Higgs
particle. These theories can be considerably constrained by
comparing current experimental data to loop calculations in
quantum field theory. A thesis on this subject would focus on
understanding one or two key experiments, performing the corresponding
loop calculations, and deriving constraints on the theories by
comparison to data. This project requires a particle physics
class as a prerequisite.

Dimensional Deconstruction

A recently-proposed class of theories that would extend or
replace the Standard Model introduces new QCD-like interactions
that would, in effect, act like and extra compact spacelike dimension.
These theories make testable predictions, and I'd like to compare those
predictions to the results of certain experiments with which I'm familiar.
A thesis on this topic would involve becoming conversant with at
least simpler versions of this model and a few collider experiments,
calculation of the consequences of the model, and comparison
between data and the results of the calculation. A particle
physics class is a prerequisite.

(5) String-theory motivated modifications to quantum mechanics

see me

I've got a few more projects involving quantum mechanics, supersymmetric
quantum mechanics, noncommutative quantum field theory, and consquences of
string theory that I think are be thesis-worthy (and will probably not
involve significant programming), and new particle physics calculations
come along all the time. But I'm running out of energy to write, so let
me just encourage interested students to come talk to me if they have
interests along these lines.

william loinaz
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William Loinaz http://www.amherst.edu/~waloinaz/
Assistant Professor, Dept. of Physics 223 Merrill Center
Amherst College Ph: (413) 542-7968
waloinaz@amherst.edu FAX: (413) 542-5821