  The isomorph theory provides an explanation for the so-called power law
density scaling which has been observed in many molecular and polymeric glass
formers, both experimentally and in simulations. Power law density scaling
(relaxation times and transport coefficients being functions of
$\rho^{\gamma_S}/T$, where $\rho$ is density, $T$ is temperature, and
$\gamma_S$ is a material specific scaling exponent) is an approximation to a
more general scaling predicted by the isomorph theory. Furthermore, the
isomorph theory provides an explanation for Rosenfeld scaling (relaxation times
and transport coefficients being functions of excess entropy) which has been
observed in simulations of both molecular and polymeric systems. Doing
molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with
rigid bonds, we here provide the first detailed test of the isomorph theory
applied to flexible chain molecules. We confirm the existence of isomorphs,
which are curves in the phase diagram along which the dynamics is invariant in
the appropriate reduced units. This holds not only for the relaxation times but
also for the full time dependence of the dynamics, including chain specific
dynamics such as the end-to-end vector autocorrelation function and the
relaxation of the Rouse modes. As predicted by the isomorph theory, jumps
between different state points on the same isomorph happen instantaneously
without any slow relaxation. Since the LJC is a simple coarse-grained model for
alkanes and polymers, our results provide a possible explanation for why
power-law density scaling is observed experimentally in alkanes and many
polymeric systems. The theory provides an independent method of determining the
scaling exponent, which is usually treated as a empirical scaling parameter.
