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 the 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 a lattice-matched and an unmatched system and study the two systems through first-principle calculation, theoretical analysis, and experiment perspectives. A discontinuity in the 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 these phenomena.