Quantum anholonomy with topology change

TL;DR

This paper investigates quantum anholonomy phenomena in a family of quantum graphs with topology changes, revealing how spectral properties evolve during smooth topological interpolations.

Contribution

It introduces a model of quantum graphs with parameter-dependent topology changes and demonstrates the occurrence of quantum anholonomy in this context.

Findings

Spectral evolution exhibits quantum anholonomy during topology change.

Constructed a sequence of parameter paths interpolating different graph topologies.

Showed that topology change affects quantum spectral properties in a measurable way.

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 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.