Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

On the coupling of the self-dual field to dynamical U(1) matter and its dual theory

We consider arbitrary U (1) charged matter non-minimally coupled to the self-dual field in d = 2 + 1. The coupling includes a linear and a rather general quadratic term in the self-dual field. By using both Lagragian gauge embedding and master action approaches we derive the dual Maxwell Chern-Simons-type model and show the classical equivalence between the two theories. At the quantum level the master action approach in general requires the addition of an awkward extra term to the Maxwell Chern-Simons-type theory. Only in the case of a linear coupling in the self-dual field can the extra term be dropped and we are able to establish the quantum equivalence of gauge invariant correlation functions in both theories.

Anomalous transport effects on magnetic field profile in a motional current sheath

The radial magnetic field profile during implosion of a reversed field current sheath in a theta-pinch was investigated through local measurements and simulation of hybrid code. The actual profile was defined by Hermite interpolation polynomial through mean value of the field at discrete radial position of measurements. Simulation profile was provided by the numerical code with appropriate initial conditions. Classical and anomalous collision process were taken in account in the theoretical model. The results indicated that anomalous effects play major role during the implosion phase of current sheath in a slow rising theta pinch device.

Kac-Moody construction of Toda type field theories

Using the coadjoint orbit method we derive a geometric WZWN action based on the extended two-loop Kac-Moody algebra. We show that under a hamiltonian reduction procedure, which respects conformal invariance, we obtain a hierarchy of Toda type field theories, which contain as submodels the Toda molecule and periodic Toda lattice theories. We also discuss the classical r-matrix and integrability properties.

Conflict between the classical equivalence principle and quantum mechanics

As far as external gravitational fields described by Newton's theory are concerned, theory shows that there is an unavoidable conflict between the universality of free fall (Galileo's equivalence principle) and quantum mechanics - a result confirmed by experiment. Is this conflict due perhaps to the use of Newton's gravity, instead of general relativity, in the analysis of the external gravitational field? The response is negative. To show this we compute the low corrections to the cross-section for the scattering of different quantum particles by an external gravitational field, treated as an external field, in the framework of Einstein's linearized gravity. To first order the cross-sections are spin-dependent; if the calculations are pushed to the next order they become dependent upon energy as well. Therefore, the Galileo's equivalence and, consequently, the classical equivalence principle, is violated in both cases. We address these issues here.

Role of the range of the dipole function in the classical dynamics of molecular dissociation

The dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses is investigated within the framework of the classical driven Morse oscillator. The interaction between the molecule and the laser field described in the dipole formulation is given by the product of a time-dependent external field with a position-dependent permanent dipole function. The effects of changing the spatial range of the dipole function in the classical dissociation dynamics of large ensembles of trajectories are studied. Numerical calculations have been performed for distinct amplitudes and carrier frequencies of the external pulses and also for ensembles with different initial energies. It is found that there exist a set of values of the dipole range for which the dissociation probability can be completely suppressed. The dependence of the dissociation on the dipole range is explained through the examination of the Fourier series coefficients of the dipole function in the angle variable of the free system. In particular, the suppression of dissociation corresponds to dipole ranges for which the Fourier coefficients associated with nonlinear resonances are null and the chaotic region in the phase space is reduced to thin layers. In this context, it is shown that the suppression of dissociation of heteronuclear molecules for certain frequencies of the external field is a consequence of the finite range of the corresponding permanent dipole. © 2013 American Physical Society.

Quantum versus classical instability of scalar fields in curved backgrounds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effective field theory methods to model compact binaries

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Closed-orbit dependence on the field direction in the anisotropic diamagnetic Kepler problem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantum-classical correspondence and the role of the dipole function in molecular dissociation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

From quantum to classical instability in relativistic stars

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Circular, elliptic and oval billiards in a gravitational field

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Generalizing the dynamic field theory of spatial cognition across real and developmental time scales

Within cognitive neuroscience, computational models are designed to provide insights into the organization of behavior while adhering to neural principles. These models should provide sufficient specificity to generate novel predictions while maintaining the generality needed to capture behavior across tasks and/or time scales. This paper presents one such model, the Dynamic Field Theory (DFT) of spatial cognition, showing new simulations that provide a demonstration proof that the theory generalizes across developmental changes in performance in four tasks—the Piagetian A-not-B task, a sandbox version of the A-not-B task, a canonical spatial recall task, and a position discrimination task. Model simulations demonstrate that the DFT can accomplish both specificity—generating novel, testable predictions—and generality—spanning multiple tasks across development with a relatively simple developmental hypothesis. Critically, the DFT achieves generality across tasks and time scales with no modification to its basic structure and with a strong commitment to neural principles. The only change necessary to capture development in the model was an increase in the precision of the tuning of receptive fields as well as an increase in the precision of local excitatory interactions among neurons in the model. These small quantitative changes were sufficient to move the model through a set of quantitative and qualitative behavioral changes that span the age range from 8 months to 6 years and into adulthood. We conclude by considering how the DFT is positioned in the literature, the challenges on the horizon for our framework, and how a dynamic field approach can yield new insights into development from a computational cognitive neuroscience perspective.

New historical archeointensity data from Brazil: Evidence for a large regional non-dipole field contribution over the past few centuries

We report new archeointensity data obtained from the analyses of baked clay elements (architectural and kiln brick fragments) sampled in Southeast Brazil and historically and/or archeologically dated between the end of the XVIth century and the beginning of the XXth century AD. The results were determined using the classical Thellier and Thellier protocol as modified by Coe, including partial thermoremanent magnetization (pTRM) and pTRM-tail checks, and the Triaxe protocol, which involves continuous high-temperature magnetization measurements. In both protocols, TRM anisotropy and cooling rate TRM dependence effects were taken into account for intensity determinations which were successfully performed for 150 specimens from 43 fragments, with a good agreement between intensity results obtained from the two procedures. Nine site-mean intensity values were derived from three to eight fragments and defined with standard deviations of less than 8%. The site-mean values vary from similar to 25 mu T to similar to 42 mu T and describe in Southeast Brazil a continuous decreasing trend by similar to 5 mu T per century between similar to 1600 AD and similar to 1900 AD. Their comparison with recent archeointensity results obtained from Northeast Brazil and reduced at a same latitude shows that: (1) the geocentric axial dipole approximation is not valid between these southeastern and northeastern regions of Brazil, whose latitudes differ by similar to 10 degrees, and (2) the available global geomagnetic field models (gufm1 models, their recalibrated versions and the CALSK3 models) are not sufficiently precise to reliably reproduce the non-dipole field effects which prevailed in Brazil for at least the 1600-1750 period. The large non-dipole contribution thus highlighted is most probably linked to the evolution of the South Atlantic Magnetic Anomaly (SAMA) during that period. Furthermore, although our dataset is limited, the Brazilian archeointensity data appear to support the view of a rather oscillatory behavior of the axial dipole moment during the past three centuries that would have been marked in particular by a moderate increase between the end of the XVIIIth century and the middle of the XIXth century followed by the well-known decrease from 1840 AD attested by direct measurements. (C) 2011 Elsevier B.V. All rights reserved.

Evolution of a dense neutrino gas in matter and electromagnetic field

We describe the system of massive Weyl fields propagating in a background matter and interacting with an external electromagnetic field. The interaction with an electromagnetic field is due to the presence of anomalous magnetic moments. To canonically quantize this system first we develop the classical field theory treatment of Weyl spinors in frames of the Hamilton formalism which accounts for the external fields. Then, on the basis of the exact solution of the wave equation for a massive Weyl field in a background matter we obtain the effective Hamiltonian for the description of spin-flavor oscillations of Majorana neutrinos in matter and a magnetic field. Finally, we incorporate in our analysis the neutrino self-interaction which is essential when the neutrino density is sufficiently high. We also discuss the applicability of our results for the studies of collective effects in spin-flavor oscillations of supernova neutrinos in a dense matter and a strong magnetic field. (C) 2011 Elsevier B.V. All rights reserved.