Ordinary superconductivity and path integrals

Summary

Functional methods are very powerful in dealing with ordinary superconductivity. The ring geometry is discussed in mean field by means of a Higgs-type Ginzburg-Landau Lagrangian. The presence of a junction in the ring, as in SQUIDs, leads to a θ-vacuum as the ground state. The variable θ is related to the phase difference of the order parameter at the junction and Josephson relations are obtained semi-classically. The system is, to any purpose, in two space dimensions, what can imply exotic statistics.

Riassunto

I metodi dell'integrazione funzionale sono molto adatti a trattare l'ordinaria superconduttività. È discussa una geometria ad anello in campo medio per mezzo di una Lagrangiana di Ginzburg-Landau del tipo di Higgs. La presenza nell'anello di una giunzione (come in uno SQUID) porta and un «θ-vacuum» come stato fondamentale. La variabile θ è legata alla differenza di fase del parametro d'ordine in corrispondenza della giunzione e le relazioni di Josephson vengono riottenute semiclassicamente. Il sistema studiato è bidimensionale e può ammettere statistiche esotiche.

Резюме

Функциональные методы являются очень удобными для рассмотрения обыкновенной сверхпроводимости. Обсуждается кольцевая геометрия в среднем поле с помщью Лагранжиана Гинзбурга-Ландау типа Хиггса. Наличие перехода в кольце, как в свепрхроводящем квантовом интерферометрическом датчике, приводит к θ-вакууму, как основному состоянию. Переменная θ связана с разностью фаз для параметра упорядоченности в переходе. Полуклассически получаются соотношения Джозефсона. Рассматриваемая система является двумерной в пространстве, что может подразумевать экзотическую статистику.

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Tagliacozzo, A., Ventriglia, F. Ordinary superconductivity and path integrals. Il Nuovo Cimento D 11, 141–156 (1989). https://doi.org/10.1007/BF02450237

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PACS 74.20.Fg

  • BCS theory
  • applications

PACS 74.50

  • Tunneling phenomenon
  • Josephson effect
  • and proximity effects

PACS 03.65.Sq

  • Semi-classical theories and applications