CHARACTERIZATION OF THE LOCAL DENSITY-OF-STATES FLUCTUATIONS NEAR THEINTEGER QUANTUM HALL TRANSITION IN A QUANTUM-DOT ARRAY

We present a calculation for the second moment of the local density of states in a model of a two-dimensional quantum dot array near the qua ntum Hall transition. The quantum dot array model is a realistic adapt ation of the lattice model for the quantum Hall transition in the two- dimensional electron gas in an external magnetic field proposed by Lud wig, Fisher, Shankar, and Grinstein. We make use of a Dirac fermion re presentation for the Green's functions in the presence of fluctuations for the quantum dot energy levels. A saddle-point approximation yield s nonperturbative results for the first and second moments of the loca l density of states, showing interesting fluctuation behavior near the quantum Hall transition. To our knowledge we discuss here one of the first analytic characterizations of chaotic behavior for a two-dimensi onal mesoscopic structure. The connection with possible experimental i nvestigations of the local density of states in the quantum dot array structures (by means of NMR Knight-shift or single-electron-tunneling techniques) and our work is also established.