Graph spectral characterisation of the XY model on complex networks
by
Sara de Nigris(Inria, ENS Lyon)
→
Europe/Rome
Aula Careri (Dipartimento di Fisica - Ed. G.Marconi)
Aula Careri
Dipartimento di Fisica - Ed. G.Marconi
Description
There is recent evidence that the XY spin model on complex networks can
display three different macroscopic states in response to the topology of the
network underpinning the interactions of the spins. In this seminar, I shall
introduce a novel way to characterise the macroscopic states of the XY spin
model based on the spectral decomposition of time series using topological
information about the underlying networks.
In this work [1], we use three different classes of networks to generate time
series of the spins for the three possible macroscopic states. We then apply
the temporal Graph Signal Transform technique to decompose the time series of
the spins on the eigenbasis of the Laplacian. From this decomposition, we
produce spatial power spectra, which summarise the activation of structural
modes by the non-linear dynamics, and thus coherent patterns of activity of
the spins. These signatures of the macroscopic states are independent of the
underlying networks and can thus be used as universal signatures for the
macroscopic states. This analysis opens new avenues to analyse and
characterise dynamics on complex networks using temporal Graph Signal
Analysis.