  We study hidden scale invariance in the glassy phase of the Kob-Andersen
binary Lennard-Jones system. After cooling below the glass transition, we
generate a so-called isomorph from the fluctuations of potential energy and
virial in the NVT ensemble -- a set of density, temperature pairs for which
structure and dynamics are identical when expressed in appropriate reduced
units. To access dynamical features we shear the system using the SLLOD
algorithm coupled with Lees-Edwards boundary conditions, and study the
statistics of stress fluctuations and the particle displacements transverse to
the shearing direction. We find good collapse of the statistical data showing
that isomorph theory works well in this regime. The analysis of stress
fluctuations, in particular the distribution of stress changes over a given
strain interval, allows us to identify a clear signature of avalanche behavior
in the form of an exponential tail on the negative side. This feature is also
isomorph invariant. The implications of isomorphs for theories of plasticity
are discussed briefly.
