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Description
A lattice of electrical circuits with some specific coupling and three oscillators per unit cell, called the diamond lattice, has the property that the three phonon bands are optical and completely flat.
The addition of a nonlinear on-site hard potential brings about the existence of breathers, that is localized periodic oscillations. The largest vibration can be located in any of the oscillators inside the unit cell, and their frequencies can be in three of the four different phonon forbidden bands. The forbidden band below the lowest flat band has no breathers due to the hardness of the on-site potential.
There are, therefore, nine different types of breathers, with different properties of stability and energy.
We consider the increase of energy in the different oscillators in a thermalized system, and let the system evolve until thermalization is achieved, measuring the thermalization time. We use a function, called the localization function, which has the property that its value at thermal equilibrium is N/2, where N being the number of oscillators in the system.
The different routes to thermalization of the different breathers are described.
Acknowledgements:
JFRA acknowledges financial help for Spanish national project MICIU PID2022-138321NB-C22 and a travel grant by the Universidad de Sevilla, VII-PPITUS-2026.
SF acknowledges funding by IBS Project No. IBS-R024-D1.