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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14640 |
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| _version_ | 1866918501560614912 |
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| author | Gerrard, Allan John Asaka, Ryo Sakai, Kazumitsu |
| author_facet | Gerrard, Allan John Asaka, Ryo Sakai, Kazumitsu |
| contents | We study scattering for continuous-time quantum walks on finite graphs with two attached leads. We derive explicit formulae for the two-terminal scattering matrix in terms of characteristic polynomials of the finite graph and its vertex-deleted subgraphs. For real-weighted two-terminal graphs, we then introduce three real quantities, $μ_1$, $μ_2$, and $ν$, which are each additive under parallel composition of graphs. In these variables, perfect transmission at fixed momentum is characterized by the condition $μ_1=μ_2$ together with a hyperbola in the corresponding $(μ,ν)$-plane, whose points determine the transmission phase. This turns the search for graphs with prescribed transmission properties into a geometric vector-sum problem for smaller building blocks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perfect transmission and parallel composition for quantum walks on graphs with two leads Gerrard, Allan John Asaka, Ryo Sakai, Kazumitsu Quantum Physics Mathematical Physics We study scattering for continuous-time quantum walks on finite graphs with two attached leads. We derive explicit formulae for the two-terminal scattering matrix in terms of characteristic polynomials of the finite graph and its vertex-deleted subgraphs. For real-weighted two-terminal graphs, we then introduce three real quantities, $μ_1$, $μ_2$, and $ν$, which are each additive under parallel composition of graphs. In these variables, perfect transmission at fixed momentum is characterized by the condition $μ_1=μ_2$ together with a hyperbola in the corresponding $(μ,ν)$-plane, whose points determine the transmission phase. This turns the search for graphs with prescribed transmission properties into a geometric vector-sum problem for smaller building blocks. |
| title | Perfect transmission and parallel composition for quantum walks on graphs with two leads |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2605.14640 |