  In a recent paper, by exploiting the notion of Morita equivalence for field
theories on noncommutative tori and choosing rational values of the
noncommutativity parameter $\theta $ (in appropriate units), a general
one-to-one correspondence between the $m$-reduced conformal field theory (CFT)
describing a quantum Hall fluid (QHF) at paired states fillings $\nu =%
\frac{m}{pm+2}$ and an Abelian noncommutative field theory (NCFT) has been
established . That allowed us to add new evidence to the relationship between
noncommutativity and quantum Hall fluids\cite% {ncmanybody}. On the other hand,
the $m$-reduced CFT is equivalent to a system of two massless scalar bosons
with a magnetic boundary interaction as introduced by Callan et al., at the so
called ``magic''\ points. We are then able to describe, within such a
framework, the dissipative quantum mechanics of a particle confined to a plane
and subject to an external magnetic field normal to it. Here we develop such a
point of view by focusing on the case $m=2$ which corresponds to a quantum Hall
bilayer. The key role of a localized impurity which couples the two layers is
emphasized and the effect of noncommutativity in terms of generalized magnetic
translations (GMT) is fully exploited. As a result, general GMT operators are
introduced, in the form of a tensor product, which act on the QHF and defect
space respectively, and a comprehensive study of their rich structure is
performed.
