Transverse transport in coupled strongly correlated electronic chains

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.