  We consider the transport of spinless fermion charge carriers in a planar
narrow rectangular geometry, with the larger dimension being periodic and the
narrow one confined to a finite strip width, and ballistic flow in the larger
dimension only. Our analysis is based on the formulation of an Effective Field
Theory (EFT) for the system, which is appropriate for discussing universal
phenomena. The EFT is constructed as a direct product of two known
one-dimensional ones obtained both from the thermodynamic limit of the
Calogero-Sutherland model. This lower dimensional EFT is known to be capable of
describing a quantum hydrodynamical flow. The resulting two-dimensional EFT
displays a ground state charge density that is constant along the large
dimension and vanishes at the boundaries of the narrow one with the shape of a
semi-circumference. This latter feature is a consequence of the specific
harmonic confining potential in the narrow dimension considered. The charge
transport is obtained by coupling the system to an external electromagnetic
field that induces a global translation. The EFT incorporates quantum solitonic
excitations along the direction of the flow and the two-dimensional electric
current density shows a Poiseuille-like behavior, indicating the presence of
non-dissipative quantum viscous effects in the direction transverse to the
flow. These two are among the most interesting features while discussing and
observing charge flow in nanoscopic structures of several types. We provide
explicit expressions for the electric current intensity, DC resistivity and
charge mobility in an example.
