  The conformational and dynamical properties of isolated flexible active polar
linear polymers (APLPs) are studied analytically. The APLPs are modeled as
Gaussian bead-spring linear chains augmented by tangential active forces, both
in a discrete and continuous representations. The polar forces lead to linear
non-Hermitian equations of motion, which are solved by an eigenfunction
expansion in terms of a biorthogonal basis set. Our calculations show that the
polymer conformations are independent of activity. On the contrary, tangential
propulsion strongly impacts the polymer dynamics and yields an active ballistic
regime as well as activity-enhanced long-time diffusion, regimes which are both
absent in passive systems. The polar forces imply a coupling of modes in the
eigenfunction representation, in particular with the translational mode, with a
respective strong influence on the polymer dynamics. The total polymer
mean-square displacement on scales smaller than their radius of gyration is
determined by the active internal dynamics rather than the collective
center-of-mass motion, in contrast to active Brownian polymers, reflecting the
distinct difference in the propulsion mechanism.
