Current magnification is studied for a system of two rings with external magnetic flux; we have considered, in addition to self-inductance, a mutual inductance between the rings. The system is studied using a method recently proposed by Li and Chen, which takes into account the charge quantization of the system, allowing for a simplified description. We find that, for some values of the external flux enclosed by one of the rings, quantum current magnification exists in the other ring. This magnification effect is a purely quantum phenomenon, which is given here an alternative explanation, different from the detailed quantum-mechanical explanation.

The problem of a dielectric slab inside a parallel-plate capacitor is considered from the point of view of a simple force calculation. The usual method of presenting this problem, found in most textbooks, is via energy considerations. The method presented here allows corrections to the well-known result to be obtained.

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In the present work, we consider a quantum LC circuit under a constant magnetic field. In particular, we derive a new discretized form of the Schrödinger equation, which is equivalent to introducing a potential in the pseudo-flux representation. We discuss the physical assumptions leading to our results, and using a direct numerical approach we calculate the energy spectrum of the LC quantum circuit as a function of a constant external magnetic flux. The results are compared with the spectrum obtained using the Li-Chen potential [Y. Q. Li and B. Chen, Phys. Rev. B 53 (1996) 4027]. Our results indicate that the energy spectra from both models are numerically different, hence they may be clearly distinguished under appropriate experimental conditions.

In a recent article [1], we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance, inductive circuit, we obtain the Stark ladder energies in yet another way; and generalize earlier results by Chandía et. al [2], for the circuit driven by a combination d.c. plus a.c. electromotive force (emf). As a second application, we investigate the effect of electrical resistance, together with charge discreteness, in the current amplitude, and resonance conditions of a general RLC quantum circuit, including nonlinear effects up to third order on the external sinusoidal emf.