Abstract
We study a family of closed quantum graphs described by one singular vertex of order n = 4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed path in the parameter space that physically corresponds to the smooth interpolation of different topologies - a ring, separate two lines, separate two rings, two rings with a contact point. We find that the spectrum of a quantum particle on this family of graphs shows quantum holonomy.
Highlights
The idea of quantum mechanics on graphs has been introduced in the last century
We examine the influence of the topology of quantum graphs on spectral properties, taking inspiration from the works [1] and [7]
We may regard that the topology change mimics a macroscopic or violent variation of systems, e.g., the rupture and connection of quantum wires
Summary
Taksu Cheon∗, Atushi Tanaka†, Ondrej Turek∗ ∗Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502, Japan. We study a family of closed quantum graphs described by one singular vertex of order n = 4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that physically corresponds to the smooth interpolation of different topologies - a ring, separate two lines, separate two rings, two rings with a contact point. We find that the spectrum of a quantum particle on this family of graphs shows the quantum anholonomy. PACS numbers: 03.65.-w: quantum graph, boundary condition, eigenvalue anholonomy arXiv:1302.3803v1 [math-ph] 15 Feb 2013
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