We propose a new method to characterize the spatial distribution of
particles' vibrations in solids with much lower computational costs compared to
the usual normal mode analysis. We excite the specific vibrational mode in a
two dimensional athermal jammed system by giving a small amplitude of active
oscillation to each particle's size with an identical driving frequency. The
response is then obtained as the real time displacements of the particles. We
show remarkable correlations between the real time displacements and the eigen
vectors obtained from conventional normal mode analysis. More importantly, from
these real time displacements, we can measure the participation ratio and
spatial polarization of particles' vibrations. From these measurements, we find
three distinct frequency regimes which characterize the spatial distribution
and correlation of particles' vibrations in jammed amorphous solids.
Furthermore, we can possibly apply this method to a much larger system to
examine the low frequency behaviour of amorphous solids with a much higher
resolution of the frequency space.Comment: Soft Matter, 201
