Harmonic vibrational excitations in graded elastic networks: transition from phonons to gradons

Abstract

We have identified a new type of transition from extended to localized vibrational states in one-dimensional graded elastic chains of coupled harmonic oscillators, in which the vibrating masses or nearest-coupling force constants vary linearly along the chain. We found that the delocalization transition occurs at the maximum frequency of the corresponding homogeneous chain, which is in a continuous single band. Although each state in the localized phase, called gradon, can be regarded as an impurity localized mode, the localization profile is clearly distinct from usual impurity modes or the Anderson localized modes. We also argue how gradons may affect the macroscopic properties of graded systems. Our results can provide insights into many analogous systems with graded characters.

LaTeX format, 7 eps figures, submitted for publications

References in corpus (6)

• Vibrations and diverging length scales near the unjamming transition
• First-principles approach to dielectric response of graded spherical particles
• Electrorotation in graded colloidal suspensions
• Excess Modes in the Vibrational Spectrum of Disordered Systems and the Boson Peak
• Continuum Theory for Piezoelectricity in Nanotubes and Nanowires
• Disorder-Induced Vibrational Localization

Cited by in corpus (6)

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• Gradient-index granular crystals: From boomerang motion to asymmetric transmission of waves
• Temperature gradient and Fourier's law in gradient-mass harmonic systems