By extending Lieb and Liniger's (1963) Bose gas analysis to many hard-core bosons confined to a one-dimensional mesoscopic ring in the presence of Aharonov-Casher flux (AC), persistent fluxon currents are investigated for the first time, and are found to be periodic in the AC flux with period Phi 0=hc/e. The interesting mesoscopic parity effects due to evenness or oddness of the particle number N are discussed. More importantly, it is demonstrated exactly that, in the absence of the external AC flux, whether a self-sustained fluxon current exists depends only upon the choice of the boundary condition.
We address the issue of whether a system of interacting electrons confined to a one-dimensional ring can sustain a spontaneous persistent current in the absence of an externally applied flux. The current-current coupling between electrons, describing radiative back-action effects, is exactly treated in the formalism of quantum electrodynamics, where the electrons interact via the exchange of virtual photons. In addition, the instantaneous screened Coulomb potential is taken into account using the Luttinger liquid model including finite-size parity effects. The partition function is calculated exactly, with the result that the system does not possess a spontaneous persistent current. We show that, in the presence of an external flux, the amplitude of the (conventional) persistent current is reduced by quantum fluctuations of the internal transverse electromagnetic field. These corrections can be expressed in terms of the self-induction of the ring and are shown to be of first and higher order in the small dimensionless parameter \ensuremath{\alpha}
vF∗/c, where \ensuremath{\alpha} is the fine-structure constant and
vF∗ the Fermi velocity renormalized through Coulomb interactions.