Tunneling between two Luttinger liquids induced by a driving field

Tunneling between two Luttinger liquids driven by a time-dependent field wi th a frequency f is investigated using the zero-mode bosonization. We show that inclusion of the zero modes is essential in order to obtain correct re sults in the limit L-T/L much greater than 1 (L is the channel length and L T is the thermal length). We find that the tunneling current is quantized i n units of "ef" and takes the form I similar to ef Sigma (infinity)(n=1) de lta[mu (F) - 2 pi /L upsilon (h) over bar (n - 1/2)].