Tunneling between two luttinger liquids induced by a driving field

Tunneling between two Luttinger liquids driven by a time-dependent field with 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 results in the limit L(T)/L>1 ( L is the channel length and L(T) is the thermal length). We find that the tunneling current is quantized in units of "ef" and takes the form I approximately ef SUM(n = 1)(infinity)deltamu(F)-2pi / LvPlanck's over 2pi(n-1 / 2)].