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Spectral determinant of Schrödinger operators on graphs

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, , Citation Jean Desbois 2000 J. Phys. A: Math. Gen. 33 L63 DOI 10.1088/0305-4470/33/7/103

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1 Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bât. 100, F-91405 Orsay Cedex, France

Dates

  1. Received 9 November 1999

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0305-4470/33/7/L63

Abstract

We study the spectral properties of the operator (- +V (x )) on a graph. ( is the Laplacian and V (x ) is some potential defined on the graph). In particular, we derive an expression for the spectral determinant that generalizes one previously obtained for the Laplacian operator.

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