Exactly Solvable Mobility Edges for Phonons in One-Dimensional Quasiperiodic Chains

Area of Science:

• Condensed matter physics
• Disordered systems
• Phononics

Background:

• Mobility edges define transitions between extended and localized states in physical systems.
• Exact mobility edges are rare, and phonon localization remains under-explored.
• Understanding localization is key in condensed matter physics.

Purpose of the Study:

• To analytically reveal mobility edges in one-dimensional quasiperiodic-modulated spring-mass chains.
• To investigate Anderson localization transitions in phonon systems.
• To provide a foundation for experimental studies on phonon localization.

Main Methods:

• Exact analytical solutions for mobility edges.
• Numerical validation using eigenfrequency spectra.
• Analysis of inverse/normalized participation ratios.
• Examination of lattice wave dynamics.

Main Results:

• Analytical mobility edges were successfully identified in the studied system.
• The findings were rigorously validated through multiple numerical methods.
• The research confirms the occurrence of Anderson localization in phonon systems.

Conclusions:

• The study analytically demonstrates mobility edges in 1D quasiperiodic chains.
• This work establishes Anderson localization in phonon systems.
• The findings pave the way for future experimental investigations into phonon localization.