6,258 research outputs found
Parton distribution functions of proton in a light-front quark-diquark model
We present the parton distribution functions (PDFs) for un- polarised,
longitudinally polarized and transversely polarized quarks in a proton using
the light-front quark diquark model. We also present the scale evolution of
PDFs and calculate axial charge and tecsor charge for and quarks at a
scale of experimental findings.Comment: XXII DAE-BRNS High Energy Physics Symposium, December 12-16, 2016,
University of Delhi, India; 4 pages, 1 figur
Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space
We discuss the quantum Lax-Phillips theory of scattering and unstable
systems. In this framework, the decay of an unstable system is described by a
semigroup. The spectrum of the generator of the semigroup corresponds to the
singularities of the Lax-Phillips -matrix. In the case of discrete (complex)
spectrum of the generator of the semigroup, associated with resonances, the
decay law is exactly exponential. The states corresponding to these resonances
(eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips
Hilbert space, and therefore all physical properties of the resonant states can
be computed.
We show that the Lax-Phillips -matrix is unitarily related to the
-matrix of standard scattering theory by a unitary transformation
parametrized by the spectral variable of the Lax-Phillips theory.
Analytic continuation in has some of the properties of a method
developed some time ago for application to dilation analytic potentials.
We work out an illustrative example using a Lee-Friedrichs model for the
underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision
Reflective Scattering and Unitarity
Interpretation of unitarity saturation as reflective scattering is discussed.
Analogies with optics and Berry phase alongside with the experimental
consequences of the proposed interpretation at the LHC energies are considered.Comment: 4 pages, 1 figure, talk given by S. Troshin at Diffraction 2008,
September 9-14, La Londe-les-Maures, Franc
Jet-like tunneling from a trapped vortex
We analyze the tunneling of vortex states from elliptically shaped traps.
Using the hydrodynamic representation of the Gross-Pitaevskii (Nonlinear
Schr\"odinger) equation, we derive analytically and demonstrate numerically a
novel type of quantum fluid flow: a jet-like singularity formed by the
interaction between the vortex and the nonhomogenous field. For strongly
elongated traps, the ellipticity overwhelms the circular rotation, resulting in
the ejection of field in narrow, well-defined directions. These jets can also
be understood as a formation of caustics since they correspond to a convergence
of trajectories starting from the top of the potential barrier and meeting at a
certain point on the exit line. They will appear in any coherent wave system
with angular momentum and non-circular symmetry, such as superfluids,
Bose-Einstein condensates, and light.Comment: 4 pages, 4 figure
Virtual photon structure functions and positivity constraints
We study the three positivity constraints among the eight virtual photon
structure functions, derived from the Cauchy-Schwarz inequality and which are
hence model-independent. The photon structure functions obtained from the
simple parton model show quite different behaviors in a massive quark or a
massless quark case, but they satisfy, in both cases, the three positivity
constraints. We then discuss an inequality which holds among the unpolarized
and polarized photon structure functions , and
, in the kinematic region , where is the mass squared of the probe (target) photon, and we examine
whether this inequality is satisfied by the perturbative QCD results.Comment: 24 pages, 13 eps figure
Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field
The long-time asymptotics is analyzed for all finite energy solutions to a
model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the
nonlinearity concentrated at a single point: each finite energy solution
converges as time goes to plus or minus infinity to the set of all ``nonlinear
eigenfunctions'' of the form \psi(x)e\sp{-i\omega t}. The global attraction
is caused by the nonlinear energy transfer from lower harmonics to the
continuous spectrum and subsequent dispersive radiation.
We justify this mechanism by the following novel strategy based on inflation
of spectrum by the nonlinearity. We show that any omega-limit trajectory has
the time-spectrum in the spectral gap [-m,m] and satisfies the original
equation. This equation implies the key spectral inclusion for spectrum of the
nonlinear term. Then the application of the Titchmarsh Convolution Theorem
reduces the spectrum of each omega-limit trajectory to a single harmonic in
[-m,m].
The research is inspired by Bohr's postulate on quantum transitions and
Schroedinger's identification of the quantum stationary states to the nonlinear
eigenfunctions of the coupled U(1)-invariant Maxwell-Schroedinger and
Maxwell-Dirac equations.Comment: 29 pages, 1 figur
Single-spin Azimuthal Asymmetries in the ``Reduced Twist-3 Approximation''
We consider the single-spin azimuthal asymmetries recently measured at the
HERMES experiment for charged pions produced in semi-inclusive deep inelastic
scattering of leptons off longitudinally polarized protons. Guided by the
experimental results and assuming a vanishing twist-2 transverse quark spin
distribution in the longitudinally polarized nucleon, denoted as ``reduced
twist-3 approximation'', a self-consistent description of the observed
single-spin asymmetries is obtained. In addition, predictions are given for the
z dependence of the single target-spin asymmetry.Comment: 8 pages, 2 figures, typos corrected, very small changes to text,
reference adde
Stable directions for small nonlinear Dirac standing waves
We prove that for a Dirac operator with no resonance at thresholds nor
eigenvalue at thresholds the propagator satisfies propagation and dispersive
estimates. When this linear operator has only two simple eigenvalues close
enough, we study an associated class of nonlinear Dirac equations which have
stationary solutions. As an application of our decay estimates, we show that
these solutions have stable directions which are tangent to the subspaces
associated with the continuous spectrum of the Dirac operator. This result is
the analogue, in the Dirac case, of a theorem by Tsai and Yau about the
Schr\"{o}dinger equation. To our knowledge, the present work is the first
mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page
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