Speaker
Description
The dynamics of a quantum particle on a square lattice subjected to an
external constant force is numerically studied. In one dimension, it is well
known that if the wave packet is wide enough, the average position over time
will evolve in an oscillatory manner, while the shape of the wave packet is pre-
served. This phenomenon is known as Bloch oscillations and is characteristic
for particles moving in periodic systems with a constant gradient. Addition-
ally, in the case of a narrow wave packet, the position of the center does not
change over time, but periodic changes in shape are observed. Such behav-
ior is often referred to as the breathing mode. Eventually, we can observe
two competing effects, where oscillations dominate for wide wave packets and
breathing dominates for narrow ones. We show that for a certain class of ini-
tial states, the problem of time evolution of the two-dimensional system can
be treated as two independent one-dimensional problems. We mainly focus
on showing that it is possible through a combination of Bloch oscillations in
both directions to obtain trajectories of a wave packet center analogous to
classical Lissajous figures. Visuaization of obtained results can be found here RESULTs.
