  We describe the low-temperature optical conductivity as a function of
frequency for a quantum-mechanical system of electrons that hop along a polymer
chain. To this end, we invoke the Su-Schrieffer-Heeger \emph{tight-binding}
Hamiltonian for non-interacting spinless electrons on a one-dimensional (1D)
lattice. Our goal is to show via asymptotics how the interband conductivity of
this system behaves as the smallest energy bandgap tends to close. Our
analytical approach includes: (i) the Kubo-type formulation for the optical
conductivity with a nonzero damping due to microscopic collisions; (ii)
reduction of this formulation to a 1D momentum integral over the Brillouin
zone; and (iii) evaluation of this integral in terms of elementary functions
via the three-dimensional Mellin transform with respect to key physical
parameters and subsequent inversion in a region of the respective complex
space. Our approach reveals an intimate connection of the behavior of the
conductivity to particular singularities of its Mellin transform. The
analytical results are found in good agreement with direct numerical
computations.
