Nonlinear Lattice Within Supersymmetric Quantum Mechanics Formalism

In the last decades, the study of nonlinear one dimensional lattices has attracted much attention of the scientific community. One of these lattices is related to a simplified model for the DNA molecule, allowing to recover experimental results, such as the denaturation of DNA double helix. Inspired by this model we construct a Hamiltonian for a reflectionless potential through the Supersymmetric Quantum Mechanics formalism, SQM. Thermodynamical properties of such one dimensional lattice are evaluated aming possible biological applications.

Thermodynamic analysis of a non linear lattice

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

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Charmonium-pion cross section from QCD sum rules

The J/psipi --> (D) over barD*, D (D) over bar*, (D) over bar *D* and (D) over barD cross sections as a function of roots are evaluated in a QCD sum rule calculation. We study the Borel sum rule for the four point function involving pseudoscalar and vector meson currents, up to dimension four in the operator product expansion. We find that our results are smaller than the J/psipi --> charmed mesons cross sections obtained with models based on meson exchange, but are close to those obtained with quark exchange models. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Electromagnetic structure and weak decay of meson K in a light-front QCD-inspired model

The kaon electromagnetic (e.m.) form factor is reviewed considering a light-front constituent quark model. In this approach, it is discussed the relevance of the quark-antiquark pair terms for the full covariance of the e.m. current. It is also verified, by considering a QCD dynamical model, that a good agreement with experimental data can be obtained for the kaon weak decay constant once a probability of about 80% of the valence component is taken into account.

Affine Toda model coupled to matter and the string tension in 2D QCD

The sl(2) affine Toda model coupled to matter is shown to describe various features, such as the spectrum and string tension, of the low-energy effective Lagrangian of two-dimensional QCD (one flavor and N colors). The corresponding string tension is computed when the dynamical quarks are in the fundamental representation of SU(N) and in the adjoint representation of SU(2).

QCD vacuum topology and glueballs

We outline a comprehensive study of spin-0 glueball properties which, in particular, keeps track of the topological gluon structure. Specifically, we implement (semi-hard) topological instanton physics as well as topological charge screening in the QCD vacuum into the operator product expansion (OPE) of the glueball correlators. A realistic instanton size distribution and the (gauge-invariant) renormalization of the instanton contributions are also implemented. Predictions for 0(++) and 0(-+) glueball properties are presented.

Freezing of the QCD coupling constant and the pion form factor

The possibility that the QCD coupling constant (alpha(s)) has an infrared finite behavior (freezing) has been extensively studied in recent years. We compare phenomenological values of the frozen QCD running coupling between different classes of solutions obtained through non-perturbative Schwinger-Dyson Equations. With these solutions were computed QCD predictions for the asymptotic pion form factor which, in turn, were compared with experiment.

The pion electromagnetic form factor in a QCD-inspired model

We present detailed numerical results for the pion space-like electromagnetic form factor obtained within a recently proposed model of the pion electromagnetic current in a confining light-front QCD-inspired model. The model incorporates the vector meson dominance mechanism at the quark level, where the dressed photon with q(+) > 0 decays in an interacting quark-antiquark pair, which absorbs the initial pion and produces the pion in the final state.

Positivity violation for the lattice Landau gluon propagator

We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80(3), 140(3)) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t is an element of[0, 3]fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-particle interpretation of the associated field theory and may be viewed as a manifestation of confinement.

Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations

We compare phenomenological values of the frozen QCD running coupling constant (alpha(s)) with two classes of infrared finite solutions obtained through nonperturbative Schwinger-Dyson equations. We use these same solutions with frozen coupling constants as well as their respective nonperturbative gluon propagators to compute the QCD prediction for the asymptotic pion form factor. Agreement between theory and experiment on alpha(s)(0) and F (pi)(Q(2)) is found only for one of the Schwinger-Dyson equation solutions.

Loss of superfluidity in a Bose-Einstein condensate on an optical lattice via a novel classical phase transition

We predict the loss of superfluidity in a Bose-Einstein condensate (BEC) trapped in a combined optical and axially-symmetric harmonic potentials during a resonant collective excitation initiated by a periodic modulation of the atomic scattering length a, when the modulation frequency equals twice the radial trapping frequency or multiples thereof. This classical dynamical transition is marked by a loss of superfluidity in the BEC and a subsequent destruction of the interference pattern upon free expansion. Suggestion for future experiment is made. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Expansion of a Bose-Einstein condensate formed on a joint harmonic and one-dimensional optical-lattice potential

We study the expansion of a Bose-Einstein condensate trapped in a combined optical-lattice and axially-symmetric harmonic potential using the numerical solution of the mean-field Gross-Pitaevskii equation. First, we consider the expansion of such a condensate under the action of the optical-lattice potential alone. In this case the result of numerical simulation for the axial and radial sizes during expansion is in agreement with two experiments by Morsch et al (2002 Phys. Rev. A 66 021601(R) and 2003 Laser Phys. 13 594). Finally, we consider the expansion under the action of the harmonic potential alone. In this case the oscillation, and the disappearance and revival of the resultant interference pattern is in agreement with the experiment by Muller et al (2003 J. Opt. B: Quantum Semiclass. Opt. 5 S38).

A QCD sum rule study of Theta(+) in nuclear matter

We consider a [ud](2)(s) over bar current, in the finite-density QCD sum rule approach, to investigate the scalar and vector self-energies of the recently observed pentaquark state Theta(+)(1540), propagating in nuclear matter. We find that, opposite to what was obtained for the nucleon, the vector self-energy is negative, and the scalar self-energy is positive. There is a substantial cancellation between them resulting in an attractive net self-energy of the same order as in the nucleon case. (C) 2004 Elsevier B.V. All rights reserved.