Year: 2026
Type: article
Abstract: We study scattering for continuous-time quantum walks on finite graphs with attached leads. The focus of our study is perfect transmission, which is essential for a given graph to be considered as a scattering gadget. To this end, we introduce three real parameters: the terminal-responses μ 1 and μ 2 , and a terminal-to-terminal coupling ν , defined in terms of characteristic polynomials of the graph and its vertex deleted subgraphs. Up to a momentum-dependent transformation, these quantities are the independent entries of an admittance matrix, and each is additive under parallel composition of graphs. In these variables the perfect transmission at a fixed momentum is characterized by a hyperbola in ( μ 1 , μ 2 , ν ) -space, the points of which determine the transmission phase. This turns the search for graphs with prescribed transmission properties into a geometric vector-sum problem for smaller building blocks.
Authors: Allan John Gerrard, Ryo Asaka, Kazumitsu Sakai
Institutions: Japan Women's University, Tokyo University of Science
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W7161316729
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