Boson and two-dimensional cluster model composed of quenching disorder eigenvalues and eigenvectors in the glass transition

Glass state problem stems from the failure of mean-field hard-sphere molecule (HSM) as quasi-independent particle. Starting from the absolute temperature, the collision satisfying de Gennes n = 0 second-order delta vector condition is a clustered collision, coupled electron-pair interface excited state emerges at the overlapping interface-plane of 0.27%, making the two HSMs suddenly become an Ising spin state, called the quenching disorder eigenvalue (QDE). Discover the space-time geometry of disordered systems: each HSM can make cluster-contact with the 16 sequentially spatial angle-line states of an adjacent HSM at constant intervals of 5.9987...° along 16 spatial angle-lines, constituting of the 16 eigenvectors of the disordered system. The vector formed by the 16 QDEs appearing sequentially is a cluster-interaction boson depicting the hopping mode of two positively charged particles in two overlapping HSMs, jumping 15 consecutive steps at tiny 0.01-step intervals. The 4 bosons that appear sequentially form the smallest 2D five-HSM cluster of dynamic equilateral hexahedron. This boson has five fundamental properties, including 20-fold symmetry and pinning, linked with various schools of thought such as cage, trap, mode-coupling, random first order transition, boson peak, Johari-Goldstein fast-slow-relaxations, heterogeneity and potential energy landscapes etc., and gives molecular cooperative motion modes as solitary waves .