|
Abstract |
I consider a model of fluid particle motion given by the reconstructed KdV
equation on a
circle. For travelling waves that are "uniformizable" in a suitable sense,
the map that governs
stroboscopic motion can be derived analytically. The particle's drift
velocity, then, is
essentially the Poincaré rotation number of that map, and has a geometric
origin: it is the sum
of a dynamical phase, a geometric/Berry phase, and an "anomalous phase". The
last two
phases are universal, as they follow entirely from the underlying Virasoro
group structure. The
Berry phase, in particular, is produced by a sequence of adiabatic conformal
transformations
due to the moving wave profile, and was previously found in two-dimensional
conformal field
theories. |
