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5 papers · 2 filters
Analytic surgery of the zeta function
Klaus Kirsten, Paul Loya
In this paper we study the asymptotic behavior (in the sense of meromorphic functions) of the zeta function of a Laplace-type operator on a closed manifold when the underlying mani…
A new numerical approach to Anderson (de)localization
Constanze Liaw
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: Th…
Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph
J. M. Harrison, B. Winn
We study the spectral statistics of the Dirac operator on a rose-shaped graph---a graph with a single vertex and all bonds connected at both ends to the vertex. We formulate a secu…
Finite pseudo orbit expansions for spectral quantities of quantum graphs
Ram Band, Jonathan M. Harrison, Christopher H. Joyner
We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irre…
Vacuum energy of Schrödinger operators on metric graphs
J. M. Harrison, K. Kirsten
We present an integral formulation of the vacuum energy of Schrödinger operators on finite metric graphs. Local vertex matching conditions on the graph are classified according to…