2020
DOI: 10.48550/arxiv.2010.12528
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

Towards Dynamic-Point Systems on Metric Graphs with Longest Stabilization Time

Abstract: In this work, dynamical systems of points on metric graphs (a discrete version of a quantum graph with localized wave packets) that have longest stabilization time are studied. It is shown that the set of dynamical systems over metric graphs that can be constructed from a given set of edges with fixed lengths always contains a system consisting of a bead graph with vertex degrees not greater than three that demonstrates longest stabilization time. Also, it is shown that dynamical systems of points on linear gr… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
4

Citation Types

0
4
0

Year Published

2022
2022
2024
2024

Publication Types

Select...
2

Relationship

0
2

Authors

Journals

citations
Cited by 2 publications
(4 citation statements)
references
References 7 publications
0
4
0
Order By: Relevance
“…Previously, the problem of representing the number of moving points in this dynamical system (the number of wave packets in the network) as a function of time was studied in detail, e.g. in [4,5,6,7,8,9,14]. In order to avoid possible confusion when looking through the mentioned papers, we explicitly warn the reader that there is no standard notation among the authors: in some papers the above process is interpreted as the 'endpoints of a random walk on a metric graph' (e.g.…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations
“…Previously, the problem of representing the number of moving points in this dynamical system (the number of wave packets in the network) as a function of time was studied in detail, e.g. in [4,5,6,7,8,9,14]. In order to avoid possible confusion when looking through the mentioned papers, we explicitly warn the reader that there is no standard notation among the authors: in some papers the above process is interpreted as the 'endpoints of a random walk on a metric graph' (e.g.…”
Section: Introductionmentioning
confidence: 99%
“…[6,14]), in others it is called either a 'DP-system' (e.g. [8,9]) or simply 'moving points' (e.g. [4,5]).…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Metric graph is a graph with lengths assigned to edges. Some results towards dynamical characteristics of systems of dynamic points flowing along undirected edges of a metric graphs in both directions were recently obtained [9][10][11][12][13]. In such systems, when a point reaches a vertex of the graph, new points start moving along all the edges incident to the vertex.…”
Section: Introductionmentioning
confidence: 99%