Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths

Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths

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 Lag...

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Main Author: Arthur Davidson
Format: Article
Language:English
Published: AIP Publishing LLC 2018-11-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/1.5041020
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spelling doaj-cb0b06940ea4471c945693b3f40bd5432020-11-24T20:58:44ZengAIP Publishing LLCAIP Advances2158-32262018-11-01811115219115219-810.1063/1.5041020078811ADVNanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengthsArthur Davidson0ECE Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USATunnel 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.http://dx.doi.org/10.1063/1.5041020
collection DOAJ
language English
format Article
sources DOAJ
author Arthur Davidson
spellingShingle Arthur Davidson
Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths
AIP Advances
author_facet Arthur Davidson
author_sort Arthur Davidson
title Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths
title_short Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths
title_full Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths
title_fullStr Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths
title_full_unstemmed Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths
title_sort nanocircuits in loop structures: continuous waves preclude gauge invariant wavelengths
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2018-11-01
description 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.
url http://dx.doi.org/10.1063/1.5041020
work_keys_str_mv AT arthurdavidson nanocircuitsinloopstructurescontinuouswavesprecludegaugeinvariantwavelengths
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