  One-particle interchain hopping in a system of coupled Luttinger liquids is
investigated by use of exact diagonalizations techniques. Firstly, the two
chain problem of spinless fermions is studied in order to see the behaviour of
the band splitting as a function of the exponent \alpha which characterizes the
1D Luttinger liquid. We give numerical evidence that inter-chain coherent
hopping (defined by a non-vanishing splitting) can be totally suppressed for
\alpha\sim 0.4 or even smaller \alpha values. The transverse conductivity is
shown to exhibit a strong incoherent part even when coherent inter-chain
hopping is believed to occur (at small \alpha values). Implications for the
optical experiments in quasi-1D organic or high-T_c superconductors is
outlined.
