Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors
ArXiv cond-mat/9606044 (1996)
Abstract:
We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order.The Supersymmetric t-J Model with a Boundary
(1996)
Essler, Korepin, and Schoutens reply.
Phys Rev Lett 76:22 (1996) 4290
Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian
ArXiv cond-mat/9605073 (1996)
Abstract:
We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness in the mass, the scalar potential, and the vector potential. Separately, we show that the network model can also be associated with a nearest neighbour, tight-binding Hamiltonian.Coupling of Surface Acoustic Waves to a Two Dimensional Electron Gas
(1996)