The wave functions in the presence of constraints - Persistent Current in Coupled Rings

We present a new method for computing the wave function in the presence of constraints. As an explicit example we compute the wave function for the many electrons problem in coupled metallic rings in the presence of external magnetic fluxes. For equal fluxes and an even number of electrons the constraints enforce a wave function with a vanishing total momentum and a large persistent current and magnetization in contrast to the odd number of electrons where at finite temperatures the current is suppressed. We propose that the even-odd property can be verified by measuring the magnetization as a function of a varying gate voltage coupled to the rings. By reversing the flux in one of the ring the current and magnetization vanish in both rings; this can be used as a non-local control device

Polarized Magnetic Wire Induced by Tunneling Through a Magnetic Impurity

Using the zero mode method we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent $\alpha(\leq 1)$. We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, the conductance as a function of temperature is $G \sim \frac{e^2}{h} (T/T_F)^{2(\alpha-2)}$, whereas for off-resonance conditions the conductance is $G \sim \frac{e^2}{h} (T/T_F)^{2(\alpha-1)}$. By applying a gate voltage and/or a magnetic field, one of the spin components can be in resonance while the other is off-resonance causing a strong asymmetry between the spin-up and spin-down conductances.Comment: 8 pages, submitted to PR