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5 papers · 2 filters
Spectral determinants and zeta functions of Schrödinger operators on metric graphs
J. M. Harrison, K. Kirsten, C. Texier
A derivation of the spectral determinant of the Schrödinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form clas…
Painleve solution of an integral equation
Y. Y. Atas, E. Bogomolny
It is demonstrated that a certain integral equation can be solved using the Painleve equation of third kind. Inversely, a special solution of this Painleve equation can be expresse…
Supersymmetric quantum mechanics with Levy disorder in one dimension
Alain Comtet, Christophe Texier, Yves Tourigny
We consider the Schroedinger equation with a supersymmetric random potential, where the superpotential is a Levy noise. We focus on the problem of computing the so-called complex L…
Algebraic and arithmetic area for planar Brownian paths
Jean Desbois, Stephane Ouvry
The leading and next to leading terms of the average arithmetic area enclosed by independent closed Brownian planar paths, with a given length and starti…
Hearing shapes of drums - mathematical and physical aspects of isospectrality
O. Giraud, K. Thas
In a celebrated paper '"Can one hear the shape of a drum?"' M. Kac [Amer. Math. Monthly 73, 1 (1966)] asked his famous question about the existence of nonisometric billiards having…