Dynamic Localization Effects in L-Ring Circuit

TL;DR

This paper develops a quantum-mechanical model of L-ring circuits with time-dependent magnetic flux, deriving dynamic localization conditions that relate to electron transport and harmonic generation in 1D conductors.

Contribution

It introduces a novel approach using magnetic flux operators and discrete derivatives to analyze dynamic localization in L-ring circuits, generalizing previous models.

Findings

Derived second order discrete Schrödinger equations for L-ring circuits.

Established equivalence with 1D electron lattices under time-dependent fields.

Formulated exact localization conditions based on zero time-averaged persistent currents.

Abstract

Using suitable magnetic flux operators established in terms of discrete derivatives leads to quantum-mechanical descriptions of LC-circuits with an external time dependent periodic voltage. This leads to second order discrete Schrodinger equations provided by discretization conditions of the electric charge. Neglecting the capacitance leads to a simplified description of the L-ring circuit threaded by a related time dependent magnetic flux. The equivalence with electrons moving on one dimensional (1D) lattices under the influence of time dependent electric fields can then be readily established. This opens the way to derive dynamic localization conditions serving to applications in several areas, like the time dependent electron transport in quantum wires or the generation of higher harmonics by 1D conductors. Such conditions, which can be viewed as an exact generalization of the ones derived before by Dunlap and Kenkre [Phys. Rev. B 34, 3625(1986)], proceed in terms of zero values of time averages of related persistent currents over one period.