Application of a Two-Parameter Quantum Algebra to Rotational Spectroscopy of Nuclei

A two-parameter quantum algebra $U_{qp}({\rm u}_2)$ is briefly investigated in this paper. The basic ingredients of a model based on the $U_{qp}({\rm u}_2)$ symmetry, the $qp$-rotator model, are presented in detail. Some general tendencies arising from the application of this model to the description of rotational bands of various atomic nuclei are summarized.Comment: 8 pages, Latex File, to be published in Reports on Mathematical Physic

Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines

We review the energy spectrum and transport properties of several types of one- dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on a SL is highly collimated. On the other hand there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytic expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the limit of {\delta}-function barriers, the transmission T through, conductance G of a finite number of barriers as well as the energy spectra of SLs are periodic functions of the dimensionless strength P of the barriers, P{\delta}(x) ~ V (x). For a Kronig-Penney SL with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for P = {\pi}/2 + n{\pi} with n an integer. In bilayer graphene, with an appropriate bias applied to the barriers and wells, we show that several new types of SLs are produced and two of them are similar to type I and type II semiconductor SLs. Similar as in single-layer graphene extra "Dirac" points are found. Non-ballistic transport is also considered.Comment: 26 pages, 17 figure

Extra Dirac points in the energy spectrum for superlattices on single-layer graphene

We investigate the emergence of extra Dirac points in the electronic structure of a periodically spaced barrier system, i.e., a superlattice, on single-layer graphene, using a Dirac-type Hamiltonian. Using square barriers allows us to find analytic expressions for the occurrence and location of these new Dirac points in k-space and for the renormalization of the electron velocity near them in the low-energy range. In the general case of unequal barrier and well widths the new Dirac points move away from the Fermi level and for given heights of the potential barriers there is a minimum and maximum barrier width outside of which the new Dirac points disappear. The effect of these extra Dirac points on the density of states and on the conductivity is investigated.Comment: 7 pages, 8 figures, accepted for publication in Phys. Rev.

An Uqp(u2)U_{qp}(u_2) Rotor Model for Rotational Bands of Superdeformed Nuclei

A nonrigid rotor model is developed from the two-parameter quantum algebra $U_{qp}({\rm u}_2)$. [This model presents the $U_{qp}({\rm u}_2)$ symmetry and shall be referred to as the qp-rotor model.] A rotational energy formula as well as a qp-deformation of E2 reduced transition probabilities are derived. The qp-rotor model is applied (through fitting procedures) to twenty rotational bands of superdeformed nuclei in the $A \sim 130$, 150 and 190 mass regions. Systematic comparisons between the qp-rotor model and the q-rotor model of Raychev, Roussev and Smirnov, on one hand, and a basic three-parameter model, on the other hand, are performed on energy spectra, on dynamical moments of inertia and on B(E2) values. The physical signification of the deformation parameters q and p is discussed.Comment: 24 pages, Latex File, to appear in IJMP

Dirac electrons in a Kronig-Penney potential: dispersion relation and transmission periodic in the strength of the barriers

The transmission T and conductance G through one or multiple one-dimensional, delta-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the delta-function barrier V(x,y) / hbar v_F = P delta(x). The dispersion relation of a Kronig-Penney (KP) model of a superlattice is also a periodic function of P and causes collimation of an incident electron beam for P = 2 pi n and n integer. For a KP superlattice with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for P = (n + 1/2) pi.Comment: 5 pages, 6 figure

The importance of habitat quality for marine reserve fishery linkages

We model marine reserve - fishery linkages to evaluate the potential contribution of habitat-quality improvements inside a marine reserve to fish productivity and fishery catches. Data from Mombasa Marine National Park, Kenya, and the adjacent fishery are used. Marine reserves increase total fish biomass directly by providing refuge from exploitation and indirectly by improving fish habitat in the reserve. As natural mortality of the fish stock decreases in response to habitat enhancement in the reserve, catches increase by up to 2.6 tonnes (t).km(-2).year(-1) and total fish biomass by up to 36 t.km(-2). However, if habitat-quality improvement reduces the propensity of fish to move out of the reserve, catches may fall by up to 0.9 t.km(-2).year(-1). Our results indicate that habitat protection in reserves can underpin fish productivity and, depending on its effects on fish movements, augment catches