Quantum dot to disordered wire crossover: A complete solution in all length scales for systems with unitary symmetry

We present an exact solution of a supersymmetric nonlinear $\sigma$-model describing the crossover between a quantum dot and a disordered quantum wire with unitary symmetry. The system is coupled ideally to two electron reservoirs via perfectly conducting leads sustaining an arbitrary number of propagating channels. We obtain closed expressions for the first three moments of the conductance, the average shot-noise power, and the average density of transmission eigenvalues. The results are complete in the sense that they are nonperturbative and are valid in all regimes and length scales.