EXAMPLES OF QUANTUM HOLONOMY WITH TOPOLOGY CHANGES

Taksu Cheon, Atushi Tanaka, Ondřej Turek

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.

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague