Ordering effect of Coulomb interaction in ballistic double-ring systems

We study a model of two concentric onedimensional rings with incommensurate areas A(1) and A(2), in a constant magnetic field. The two rings are coupled by an nonhomogeneous inter-ring tunneling amplitude, which makes the one-particle spectrum chaotic. For noninteracting particles the energy of the many-body ground state and the first excited state exhibit random fluctuations characterized by the Winger-Dyson statistics. In contrast, we show that the electron-electron interaction orders the magnetic field dependence of these quantities, forcing them to become periodic functions, with period proportional to 1/(A(1) + A(2)). In such a strongly correlated system the only possible source of disorder comes from charge fluctuations, which can be controlled by a tunable inter-ring gate voltage. (C) 1997 Published by Elsevier Science Ltd.