Characterization of Break in Quantum Grid

M. Archibalda, S. Curriea, M. Nowaczykb aThe John Knopfmacher Center for Applicable Analysis and Number Theory, University of the Witwatersrand, Johannesburg, South Africa bAGH University of Science and Technology, Kraków, Poland

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A finite rectangular grid can be used to model many applications in physics and related areas, where finite periodic orbits on this grid can be altered if a break occurs on the grid. For a break at a node, it is useful to be able to identify the position and type of the break without having to examine the whole grid. By calculating how much the sum of the amplitude numbers over all periodic orbits changes in the event of a break for a fixed length, we aim to pinpoint the position and type of the break merely by looking at the (unique) sum of the amplitude numbers for small grids.

DOI:10.12693/APhysPolA.138.383 topics: quantum graph, periodic orbit, break in a nanowire grid\\vs*{-9pt}