A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with matrix size. We use this method and an imaginary-time version of it to compute the energy and the specific heat of three different, exactly solvable, spin-1/2 models and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.

We study chiral symmetry breaking in three-dimensional QED with Nf flavors of four-component fern&ns. A closed system of Schwinger-Dyson equations for fermion and photon propagators and the full fermion-photon vertex is proposed, which is consistent with the Ward-Takahashi identity. A simplified version of that set of equations is reduced (in the nonlocal gauge) to the equation for a dynamical fermion mass function, where the one-loop vacuum polarization with dynamically massive fermions has been taken into account. The linearized equation for the fermion mass function is analyzed in real space. The analytical solution is compared with the results of numerical calculations of the nonlinear integral equation in momentum space.

A nonlinear Schwinger-Dyson ͑SD͒ equation for the gauge boson propagator of massless QED in one time and two spatial dimensions is studied. It is shown that the nonperturbative solution leads to a nontrivial renormalization-group infrared fixed point quantitatively close to the one found in the leading order of the 1/N expansion, with N the number of fermion flavors. In the gauged Nambu-Jona-Lasinio ͑GNJL͒ model an equation for the Yukawa vertex is solved in an approximation given by the one-photon exchange and an analytic expression is derived for the propagator of the scalar fermion-antifermion composites. Subsequently, the mass and width of the scalar composites near the phase transition line are calculated as functions of the four-fermion coupling g and flavor number N. The possible relevance of these results for describing particlehole excitations, in particular antiferromagnetic correlations, observed in the underdoped cuprates, is briefly discussed.

We describe a quantum computer emulator for a generic, general purpose quantum computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulator through various implementations of the Deutsch-Jozsa and Grover's database search algorithm.

We examine the effect of the dynamics of the internal magnetic field on the staircase magnetization curves observed in large-spin molecular magnets. We show that the size of the magnetization steps depends sensitively on the intermolecular interactions, even if these are very small compared to the intra-molecular couplings.