Analytical and numerical treatment of the Mott-Hubbard insulator in infinite dimensions

We calculate the density of states in the half-filled Hubbard model on a Bethe lattice with infinite connectivity. Based on our analytical results to second order in t/U, we propose a new Fixed-Energy Exact Diagonalization scheme for the numerical study of the Dynamical Mean-Field Theory. Corroborated by results from the Random Dispersion Approximation, we find that the gap opens at . Moreover, the density of states near the gap increases algebraically as a function of frequency with an exponent in the insulating phase. We critically examine other analytical and numerical approaches and specify their merits and limitations when applied to the Mott-Hubbard insulator.Received: 14 July 2003, Published online: 2 October 2003PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27.+a Strongly correlated electron systems; heavy fermions - 71.30.+h Metal-insulator transitions and other electronic transitions     

Automated phase retrieval of a single-material object using a single out-of-focus image

Phase retrieval is widely used in phase contrast microscopy. Here we present an autofocus algorithm that allows the phase of the exit wave function, from a single-material object, to be reconstructed at medium resolution from a single phase contrast image without any a priori knowledge of the imaging system or object. The algorithm is demonstrated on coherent out-of-focus electron micrographs of 30 nm latex sphere calibration standards, giving <10% RMS error over a large defocus range.