  Spectrum of boson fields and two-point correlators are analyzed in quantum
crossbars (QCBs, a superlattice formed by m crossed interacting arrays of
quantum wires), with short range inter-wire capacitive interaction. Spectral
and correlation properties of double (m=2) and triple (m-3) QCBs are studied.
It is shown that the standard bosonization procedure is valid, and the system
behaves as a sliding Luttinger liquid 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 elementary cell of
reciprocal lattice. As a result, the crossover from 1D to 2D regime may be
experimentally observed. It manifests itself as appearance of additional peaks
of optical absorption, non-zero transverse space correlators and periodic
energy transfer between arrays ("Rabi oscillations").
