Corpus ID: 236469256

A combinatorial approach to counting primitive periodic and primitive pseudo orbits on circulant graphs

@inproceedings{Engelthaler2021ACA,
  title={A combinatorial approach to counting primitive periodic and primitive pseudo orbits on circulant graphs},
  author={Lauren Engelthaler and Isaac Hellerman and Tori Hudgins},
  year={2021}
}
We count the numbers of primitive periodic orbits on families of 4-regular directed circulant graphs with n vertices. The relevant counting techniques are then extended to count the numbers of primitive pseudo orbits (sets of distinct primitive periodic orbits) up to length n that lack self-intersections, or that never intersect at more than a single vertex at a time repeated exactly twice for each self-intersection (2-encounters of length zero), for two particular families of graphs. We then… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 30 REFERENCES
Complete Dynamical Evaluation of the Characteristic Polynomial of Binary Quantum Graphs
We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example of a chaotic quantum system where a spectralExpand
Periodic orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit
We evaluate the variance of coefficients of the characteristic polynomial of the quantum evolution operator for chaotic 4-regular quantum graphs (networks) via periodic orbits without taking theExpand
Lyndon word decompositions and pseudo orbits on q-nary graphs
A foundational result in the theory of Lyndon words (words that are strictly earlier in lexicographic order than their cyclic permutations) is the Chen-Fox-Lyndon theorem which states that every wordExpand
Spectral properties of quantum circulant graphs
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs withExpand
Diameters of random circulant graphs
TLDR
It is shown that the diameter of a random circulant 2k-regular graph with n vertices scales as n1/k, and a limit theorem for the distribution of their diameters is established. Expand
Finite pseudo orbit expansions for spectral quantities of quantum graphs
We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and whereExpand
Introduction to Quantum Graphs
A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics,Expand
An efficient approach for counting the number of spanning trees in circulant and related graphs
TLDR
This paper obtains an efficient approach (another kind of recursive formula) for counting the number of spanning trees in a directed or undirected circulant graph which has fixed or non-fixed jumps and the technique is also applied to the graphs G=K"n+/-C, where K"n is the complete graph on n vertices and C is a circular graph. Expand
Periodic-orbit theory of universal level correlations in quantum chaos
Using Gutzwiller's semiclassical periodic-orbit theory, we demonstrate universal behavior of the two-point correlator of the density of levels for quantum systems whose classical limit is fullyExpand
Quantum Chaos?
A referee of one of my grant proposals complained recently that the text did not explain “what is quantum chaos”; the desire for an answer to that question was the sole reason he had agreed to reviewExpand
...
1
2
3
...