Resonance frequency band structure in heterojunction of one-dimension string-ball chain system

Using the concept of heterostructures in Semiconductor Physics and the similarity between Schrödinger Equation and the vibration equation of the one-dimension string-ball chain system, we create a heterojunction in our string-ball chain system by assembling a string-ball chain with two kinds of mass in lattice-matched and the unmatched system and study the two systems in first principle calculation, theoretical analysis, and experiment perspectives. A discontinuity in frequency dependence is observed in the matched system, while a phase transition is discovered in the unmatched system. A proper theoretical analysis based on the wave function is also given to explain those phenomena.