4,822 research outputs found
High-ordered spectral characterization of unicyclic graphs
In this paper we will apply the tensor and its traces to investigate the
spectral characterization of unicyclic graphs. Let be a graph and be
the -th power (hypergraph) of . The spectrum of is referring to its
adjacency matrix, and the spectrum of is referring to its adjacency
tensor. The graph is called determined by high-ordered spectra (DHS for
short) if, whenever is a graph such that is cospectral with for
all , then is isomorphic to . In this paper we first give formulas
for the traces of the power of unicyclic graphs, and then provide some
high-ordered cospectral invariants of unicyclic graphs. We prove that a class
of unicyclic graphs with cospectral mates is DHS, and give two examples of
infinitely many pairs of cospectral unicyclic graphs but with different
high-ordered spectra
Steady Bell state generation via magnon-photon coupling
We show that parity-time () symmetry can be spontaneously
broken in the recently reported energy level attraction of magnons and cavity
photons. In the -broken phase, magnon and photon form a
high-fidelity Bell state with maximum entanglement. This entanglement is steady
and robust against the perturbation of environment, in contrast to the general
wisdom that expects instability of the hybridized state when the symmetry is
broken. This anomaly is further understood by the compete of non-Hermitian
evolution and particle number conservation of the hybridized system. As a
comparison, neither -symmetry broken nor steady magnon-photon
entanglement is observed inside the normal level repulsion case. Our results
may open a novel window to utilize magnon-photon entanglement as a resource for
quantum technologies.Comment: 5 pages, 4 figure
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