Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method. (C) 2007 Elsevier B.V. All rights reserved.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fluctuating solutions for the evolution of domain walls

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonpolynomial potentials with deformable topological structures

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Fermion localization on a split brane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análise da deformação pós-Rifte na Bacia do Araripe, Nordeste do Brasil

The Araripe Basin is located over Precambrian terrains of the Borborema Province, being part of Northeast Brazil inner basins. Its origin is related to the fragmentation of the Gondwana supercontinent and consequently opening of South Atlantic during early Cretaceous. The basin has a sedimentary infill encompassing four distinct evolution stages, comprising Paleozoic syneclisis, pre-rift, rift and post-rift. The target of this study comprises the post-rift section of the basin focusing deformational styles which affect evaporates from Ipubi Member of the Santana Formation, which is composed by gypsum and anidrite layers interbedded with shales. These units occur widespread across the basin. In the central part of the basin, near Nova Olinda-Santana do Cariri, evaporites are affected by an essentialy brittle deformation tipified by fibrous gypsum filled fractures, cutting massive layers of gypsum and anidrite. Veins with variable orientations and dips are observed in the region distributed over three main populations: i) a dominant NWSE with shallow to moderate NE dipping population, consisting of gypsum filled veins in which fibers are normal to vein walls; i) NE-SW veins with moderate SE dips containing subhorizontal growth fibers; and iii) N-S veins with shallow E-W dips with fibers oblique to vein walls. In the west portion of the basin, near Trindade-Ipubi-Araripina towns, evaporate layers are dominantly constituted by gypsum/anidrite finely stratified, showing a minor density of veins. These layers are affected by a unique style of deformation, more ductile, typified by gentle to open horizontal normal folding with several tens of meters length and with double plunging NW-SE or NE-SW hinges, configuring domic features. In detail, gypsum/anidrite laminae are affected by metre to decimeter scale close to tight folding, usually kinked, with broken hinges, locally turning into box folds. Veins show NE-SW main directions with shallow NE dips, growth fibers are parallel to vein walls, constituting slickenfibers. This region is marked by faults that affect Araripina Formation with NW-SE, NE-SW and E-W directions. The main structural styles and general orientations of structures which affected the post-rift section of Araripe Basin yielded important kinematic information analysis which led us to infer a E-W to NE-SW extension direction to the northeastern part of the Basin, whereas in the southeastern part, extension occurred in N-S direction. Thus, it was possible to determine a regional kinematic setting, through this analysis, characterizing a NE-SW to ENE-WSW system for the post-rift section, which is compatible with the tension settings for the Sout American Plate since Albian. Local variations at the fluid pressure linked (or not) to sedimentary overload variation define local tension settings. This way, at the northeastern portion of the basin, the post-rift deformation was governed by a setting which σ 1 is sub-horizontal trending NE-SW and, σ 3 is sub-vertical, emphasizing a reverse fault situation. At the southwestern portion however there was characterized a strike slip fault setting, featuring σ 1 trending ENEWSW and σ3 trending NNW-SSE

Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure

We discuss the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4 > q greater than or equal to 2. We also note a curious appearance of the extended last line of Freudenthal's magic square in connection with the Potts models. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken phi(4) theories in 1 + 1 dimensions. (C) 2003 Elsevier B.V. All rights reserved.

Semiclassical particle spectrum of double sine-Gordon model

We present new theoretical results on the spectrum of the quantum field theory of the double sine-Gordon model. This non-integrable model displays different varieties of kink excitations and bound states thereof. Their mass can be obtained by using a semiclassical expression of the matrix elements of the local fields. In certain regions of the coupling-constants space the semiclassical method provides a picture which is complementary to the one of the form factor perturbation theory, since the two techniques give information about the mass of different types of excitations. In other regions the two methods are comparable, since they describe the same kind of particles. Furthermore, the semiclassical picture is particularly suited to describe the phenomenon of false vacuum decay, and it also accounts in a natural way the presence of resonance states and the occurrence of a phase transition. (C) 2004 Elsevier B.V. All rights reserved.

Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 Elsevier B.V. All rights reserved.

Black-hole back-reaction - a toy model

Using a kink of arbitrary shape as a toy model for a black hole ( horizon), we study the back-reaction of the evaporation process and find that the horizon is always pushed back ( as in the gravitational case). The associated heat capacity and entropy variation, on the other hand, can be positive or negative, depending on the parameters.

Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

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Looking for a Matrix model for ABJM theory

Encouraged by the recent construction of fuzzy sphere solutions in the Aharony, Bergman, Jafferis, and Maldacena (ABJM) theory, we re-analyze the latter from the perspective of a Matrix-like model. In particular, we argue that a vortex solution exhibits properties of a supergraviton, while a kink represents a 2-brane. Other solutions are also consistent with the Matrix-type interpretation. We study vortex scattering and compare with graviton scattering in the massive ABJM background, however our results are inconclusive. We speculate on how to extend our results to construct a Matrix theory of ABJM.

Deformational evolution of a Cretaceous subduction complex: Elephant Island, South Shetland Islands, Antarctica

New structural data from Elephant Island and adjacent islands are presented with the objective to improve the understanding of subduction kinematics in the area northeast of the Antarctic Peninsula. on the island, a first deformation phase, D-1, produced a strong SL fabric with steep stretching and mineral lineations, partly defined by relatively high pressure minerals, such as crossite and glaucophane. D-1 is interpreted to record southward subduction along an E-W trench with respect to the present position of the island. A second phase, D-2, led to intense folding with steep E-W-trending axial surfaces. The local presence of sinistral C'-type sheer bands related to this phase and the oblique inclination of the L-2 stretching lineations are the main arguments to interpret this phase as representing oblique sinistral transpressive shear along steep, approximately E-W-trending shear zones, with the northern (Pacific) block going down with respect to the southern (Antarctic Peninsula) block. The sinistral strike-slip component may represent a trench-linked strike-slip movement as a consequence of oblique subduction. Lithostatic pressure decreased and temperature increased to peak values during D-2, interpreted to represent the collision of thickened oceanic crust with the active continental margin. The last deformation phase, D-3, is characterised by post-metamorphic kink bands, partially forming conjugate sets consistent with E-W shortening and N-S extension. The rock units that underlie the island probably rotated during D-3, in Cenozoic times, together with the trench, from an NE-SW to the present ENE-WSW position, during the progressive opening of the Scotia Sea. The similarity between the strain orientation of D-3 and that of the sinistral NE-SW Shackleton Fracture Zone is consistent with this interpretation. (C) 2000 Elsevier B.V. B.V. All rights reserved.

SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.