Coulomb drag shot noise in coupled Luttinger liquids

Coulomb drag shot noise has been studied theoretically for 1D interacting electron systems, which are realized, e.g., in single-wall nanotubes. We show that under adiabatic coupling to external leads, the Coulomb drag shot noise of two coupled or crossed nanotubes contains surprising effects, in particular, a complete locking of the shot noise in the tubes. In contrast to Coulomb drag of the average current, the noise locking is based on a symmetry of the underlying Hamiltonian and is not limited to asymptotically small energy scales.