Dual Fermion Method for Disordered Electronic Systems

While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual fermion approach to disordered non-interacting systems using the replica method. Results for single- and two- particle quantities show good agreement with cluster extensions of the CPA; moreover, weak localization is captured. As a natural extension of the CPA, our method presents an alternative to the existing cluster theories. It can be used in various applications, including the study of disordered interacting systems, or for the description of non-local effects in electronic structure calculations.Comment: 5 pages, 4 figure

Mean-field embedding of the dual fermion approach for correlated electron systems

To reduce the rapidly growing computational cost of the dual fermion lattice calculation with increasing system size, we introduce two embedding schemes. One is the real fermion embedding, and the other is the dual fermion embedding. Our numerical tests show that the real fermion and dual fermion embedding approaches converge to essentially the same result. The application on the Anderson disorder and Hubbard models shows that these embedding algorithms converge more quickly with system size as compared to the conventional dual fermion method, for the calculation of both single-particle and two-particle quantities.Comment: 10 pages, 10 figure

Algebraic symmetries of generic (m+1)(m+1) dimensional periodic Costas arrays

In this work we present two generators for the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\mathbb{Z}_p)^m$ groups: one that is defined by multiplication on $m$ dimensions and the other by shear (addition) on $m$ dimensions. Through exhaustive search we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\mathbb{Z}_p)^m$ groups

Enhancing Transport Efficiency by Hybrid Routing Strategy

Traffic is essential for many dynamic processes on real networks, such as internet and urban traffic systems. The transport efficiency of the traffic system can be improved by taking full advantage of the resources in the system. In this paper, we propose a dual-strategy routing model for network traffic system, to realize the plenary utility of the whole network. The packets are delivered according to different "efficient routing strategies" [Yan, et al, Phys. Rev. E 73, 046108 (2006)]. We introduce the accumulate rate of packets, {\eta} to measure the performance of traffic system in the congested phase, and propose the so-called equivalent generation rate of packet to analyze the jamming processes. From analytical and numerical results, we find that, for suitable selection of strategies, the dual- strategy system performs better than the single-strategy system in a broad region of strategy mixing ratio. The analytical solution to the jamming processes is verified by estimating the number of jammed nodes, which coincides well with the result from simulation.Comment: 6 pages, 3 figure

Lifshitz Transition in the Two Dimensional Hubbard Model

Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two dimensional Hubbard model with next-nearest-neighbor hopping ($t'$), chemical potential and temperature as control parameters. At $t'\le0$, we identify a line of Lifshitz transition points associated with a change of the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects, and becomes more singular when $t'$ becomes more negative. The resulting temperature dependence on the bare d-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at $t'\le0$ extends our understanding of the quantum critical region in the phase diagram, and shines lights on future investigations of the nature of the quantum critical point in the two dimensional Hubbard model.Comment: 9 pages, 8 figures, accepted for publication in Physics Review

A Typical Medium Dynamical Cluster Approximation for the Study of Anderson Localization in Three Dimensions

We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in the low and large disorder regimes, and allows us to study the localization in different momenta cells, which renders the discovery that the Anderson localization transition occurs in a cell-selective fashion. As a function of cluster size, our method systematically recovers the re-entrance behavior of the mobility edge and obtains the correct critical disorder strength for Anderson localization in 3D.Comment: 5 Pages, 4 Figures and Supplementary Material include

Algebraic computation of some intersection D-modules

Let $X$ be a complex analytic manifold, $D\subset X$ a locally quasi-homogeneous free divisor, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $X-D$. In this paper we give an algebraic description in terms of $E$ of the regular holonomic D-module whose de Rham complex is the intersection complex associated with $L$. As an application, we perform some effective computations in the case of quasi-homogeneous plane curves.Comment: 18 page

Far-infrared photometric observations of the outer planets and satellites with Herschel-PACS

We present all Herschel PACS photometer observations of Mars, Saturn, Uranus, Neptune, Callisto, Ganymede, and Titan. All measurements were carefully inspected for quality problems, were reduced in a (semi-)standard way, and were calibrated. The derived flux densities are tied to the standard PACS photometer response calibration, which is based on repeated measurements of five fiducial stars. The overall absolute flux uncertainty is dominated by the estimated 5% model uncertainty of the stellar models in the PACS wavelength range between 60 and 210 micron. A comparison with the corresponding planet and satellite models shows excellent agreement for Uranus, Neptune, and Titan, well within the specified 5%. Callisto is brighter than our model predictions by about 4-8%, Ganymede by about 14-21%. We discuss possible reasons for the model offsets. The measurements of these very bright point-like sources, together with observations of stars and asteroids, show the high reliability of the PACS photometer observations and the linear behavior of the PACS bolometer source fluxes over more than four orders of magnitude (from mJy levels up to more than 1000 Jy). Our results show the great potential of using the observed solar system targets for cross-calibration purposes with other ground-based, airborne, and space-based instruments and projects. At the same time, the PACS results will lead to improved model solutions for future calibration applications.Comment: 25 pages, 11 figures, 11 table

Observation of Enhanced Beaming from Photonic Crystal Waveguides

We report on the experimental observation of the beaming effect in photonic crystals enhanced via surface modes. We experimentally map the spatial field distribution of energy emitted from a subwavelength photonic crystal waveguide into free-space, rendering with crisp clarity the diffractionless beaming of energy. Our experimental data agree well with our numerical studies of the beaming enhancement in photonic crystals with modulated surfaces. Without loss of generality, we study the beaming effect in a photonic crystal scaled to microwave frequencies and demonstrate the technological capacity to deliver long-range, wavelength-scaled beaming of energy.Comment: 4 pages, 6 figure

High-capacity wave energy conversion by multi-floats, multi-PTO, control and prediction: generalised state-space modelling with linear optimal control and arbitrary headings

Wave energy converters with capacity similar to, or greater than, wind turbines are desirable for the supply of electricity to the grid. It is shown that this may be provided by multiple floats in a hinged raft-type configuration with multimode forcing. The case analysed has 8 floats and 4 power take off (PTO) units. Analysis is based on linear diffraction-radiation modelling, validated in wave basin experiments with a smaller number of floats. Control is desirable to improve energy capture, mainly demonstrated for point absorbers, but this has not previously been applied to such a complex problem with many freedoms. The linear hydrodynamic model in a state-space form makes it possible to implement advanced control algorithms in real time. Linear non-causal optimal control (LNOC) is applied with wave force prediction from auto-regression. For the design case with zero heading, as the configuration heads naturally into the wave direction, energy capture is improved by between 21% and 83%. The energy capture is about 62% the maximum possible from idealised analyses. Off-design, non-zero headings are also analysed to indicate how energy capture can be reduced; this is again improved by control, by several times at 90 degrees heading