Abstract

We study the capacitively coupled, quantum transmission line with charge discreteness, discussed in an earlier paper. Due to the difficulties of dealing with a highly nonlinear system, only a low-lying propagating wave solution was obtained then, the so-called cirquiton. In this work, we obtain a wave-front solution, valid for the long-wavelengh approximation. The propagation velocity v of the wave front depends on the (pseudo) flux parameter f; the physical requirement that v should be real implies the existence of allowed and forbidden regions (gaps) in the space of the parameter f. A study of the stability of the solutions is presented. We remark that it is possible to make a connection between our system and the (quantum) Toda lattice. © 2006 The American Physical Society.