Mesoscopic circuits with charge discreteness:  Quantum current magnification for mutual inductances

Abstract

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.

From least action in electrodynamics to magnetomechanical energy—a review

“…The books by Bueno and Assis [44] and by Grover [59] may be mentioned. Technical papers are [60,61,62], and a few applications of ideas concerning self-inductance can be found in [63,64,65].…”

Lagrangian for RLC circuits using analogy with the classical mechanics concepts

“…The quantum mechanics treatment of the RLC circuit with discrete charge and semiclassical consideration can be found in Utreras-Diaz [6] that obtained the approximation of energy eigenvalues in term of a dimensionless parameter h e C L 2 (e is the electron charge, and h is the Planck constant). In literature, we found most analysis of the RC, RL, LC, and RLC circuits, as a mesoscopic system or nanophysics, are commonly discussed and formulated by using the concept of quantum mechanics [7][8][9][10]. As we have already known that the energy operator in quantum mechanics is the Hamiltonian which is defined as the sum of energy kinetic and energy potential of the physical system.…”

Semiclassical Nonlinear Approach for Mesoscopic Circuit

“…In a series of articles Li and Chen [1,2] and Flores et al [3,4,5,6,7], have developed a theory of quantum electrical systems, based on a treating such systems as quantum LC circuits; that is, electrical systems described by two parameters: an inductance L, and a capacitance C. Such quantum theory of circuits is expected to apply when the transport dimension becomes comparable with the charge carrier coherence length, taking into account both the quantum mechanical properties of the electron system, and also the discrete nature of electric charge. Now, we propose a semiclassical theory of quantum electrical circuits, to obtain useful predictions of the theory from very simple calculations of energy consideration , and to push the circuit analogy one step further, generalizing the Heisenberg equations of motion .…”