Nanocircuits in loop structures: continuous waves preclude gauge invariant wavelengths

TL;DR

This paper challenges the conventional understanding of gauge invariance in quantum loops, showing that continuous waves cannot produce gauge-invariant wavelengths, and links phenomena like persistent current and Coulomb blockade through a unified theory.

Contribution

It introduces a gauge function derived from the Lagrangian that demonstrates the violation of gauge invariance for continuous waves on a loop, unifying persistent current and Coulomb blockade phenomena.

Findings

Continuous waves on a loop violate gauge invariance of de Broglie wavelength.

A gauge function relates the Lagrangians of electrons on rings and charges on junctions.

Persistent current and Coulomb blockade are described by the same dynamical theory.

Abstract

Tunnel junctions for quantum computing require discrete spectra from continuous waves on a doubly connected coordinate or loop. For an electron on a metal ring discrete spectra follow from discontinuous Bloch waves. Can both propositions be true? We find using a gauge function originating in the Lagrangian that continuity on a ring or loop violates gauge invariance of the de Broglie wavelength. This same gauge function shows that Lagrangians for the electron on a ring and the charge on a junction are mutual transforms. Thus persistent current on a metal ring and the Coulomb blockade on a tunnel junction seem to be the same dynamical theory based on discontinuous Bloch waves on the compact perimeter of a circle