Discontinuité de la phase géométrique

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Discontinuité de la phase géométrique


La phase géométrique accumulée le long d’une trajectoire fermée (dans certains espaces de paramètres) doit-elle être continue?

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 David Bar Moshe

La phase géométrique peut connaître une dépendance discontinue de l’espace des paramètres au voisinage des points diaboliques (c’est-à-dire des points où les valeurs propres hamiltoniennes sont dégénérées mais les vecteurs propres sont distincts) et des points exceptionnels où les valeurs propres et les vecteurs propres sont dégénérés. Des points exceptionnels apparaissent dans les hamiltoniens non hermitiens utilisés pour modéliser les systèmes quantiques ouverts.

Veuillez consulter l’ article suivant de: Nesterov et de la Cruz pour une exposition détaillée.

La courbure de Berry présente une singularité monopolaire aux points diaboliques. Les points diaboliques correspondant à des classes supérieures de dégénérescences peuvent donner lieu à des nombres de Chern plus élevés, veuillez consulter l’ article suivant de: Garg.

Ce sujet fait encore l’objet de recherches très actives, voir par exemple les travaux suivants de Viennot

 

#de, #la, Discontinuité, géométrique, phase

 

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