Localization and compactness of Operators on Fock Spaces

For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $F^{p}_\varphi$, we characterize the compact operators in the algebra generated by weakly localized operators. As an application, for $0<p<\infty$ we prove that an operator $T$ in the algebra generated by bounded Toeplitz operators with $\textrm{BMO}$ symbols is compact on $F^p_\varphi$ if and only if its Berezin transform satisfies certain vanishing property at $\infty$. In the classical Fock space, we extend the Axler-Zheng condition on linear operators $T$, which ensures $T$ is compact on $F^p_{\alpha}$ for all possible $0<p<\infty$.Comment: 23 Page

Flux-lattice melting in LaO1−x_{1-x}Fx_{x}FeAs: first-principles prediction

We report the theoretical study of the flux-lattice melting in the novel iron-based superconductor $LaO_{0.9}F_{0.1}FeAs$ and $LaO_{0.925}F_{0.075}FeAs$. Using the Hypernetted-Chain closure and an efficient algorithm, we calculate the two-dimensional one-component plasma pair distribution functions, static structure factors and direct correlation functions at various temperatures. The Hansen-Verlet freezing criterion is shown to be valid for vortex-liquid freezing in type-II superconductors. Flux-lattice meting lines for $LaO_{0.9}F_{0.1}FeAs$ and $LaO_{0.925}F_{0.075}FeAs$ are predicted through the combination of the density functional theory and the mean-field substrate approach.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases

We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the 2D mean-field theory indicates that the quantum fluctuations are much more pronounced than those in 3D. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of 2D Bose gases and determine the ratio of the composite boson scattering length $a_{\rm B}$ to the fermion scattering length $a_{\rm 2D}$. We find $a_{\rm B}\simeq 0.56 a_{\rm 2D}$, in good agreement with the exact four-body calculation. We compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements.Comment: Published versio

Solid waste mixtures combustion in a circulating fluidized Bed: emission properties of NOx, Dioxin, and Heavy Metals

To efficiently and environment friendly combust the domestic garbage, sludge, and swill waste fuels, five different fuels are prepared by mixing the waste fuels together with coal, and grass biomass at different mixing ratios, and finally those fuels were combusted in a circulating fluidized bed (CFB) reactor. The emission performances of NOx, dioxin, and heavy metal during the combustion tests are studied. The results showed that a stable furnace temperature can be reached at approximately 850 °C when combusting all studied mixed fuels, benefiting the thermal processes of sludge and domestic garbage and thus realizing the purpose of waste-to-fuel. In addition, the dioxin emissions are much lower than the emission standards, and NOx emissions could be reduced significantly by adjusting the ratio of waste fuels. However, the emissions of mercury, lead, and the combinations of chromium, tin, antimony, cupper and manganese components all exceeded the pollution control standard for hazardous wastes incineration, a further technology is required for heavy metal reductions to achieve the emission standards

Phase transition in site-diluted Josephson junction arrays: A numerical study

We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson-junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that, with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied, evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings, but also shed some light on the relevant phase transitions.Comment: 7 pages, 8 figures, Phys. Rev. B (in press