A remark on zeta functions of finite graphs via quantum walks
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Publication:6250502
DOI10.1186/S40736-014-0009-6arXiv1404.1553WikidataQ59396842 ScholiaQ59396842MaRDI QIDQ6250502
Yusuke Higuchi, Norio Konno, Iwao Sato, Etsuo Segawa
Publication date: 6 April 2014
Abstract: From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to say, the square of the evolution matrix of a quantum walk. Then we give to such a function two types of determinant expressions and derive from it some geometric properties of a finite graph. As an application, we illustrate the distribution of poles of this function comparing with those of the usual Ihara zeta function.
Sums of independent random variables; random walks (60G50) Quantum stochastic calculus (81S25) Relations with random matrices (11M50) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)
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