Barrier penetration for supersymmetric shape-invariant potentials

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wavefunctions obtained via the introduction of new generalized ladder operators. The general form of the wavefunction is obtained by the use of the F(-infinity, +infinity)-matrix formalism of Froman and Froman which is related to the evolution of asymptotic wavefunction coefficients.

The non-adiabatic hyperspherical approach to the two-dimensional D- ion in the presence of a magnetic field

We have used the adiabatic hyperspherical approach to determine the energies and wave functions of the ground state and first excited states of a two-dimensional D- ion in the presence of a magnetic field. Using a modified hyperspherical angular variable, potential energy curves are analytically obtained, allowing an accurate determination of the energy levels of this system. Upper and lower bounds for the ground-state energy have been determined by a non-adiabatic procedure, as the purpose is to improve the accuracy of method. The results are shown to be comparable to the best variational calculations reported in the literature.

Nonadiabatic calculations of the oscillator strengths for the helium atom in the hyperspherical adiabatic approach

Energies and wavefunctions are calculated for the bound states of the helium atom in the hyperspherical adiabatic approach by the full inclusion of nonadiabatic couplings. We show that the use of appropriate asymptotic radial boundary conditions not only allows the efficient calculation of energies accurate up to a few ppm for the ground state but also gives increasingly precise results for high-lying excited states with a unique set of equations. The accuracy of the wavefunctions is demonstrated by the calculation of oscillator strengths in the length form for transitions between stares ii S-1(e) and (n + 1) P-1(0) up to n = 29, in agreement with variational calculations.

Supersymmetric and shape-invariant generalization for nonresonant and intensity-dependent Jaynes-Cummings systems

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the coupled-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent Jaynes-Cummings Hamiltonians, widely used in quantized theories of lasers. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.

Critical exponents for a transition from integrability to non-integrability via localization of invariant tori in the Hamiltonian system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Highly excited states for the helium atom in the hyperspherical adiabatic approach

The hyperspherical adiabatic approach is used to obtain the highly excited series 1sns 1S e and 1s(n + 1)p 1P o of the helium atom. The introduction of appropriate asymptotic conditions at large values of the hyperspherical radius results in a stable algorithm that allows the calculation of the full atomic spectrum with precision of a few parts per million. Comparison with the variational calculations available in the literature shows that the accuracy of the results improves with increasing principal quantum number. We present the energies up to n = 31 which is the typical value used in multiphoton excitation experiments.

Generalized ladder operators for shape-invariant potentials

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.

Comment on 'Relativistic extension of shape-invariant potentials'

This comment criticizes the recently published approach of Alhaidari for solving relativistic problems. It is shown that his gauge considerations are inaccurate and that the class of exactly solvable relativistic problems is not as large as the author claims.

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the regularization via relocalization scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples. © 2006 The American Physical Society.

LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ. © 2011 Elsevier B.V. All rights reserved.

On switched control design of linear time-invariant systems with polytopic uncertainties

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure. © 2013 Wallysonn A. de Souza et al.

Conformally and gauge invariant spin-2 field equations

Using an approach based on the Casimir operators of the de Sitter group, conformally invariant equations for a fundamental spin-2 field are obtained, and their consistency is discussed. It is shown that only when the spin-2 field is interpreted as a 1-form assuming values in the Lie algebra of the translation group, rather than a symmetric second-rank tensor, the field equation is both conformally and gauge invariant. © 2013 Pleiades Publishing, Ltd.

Periodic compression of an adiabatic gas: Intermittency-enhanced Fermi acceleration

A gas of non-interacting particles diffuses in a lattice of pulsating scatterers. In the finite-horizon case with bounded distance between collisions and strongly chaotic dynamics, the velocity growth (Fermi acceleration) is well described by a master equation, leading to an asymptotic universal non-Maxwellian velocity distribution scaling as v∼t. The infinite-horizon case has intermittent dynamics which enhances the acceleration, leading to v∼t ln t and a non-universal distribution. © Copyright EPLA, 2013.

Scale-invariant resonance tagging in multijet events and new physics in Higgs pair production

We study resonant pair production of heavy particles in fully hadronic final states by means of jet substructure techniques. We propose a new resonance tagging strategy that smoothly interpolates between the highly boosted and fully resolved regimes, leading to uniform signal efficiencies and background rejection rates across a broad range of masses. Our method makes it possible to efficiently replace independent experimental searches, based on different final state topologies, with a single common analysis. As a case study, we apply our technique to pair production of Higgs bosons decaying into b\overline{b} pairs in generic New Physics scenarios. We adopt as benchmark models radion and massive KK graviton production in warped extra dimensions. We find that despite the overwhelming QCD background, the 4b final state has enough sensitivity to provide a complementary handle in searches for enhanced Higgs pair production at the LHC. © 2013 SISSA.