Massive Jackiw-Rebbi Model

In this paper we analyze a generalized Jackiw-Rebbi (J-R) model in which a massive fermion is coupled to the kink of the $\lambda\phi^4$ model as a prescribed background field. We solve this massive J-R model exactly and analytically and obtain the whole spectrum of the fermion, including the bound and continuum states. The mass term of the fermion makes the potential of the decoupled second order Schrodinger-like equations asymmetric in a way that their asymptotic values at two spatial infinities are different. Therefore, we encounter the unusual problem in which two kinds of continuum states are possible for the fermion: reflecting and scattering states. We then show the energies of all the states as a function of the parameters of the kink, i.e. its value at spatial infinity ($\theta_0$) and its slope at $x=0$ ($\mu$). The graph of the energies as a function of $\theta_0$, where the bound state energies and the two kinds of continuum states are depicted, shows peculiar features including an energy gap in the form of a triangle where no bound states exist. That is the zero mode exists only for $\theta_0$ larger than a critical value $(\theta_0^{\textrm{c}})$. This is in sharp contrast to the usual (massless) J-R model where the zero mode and hence the fermion number $\pm1/2$ for the ground state is ever present. This also makes the origin of the zero mode very clear: It is formed from the union of the two threshold bound states at $\theta_0^{\textrm{c}}$, which is zero in the massless J-R model.Comment: 10 pages, 3 figure

Using airborne lidar to discern age classes of cottonwood trees in a riparian area

Airborne lidar (light detecting and ranging) is a useful tool for probing the structure of forest canopies. Such information is not readily available from other remote sensing methods and is essential for modern forest inventories. In this study, small-footprint lidar data were used to estimate biophysical properties of young, mature, and old cottonwood trees in the San Pedro River basin near Benson, Arizona. The lidar data were acquired in June 2004, using Optech's 1233 ALTM during flyovers conducted at an altitude of 600 m. Canopy height, crown diameter, stem dbh, canopy cover, and mean intensity of return laser pulses from the canopy surface were estimated for the cottonwood trees from the data. Linear regression models were used to develop equations relating lidar-derived tree characteristics with corresponding field acquired data for each age class of cottonwoods. The lidar estimates show a good degree of correlation with ground-based measurements. This study also shows that other parameters of young, mature, and old cottonwood trees such as height and canopy cover, when derived from lidar, are significantly different (P < 0.05). Additionally, mean crown diameters of mature and young trees are not statistically different at the study site (P = 0.31). The results illustrate the potential of airborne lidar data to differentiate different age classes of cottonwood trees for riparian areas quickly and quantitatively. Copyright © 2006 by the Society of American Foresters

Composite fermions close to the one-half filling of the lowest Landau level revisited

By strictly adhering to the microscopic theory of composite fermions for the Landau-level filling fractions nu_e = p/(2 p + 1), we reproduce, with remarkable accuracy, the surface-acoustic-wave (SAW)-based experimental results by Willett and co-workers concerning two-dimensional electron systems with nu_e close to 1/2. Our results imply that the electron band mass m_b, as distinct from the composite fermion mass m_*, must undergo a substantial increase under the conditions corresponding to nu_e approximately equal to 1/2. In view of the relatively low aerial electronic densities n_e to which the underlying SAW experiments correspond, our finding conforms with the experimental results by Shashkin et al. [Phys. Rev. B 66, 073303 (2002)], concerning two-dimensional electrons in silicon, that signal sharp increase in m_b for n_e decreasing below approximately 2 x 10^{11} cm^{-2}. We further establish that a finite mean-free path l_0 is essential for the observed linearity of the longitudinal conductivity sigma_{xx}(q) as deduced from the SAW velocity shifts.Comment: 5 pages, 2 postscript figure

Charge response function and a novel plasmon mode in graphene

Polarizability of non-interacting 2D Dirac electrons has a 1/\sqrt{qv-\omega} singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N -> infinity, where N is the ``color'' degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the n-th order ladder term to the same order RPA contribution is (\ln|qv-\omega|)^n/N^n$. We perform analytical summation of the infinite series of ladder diagrams which describe excitonic effect. Beyond the threshold, qv>\omega, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.Comment: 4 pages, 3 figures,typos correcte

The Islamic Legal System in Malaysia

This article describes the historical evolution and the current structure of the Islamic legal system in Malaysia. The structure of the modern Malaysian state has its roots in the region’s colonial history. By the end of the nineteenth century the territory that comprises contemporary Malaysia had been subjected to British colonial authority. The British did not, however, rule the region as a single colonial unit. In the directly ruled colonies most matters were governed by English common law, and while Islamic doctrine governed family law, it was applied by colonial courts that were staffed by British or British-trained judges. In the colonies subject to indirect rule an English resident exercised authority over matters of British interest while Malay sultans retained their hereditary titles, and local courts exercised the sultan’s authority in matters of Malay adat (custom) and Islam. When the state of Malaysia was created in 1957, the constitution established a federal structure that reflected the pluralistic colonial system. Malaysia is currently comprised of 13 states and three federal territories. Under the constitution, most areas of life are governed by a uniform body of federal law applied by a system of national courts. However, the constitution grants the states the power to apply a version of Islamic law on certain topics enumerated in the constitution, and to create Shari‛a courts to adjudicate disputes involving Muslims relating to matters of Islamic law. The subjects included within the states’ legislative power include, in addition to personal law and matters related to religious practice, offenses deemed to be against the precepts of Islam. All of the states have exercised the powers granted by the constitution to legislate on matters related to Islam, and every state has established Shari‛a courts to adjudicate disputes based on Islamic legislation. A constitutional amendment approved in 1988 eliminated the power of civil courts to hear appeals from decisions of the Syariah courts. At the same time that they are achieving greater autonomy, the Shari‛a courts are also seeking to “upgrade” in ways that emulate the civil courts

Riparian vegetation classification from airborne laser scanning data with an emphasis on cottonwood trees

The high point density of airborne laser mapping systems enables achieving a detailed description of geographic objects and the terrain. Growing experience indicates, however, that extracting useful information directly from the data can be difficult. In this study, small-footprint lidar data were used to differentiate between young, mature, and old cottonwood trees in the San Pedro River Basin near Benson, Arizona, USA. The lidar data were acquired in June 2003, using the Optech Incorporated ALTM 1233 (Optech Incorporated, Toronto, Ont.), during flyovers conducted at an altitude of 750 m. The lidar data were preprocessed to create a two-band image of the study site: a high-accuracy canopy altitude model band, and a near-infrared intensity band. These lidar-derived images provided the basis for supervised classification of cottonwood age categories, using a maximum likelihood algorithm. The results of classification illustrate the potential of airborne lidar data to differentiate age classes of cottonwood trees for riparian areas quickly and accurately. © 2006, Taylor & Francis Group, LLC. All rights reserved