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Average scattering entropy of quantum graphs
Quantum Physics · Submitted 13 Jan 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim And the other, which contains graphs of the fishbone type, where the scattering entropy depends on the boundary conditions on the vertices of degree $1$, with the corresponding values decreasing and saturating very rapidly, as we increase the number of elementary structures in the graphs.
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The abstract, sentence by sentence
The scattering amplitude in simple quantum graphs is a well-known process which may be highly complex. In this work, motivated by the Shannon entropy, we propose a methodology that associates to a graph a scattering entropy, which we call the average scattering entropy. It is defined by taking into account the period of the scattering amplitude which we calculate using the Green's function procedure. We first describe the methodology on general grounds, and then exemplify our findings considering several distinct groups of graphs. We go on and investigate other possibilities, one that contains groups of graphs with the same number of vertices, with the same degree, and the same number of edges, with the same length, but with distinct topologies and with different entropies. And the other, which contains graphs of the fishbone type, where the scattering entropy depends on the boundary conditions on the vertices of degree $1$, with the corresponding values decreasing and saturating very rapidly, as we increase the number of elementary structures in the graphs.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The scattering amplitude in simple quantum graphs is a well-known process which may be highly complex. | background 1.00 | 0.04 | 0.02 | hedged possibility 0.56 |
| s1 | In this work, motivated by the Shannon entropy, we propose a methodology that associates to a graph a scattering entropy, which we call the average scattering entropy. | contribution 1.00 | 0.91 | 0.22 | asserted 0.99 |
| s2 | It is defined by taking into account the period of the scattering amplitude which we calculate using the Green's function procedure. | method 1.00 | 0.79 | 0.05 | asserted 1.00 |
| s3 | We first describe the methodology on general grounds, and then exemplify our findings considering several distinct groups of graphs. | method 0.62 | 0.83 | 0.05 | asserted 0.92 |
| s4 | We go on and investigate other possibilities, one that contains groups of graphs with the same number of vertices, with the same degree, and the same number of edges, with the same length, but with distinct topologies and with different entropies. | result 0.55 | 0.89 | 0.13 | asserted 0.71 |
| s5 | And the other, which contains graphs of the fishbone type, where the scattering entropy depends on the boundary conditions on the vertices of degree $1$, with the corresponding values decreasing and saturating very rapidly, as we increase the number of elementary structures in the graphs. | result 0.97 | 0.92 | 0.22 | asserted 1.00 |
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Original abstract
The scattering amplitude in simple quantum graphs is a well-known process which may be highly complex. In this work, motivated by the Shannon entropy, we propose a methodology that associates to a graph a scattering entropy, which we call the average scattering entropy. It is defined by taking into account the period of the scattering amplitude which we calculate using the Green's function procedure. We first describe the methodology on general grounds, and then exemplify our findings considering several distinct groups of graphs. We go on and investigate other possibilities, one that contains groups of graphs with the same number of vertices, with the same degree, and the same number of edges, with the same length, but with distinct topologies and with different entropies. And the other, which contains graphs of the fishbone type, where the scattering entropy depends on the boundary conditions on the vertices of degree $1$, with the corresponding values decreasing and saturating very rapidly, as we increase the number of elementary structures in the graphs.
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Another line of investigation concerns the very recent work of Melnikov [ref] , in which the author studied issues related to the problem of signal transmission in quantum mechanics in terms of topological theories, using the analogy between quantum amplitudes and knot diagrams.
Knots and signal transmission in topological quantum devices · Conclusion · 0.97
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