Different Transmission Regimes of Two Quantum Point Contacts in a Magnetic Field

We calculate how the Aharonov-Bohm transmission oscillations of a cavity formed by two quantum point contacts superimpose on those induced by a magnetic field in a single point contact. The series of two Quantum Point Contacts (QPCs) amplifies in an irregular, noisy way the magnetic field induced transmission oscillations of a single QPC. The total transmission, given by the Airy formula, shows a great sensitivity to the values of the parameters of the barrier representing the QPC. However the system cannot exhibit a deterministic chaotic behaviour: the Airy formula corresponds to a linear map in the complex plane of the transmitted amplitude. We have a coherent transport in a structure with two characteristic lengths: the length $L$ of the cavity and that of its walls, $L_0$. When these lengths are close each other, the transmission as a function of the field shows a disordered look. On the contrary if $L$ is much larger than $L_0$, the transmission oscillations of the single quantum point contact, due to phase vortices trapped within the walls, simply modulate and make more regular the real Aharonov-Bohm oscillations of the cavity