The maximum number of highly localized Lyapunov vectors at low density

The localization spectra, which describes the magnitude of the localization of the Lyapunov vectors in many-particle systems, exhibit a characteristic bending behavior at low density. It is shown that this behavior is due to a restriction on the maximum number of the most localized Lyapunov vectors determined by the system configuration and mutual orthogonality. For a quasi-one-dimensional system, using a randomly distributed brick model, this leads to a predicted bending point at nc≈0.432N for an N particle system. Numerical evidence is presented that confirms this predicted bending point as a function of the number of particles N.