Quantum mechanic plus chaos theory.
Chaos theory tells us that a billiard-ball rolling around in a bath
follows a chaotic
path. This means that any error you make in
measuring the initial postion or velocity of the ball
will lead to an error in your prediction of its motion
which grows exponentially with time, until fairly soon
your prediction becomes completely wrong! In such cases, one can use chaos
theory to make statistical predictions
(i.e. "there is a 10% chance of the ball going there")
much like a weather forecast
(i.e. "there is a 10% chance of rain").
Quantum mechanics tells us that electrons
(unlike billiard-balls) move as waves. Imagine filling the
bath with water and
looking at how ripples move on the surface of the water.
The bath is the same, but now you are studying
how waves (not particles) move within it.
These waves do many things that particles (such as billiard balls) do not.
They go to many places at once.
They diffract, tunnel and interfere.
Electrons in a typical semiconductor
quantum dot do the same.
We ask how the wave nature of electrons affects their
chaotic motion. Using the semiclassical limit of
(the "ray-optics" limit), we go beyond
"Berry's diagonal approximation"
to look at interference and other wave effects.
MORE INFO: Summary of our
Quantum Chaos Workshop in Canada 2008 (pdf)
I have been particularly interested in
particle flow through open quantum chaotic systems.
I study how quantum chaos induces
interference effects such as weak-localization and conductance fluctuations,
and have proposed huge intereference effects in quantum chaotic systems
with a discrete symmetry (mirror-symmetry).
I have also study quantum noise in such systems.
Added in 2012. Since 2011, I have mainly worked to understand thermoelectric effects
associated with such quantum particle flows
(when an electrical current flow induces a heat flow, and vice versa).
I am particularly interested in the connection between this and quantum thermodynamics.
MORE INFO: thermoelectricity and quantum thermodynamics