  One-dimensional structures of non-Hermitian plasmonic metallic nanospheres
are studied in this paper. For a single sphere, solving Maxwell's equations
results in quasi-stationary eigenmodes with complex quantized frequencies.
Coupled mode theory is employed in order to study more complex structures. The
similarity between the coupled mode equations and the effective non-Hermitian
Hamiltonians governing open quantum systems allows us to translate a series of
collective phenomenon emerging in condensed matter and nuclear physics to the
system of plasmonic spheres. A nontrivial physics emerges as a result of strong
non-radiative near field coupling between adjacent spheres. For a system of two
identical spheres, this occurs when the width of the plasmonic resonance of the
uncoupled spheres is twice the imaginary component of the coupling constant.
The two spheres then become coupled through a single continuum channel and the
effect of coherent interaction between the spheres becomes noticeable. The
eigenmodes of the system fall into two distinct categories: superradiant states
with enhanced radiation and dark states with no radiation. The transmission
through one-dimensional chains with an arbitrary number of spheres is also
considered within the effective Hamiltonian framework which allows us to
calculate observables such as the scattering and transmission amplitudes. This
nano-scale waveguide can undergo an additional superradiance phase transition
through its coupling to the external world. It is shown that perfect
transmission takes place when the superradiance condition is satisfied.
