Quantum theory for mesoscopic electric circuits

TL;DR

This paper develops a quantum theoretical framework for mesoscopic electric circuits, solving key equations exactly, deriving uncertainty relations, and explaining persistent currents via magnetic flux from a novel perspective.

Contribution

It introduces a quantum theory for mesoscopic circuits considering charge discreteness, providing exact solutions and a new approach to persistent currents.

Findings

Exact solutions to Schrödinger equations for quantum LC and L circuits.

Derived uncertainty relations for charge and current.

Presented a new formula for persistent current from magnetic flux.

Abstract

A quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges is proposed. On the basis of the theory, Schr\"{o}dinger equation for the quantum LC-design and L-design is solved exactly. The uncertainty relation for electric charge and current is obtained and a minimum uncertainty state is solved. By introducing a gauge field, a formula for persistent current arising from magnetic flux is obtained from a new point of view.