Nonlinear Science at the Dawn of the 21st Century (7).pdf

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7
Dynamics of Vortices in
Two-Dimensional s
Franz G. Mertens
Alan R. Bishop
ABSTRACT Theories, simulations and experiments on vortex dynamics
in quasi-two-dimensional ic materials are reviewed. These materials
can be modelled by the classical two-dimensional anisotropic Heisenberg
model with XY (easy-plane) symmetry. There are two types of vortices,
characterized by their polarization (a second topological charge in addi-
tion to the vorticity): Planar vortices have Newtonian dynamics (even-
order equations of motion) and exhibit strong discreteness effects, while
non-planar vortices have non-Newtonian dynamics (odd-order equations of
motion) and smooth trajectories. These results are obtained by a collective
variable theory based on a generalized travelling wave ansatz which allows
a dependence of the vortex shape on velocity, acceleration etc.. An alterna-
tive approach is also reviewed pared, namely the coupling of the
vortex motion to certain quasi-local spinwave modes.
The influence of thermal fluctuations on single vortices is investigated. Dif-
ferent types of noise and damping are discussed and implemented into the
microscopic equations which yields stochastic equations of motion for the
vortices. The stochastic forces can be explicitly calculated and a vortex
diffusion constant is defined. The solutions of the stochastic equations are
compared with Langevin dynamics simulations. Moreover, noise-induced
transitions between opposite polarizations of a vortex are investigated.
For temperatures above the Kosterlitz-Thouless vortex-antivortex unbind-
ing transition, a phenomenological theory, namely the vortex gas approach,
yields central peaks in the dynamic form factors for the spin correlations.
Such peaks are observed both bined Monte Carlo- and Spin Dyna-
mics-Simulations and in inelastic neutron scattering experiments. However,
the assumption of ballistic vortex mot