  Quantum wire networks (``quantum crossbars'', QCB) represent a 2D grid formed
by superimposed crossing arrays of parallel conducting quantum wires, molecular
chains or metallic single-wall carbon nanotubes. QCB coupled only by capacitive
interaction in the crosses have similar low-energy, long-wave properties
characterized as a crossed sliding Luttinger liquid (CSLL) phase. In this
Thesis we develop a theory of interacting Bose excitations (plasmons) in QCB.
We analyze spectrum of boson fields and two-point correlators in QCB. We show
that the standard bosonization procedure is valid, and the system behaves as a
CSLL in the infrared limit, but the high frequency spectral and correlation
characteristics have either 1D or 2D nature depending on the direction of the
wave vector in the 2D BZ of reciprocal lattice. As a result, the crossover from
1D to 2D regime may be experimentally observed. An effective tool for probing
QCB spectral properties is the optical spectroscopy. The characteristic values
of QCB frequencies and wave vectors determine two possible directions of such
an experimental observation. The first of them is IR spectroscopy of QCB where
the frequency of an external ac field lies at the same region as the QCB
frequency. The second one is an UV scattering on QCB where the wave vector of a
scattered field lies in the same region as that of the QCB wave vectors. In
both cases, 1D to 2D crossover manifests itself as a splitting of single lines
into multiplets.
