Phase transition of random system and matrix model

点击翻译按钮获取中文摘要

For the random matrix model, various universality and their crossover have been studied in the relation to the phase transition of the random system. The random matrix with external source has been studied for the n-point covelation function, the form factor and the level spacing distribution, and the exact integral replesentation for them are obtained. In the large N limit, the universality of the covelation function has been discussed. The esternal source makes the basic approach for the crossover form the deterministic Hamiltonion to random Hamiltonian. As application, the complex random matrix and the superconductor vortex excitation have been unsidued. The crossover form the clear ease to the dirty case for the vortex excitation has been studied. Related to the cluiral in variouce, two states of the quanfized Hall effect(spin state) is also studied for the deusify of state and for the conductivity.