Catégorie : Collaborations

Abstract : We study the spectral determinant of the Laplacian on finite graphs characterized by their number of vertices V and of bonds B. We present a path integral derivation which leads to two equivalent expressions of the spectral determinant of the Laplacian either in terms of a V x V vertex matrix or a 2B x 2B link matrix that couples the arcs (oriented bonds) together. This latter expression allows us to rewrite the spectral determinant as an infinite product of contributions of periodic orbits on the graph. We also present a diagrammatic method that permits us to write the spectral determinant in terms of a finite number of periodic orbit contributions. These results are generalized to the case of graphs in a magnetic field. Several examples illustrating this formalism are presented and its application to the thermodynamic and transport properties of weakly disordered and coherent mesoscopic networks is discussed.

Eric Akkermans 1, 2, 3 Alain Comtet 3 Jean Desbois 3 Gilles Montambaux 2 Christophe Texier 3, 4
1 Department of Physics [Haifa]
2 LPS – Laboratoire de Physique des Solides
3 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
4 Département de Physique Théorique

Abstract : We present an x-ray study of doped charge density waves systems. When a 2k_f-charge density wave is strongly pinned to impurities, an interference effect gives rise to an asymmetry between the intensities of the +2k_f and -2k_f satellite reflections. Moreover, profile asymmetry of the satellite reflections indicates the existence of Friedel oscillations (FOs) around the defects. We have studied these effects in V- and W-doped blue bronzes. A syncrotron radiation study of the V-doped blue bronze clearly reveals the presence of FO around the V atoms.

S. Rouziere 1 S. Ravy 2 S. Brazovskii 3 J. -P. Pouget 2
1 School of Chemistry, Physics and Environmental Science
2 LPS – Laboratoire de Physique des Solides
3 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques