QCD radiative and power corrections and Generalized GDH sum rules

We extend the earlier suggested QCD-motivated model for the $Q^2$-dependence of the generalized Gerasimov-Drell-Hearn (GDH) sum rule which assumes the smooth dependence of the structure function $g_T$, while the sharp dependence is due to the $g_2$ contribution and is described by the elastic part of the Burkhardt-Cottingham sum rule. The model successfully predicts the low crossing point for the proton GDH integral, but is at variance with the recent very accurate JLAB data. We show that, at this level of accuracy, one should include the previously neglected radiative and power QCD corrections, as boundary values for the model. We stress that the GDH integral, when measured with such a high accuracy achieved by the recent JLAB data, is very sensitive to QCD power corrections. We estimate the value of these power corrections from the JLAB data at $Q^2 \sim 1 {GeV}^2$. The inclusion of all QCD corrections leads to a good description of proton, neutron and deuteron data at all $Q^2$.Comment: 10 pages, 4 figures (to be published in Physical Review D

On scattering of solitons for the Klein-Gordon equation coupled to a particle

We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein-Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of the soliton solutions. We show that in the large time approximation any finite energy solution, with the initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution of the free Klein-Gordon equation. It is assumed that the charge density satisfies the Wiener condition which is a version of the ``Fermi Golden Rule''. The proof is based on an extension of the general strategy introduced by Soffer and Weinstein, Buslaev and Perelman, and others: symplectic projection in Hilbert space onto the solitary manifold, modulation equations for the parameters of the projection, and decay of the transversal component.Comment: 47 pages, 2 figure

Information-theoretic significance of the Wigner distribution

A coarse grained Wigner distribution p_{W}(x,u) obeying positivity derives out of information-theoretic considerations. Let p(x,u) be the unknown joint PDF (probability density function) on position- and momentum fluctuations x,u for a pure state particle. Suppose that the phase part Psi(x,z) of its Fourier transform F.T.[p(x,u)]=|Z(x,z)|exp[iPsi(x,z)] is constructed as a hologram. (Such a hologram is often used in heterodyne interferometry.) Consider a particle randomly illuminating this phase hologram. Let its two position coordinates be measured. Require that the measurements contain an extreme amount of Fisher information about true position, through variation of the phase function Psi(x,z). The extremum solution gives an output PDF p(x,u) that is the convolution of the Wigner p_{W}(x,u) with an instrument function defining uncertainty in either position x or momentum u. The convolution arises naturally out of the approach, and is one-dimensional, in comparison with the two-dimensional convolutions usually proposed for coarse graining purposes. The output obeys positivity, as required of a PDF, if the one-dimensional instrument function is sufficiently wide. The result holds for a large class of systems: those whose amplitudes a(x) are the same at their boundaries (Examples: states a(x) with positive parity; with periodic boundary conditions; free particle trapped in a box).Comment: pdf version has 16 pages. No figures. Accepted for publ. in PR

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides

Selection of the ground state for nonlinear Schroedinger equations

We prove for a class of nonlinear Schr\"odinger systems (NLS) having two nonlinear bound states that the (generic) large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and dispersive radiation. Our analysis elucidates the mechanism through which initial conditions which are very near the excited state branch evolve into a (nonlinear) ground state, a phenomenon known as {\it ground state selection}. Key steps in the analysis are the introduction of a particular linearization and the derivation of a normal form which reflects the dynamics on all time scales and yields, in particular, nonlinear Master equations. Then, a novel multiple time scale dynamic stability theory is developed. Consequently, we give a detailed description of the asymptotic behavior of the two bound state NLS for all small initial data. The methods are general and can be extended to treat NLS with more than two bound states and more general nonlinearities including those of Hartree-Fock type.Comment: Revision of 2001 preprint; 108 pages Te

A Schroedinger link between non-equilibrium thermodynamics and Fisher information

It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both non-equilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground state solution, and non-equilibrium thermodynamics corresponds to excited state solutions, of a Schroedinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium- and non-equilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis.Comment: 12 pages, no figure

The GDH Sum Rule and Related Integrals

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.Comment: 15 pages LaTeX including 5 figure