Numéro
J. Phys. I France
Volume 1, Numéro 5, May 1991
Page(s) 613 - 620
DOI https://doi.org/10.1051/jp1:1991156
DOI: 10.1051/jp1:1991156
J. Phys. I France 1 (1991) 613-620

Replica approach to directed Feynman paths with random phases

Thomas Blum, Yonathan Shapir and Daniel S. Koltun

Department of Physics and Astronomy University of Rochester, Rochester, NY , U.S.A.


(Received 19 February 1991, accepted 11 March 1991)

Abstract
Directed Feynman paths in 1+1 dimensions that acquire random phases, encountered in the study of electron and light propagation in disordered media, are examined by means of the replica trick. Two models are considered - one with short-range correlations, the other with very long-range correlations. The large and small (finite) n behavior of the resulting 2n-body quantum Hamiltonians with competing interactions is calculated. The difficulties that arise in extrapolating the results to $n \rightarrow 0$ and the possibility of replica symmetry breaking are discussed.

Résumé
Les chemins de Feynman dirigés qui accumulent des phases aléatoires font partie des études récentes de la propagation d'électrons ou d'ondes électromagnetiques en milieux désordonnés. Nous examinons leurs propriétés d'échelle en utilisant la théorie des répliques. Deux modèles avec corrélations de courte et de très longue portée en 1+1 dimensions sont étudiés. Nous évaluons le comportement à grandes et petites valeurs (finies) de n des modèles quantiques à 2n corps avec interactions attractives et répulsives qui en resultent. Nous soulignons les difficultés qui sugissent dans la limite $n \rightarrow 0$ et la possibilité de brisure de symétrie des répliques.



© Les Editions de Physique 1991

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