  The local deformation of two-dimensional Lennard-Jones glasses under imposed
shear strain is studied via computer simulations. Both the mean squared
displacement and mean squared strain rise linearly with the length of the
strain interval $\Delta \gamma$ over which they are measured. However, the
increase in displacement does not represent single-particle diffusion. There
are long-range spatial correlations in displacement associated with slip lines
with an amplitude of order the particle size. Strong dependence on system size
is also observed. The probability distributions of displacement and strain are
very different. For small $\Delta \gamma$ the distribution of displacement has
a plateau followed by an exponential tail. The distribution becomes Gaussian as
$\Delta \gamma$ increases to about .03. The strain distributions consist of
sharp central peaks associated with elastic regions, and long exponential tails
associated with plastic regions. The latter persist to the largest $\Delta
\gamma$ studied.
