Wavefront solution in extended quantum circuits with charge discreteness
  A wavefront solution for quantum (capacitively coupled) transmission lines with charge discreteness (PRB {\bf 64}, 235309 (2001)) is proposed for the first time. The nonlinearity of the system becomes deeply related to charge discreteness. The wavefront velocity is found to depend on a step discontinuity on the (pseudo) flux variable, $f$, displaying allowed and forbidden regions (gaps), as a function of $f$. A preliminary study of the stability of the solutions is presented. The dual transmission line hamiltonian is proposed and finally, we find a connection with the (quantum) Toda lattice. 
J. C. Flores, Mauro Bologna, K. J. Chand\'ia, (Departamento de   F\'isica, Universidad de Tarapac\'a, Casilla 7-D, Arica, Ch...