Charge Dynamics from Copper Oxide Materials

The charge dynamics of the copper oxide materials in the underdoped and optimal doped regimes is studied within the framework of the fermion-spin theory. The conductivity spectrum shows the non-Drude behavior at low energies and unusual midinfrared peak, and the resistivity exhibits a linear behavior in the temperature, which are consistent with experiments and numerical simulations.Comment: 10 pages, the figures are not included and can be air-mailed by reques

Optical and transport properties in doped two-leg ladder antiferromagnet

Within the t-J model, the optical and transport properties of the doped two-leg ladder antiferromagnet are studied based on the fermion-spin theory. It is shown that the optical and transport properties of the doped two-leg ladder antiferromagnet are mainly governed by the holon scattering. The low energy peak in the optical conductivity is located at a finite energy, while the resistivity exhibits a crossover from the high temperature metallic-like behavior to the low temperature insulating-like behavior, which are consistent with the experiments.Comment: 13 pages, 5 figures, accepted for publication in Phys. Rev. B65 (2002) (April 15 issue

Coexistence of the Electron Cooper Pair and Antiferromagnetic Short-Range Correlation in Copper Oxide Materials

Within the fermion-spin theory, the physical properties of the electron pairing state in the copper oxide materials are discussed. According to the common form of the electron Cooper pair, it is shown that there is a coexistence of the electron Cooper pair and magnetic short-range correlation, and hence the antiferromagnetic short-range correlation can persist into the superconducting state. Moreover, the mean-field results indicate that the electron pairing state originating from the pure magnetic interaction in the two-dimensional t-J model is the local state, and then does not reveal the true superconducting ground-state.Comment: 6 pages, Revtex, Four figures are adde

A novel and simple spectral method for nonlocal PDEs with the fractional Laplacian

We propose a novel and simple spectral method based on the semi-discrete Fourier transforms to discretize the fractional Laplacian $(-\Delta)^\frac{\alpha}{2}$. Numerical analysis and experiments are provided to study its performance. Our method has the same symbol $|\xi|^\alpha$ as the fractional Laplacian $(-\Delta)^\frac{\alpha}{2}$ at the discrete level, and thus it can be viewed as the exact discrete analogue of the fractional Laplacian. This {\it unique feature} distinguishes our method from other existing methods for the fractional Laplacian. Note that our method is different from the Fourier pseudospectral methods in the literature, which are usually limited to periodic boundary conditions (see Remark \ref{remark0}). Numerical analysis shows that our method can achieve a spectral accuracy. The stability and convergence of our method in solving the fractional Poisson equations were analyzed. Our scheme yields a multilevel Toeplitz stiffness matrix, and thus fast algorithms can be developed for efficient matrix-vector products. The computational complexity is ${\mathcal O}(2N\log(2N))$, and the memory storage is ${\mathcal O}(N)$ with $N$ the total number of points. Extensive numerical experiments verify our analytical results and demonstrate the effectiveness of our method in solving various problems

Disorder effects on the quantum coherence of a many-boson system

The effects of disorders on the quantum coherence for many-bosons are studied in a double well model. For the ground state, the disorder enhances the quantum coherence. In the deep Mott regime, dynamical evolution reveals periodical collapses and revivals of the quantum coherence which is robust against the disorder. The average over variations in both the on-site energy and the interaction reveals a beat phenomenon of the coherence-decoherence oscillation in the temporal evolution.Comment: 4 figure