435 research outputs found
Semiclassical approach to the nonlocal nonlinear Schr\"{o}dinger equation with a non-Hermitian term
The nonlinear Sch\"{o}dinger equation (NLSE) with a non-Hermitian term is the
model for various phenomena in nonlinear open quantum systems. We deal with the
Cauchy problem for the nonlocal generalization of multidimensional NLSE with a
non-Hermitian term. Using the ideas of the Maslov method, we propose the method
of constructing asymptotic solutions to this equation within the framework of
semiclassically concentrated states. The semiclassical nonlinear evolution
operator and symmetry operators for the leading term of asymptotics are
derived. Our approach is based on the solutions of the auxiliary dynamical
system that effectively linearize the problem under certain algebraic
conditions. The formalism proposed is illustrated with the specific example of
the NLSE with a non-Hermitian term that is the model of an atom laser. The
analytical asymptotic solution to the Cauchy problem is obtained explicitly for
this example.Comment: 29 pages, 1 figur
Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
We construct quasiparticles-like solutions to the one-dimensional
Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) with a nonlocal nonlinearity using
the method of semiclassically concentrated states in the weak diffusion
approximation. Such solutions are of use for predicting the dynamics of
population patterns. The interaction of quasiparticles stems from nonlocal
competitive losses in the FKPP model. We developed the formalism of our
approach relying on ideas of the Maslov method. The construction of the
asymptotic expansion of a solution to the original nonlinear evolution equation
is based on solutions to an auxiliary dynamical system of ODEs. The asymptotic
solutions for various specific cases corresponding to various spatial profiles
of the reproduction rate and nonlocal competitive losses are studied within the
framework of the approach proposed.Comment: 27 pages, 2 figure
The comparative analysis of master’s degree curriculums in the majorof “Electronics and nanoelectronics” in TPU (Russia) and “Solid state systems” in Czech Technical University (Prague)
Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity
We apply the original semiclassical approach to the kinetic ionization
equation with the nonlocal cubic nonlinearity in order to construct the family
of its asymptotic solutions. The approach proposed relies on an auxiliary
dynamical system of moments of the desired solution to the kinetic equation and
the associated linear partial differential equation. The family of asymptotic
solutions to the kinetic equation is constructed using the symmetry operators
acting on functions concentrated in a neighborhood of a point determined by the
dynamical system. Based on these solutions, we introduce the nonlinear
superposition principle for the nonlinear kinetic equation. Our formalism based
on the Maslov germ method is applied to the Cauchy problem for the specific
two-dimensional kinetic equation. The evolution of the ion distribution in the
kinetically enhanced metal vapor active medium is obtained as the nonlinear
superposition using the numerical-analytical calculations.Comment: 29 pages, 3 figures, 1 table, minor improvements, the article is
published in Symmetr
Next-to-Leading Order perturbative QCD corrections to baryon correlators in matter
We compute the next-to-leading order perturbative QCD corrections to the
correlators of nucleon interpolating currents in relativistic nuclear matter.
The main new result is the calculation of the O(alpha_s) perturbative
corrections to the coefficient functions of the vector quark condensate in
matter. This condensate appears in matter due to the violation of Lorentz
invariance. The NLO perturbative QCD corrections turn out to be large which
implies that the NLO corrections must be included in a sum rule analysis of the
properties of both bound nucleons and relativistic nuclear matter.Comment: 19 pages in LaTeX, including 5 Postscript figure
The reflectivity of relativistic ultra-thin electron layers
The coherent reflectivity of a dense, relativistic, ultra-thin electron layer
is derived analytically for an obliquely incident probe beam. Results are
obtained by two-fold Lorentz transformation. For the analytical treatment, a
plane uniform electron layer is considered. All electrons move with uniform
velocity under an angle to the normal direction of the plane; such electron
motion corresponds to laser acceleration by direct action of the laser fields,
as it is described in a companion paper. Electron density is chosen high enough
to ensure that many electrons reside in a volume \lambda_R^3, where \lambda_R
is the wavelength of the reflected light in the rest frame of the layer. Under
these conditions, the probe light is back-scattered coherently and is directed
close to the layer normal rather than the direction of electron velocity. An
important consequence is that the Doppler shift is governed by
\gamma_x=(1-(V_x/c)^2)^{-1/2} derived from the electron velocity component V_x
in normal direction rather than the full \gamma-factor of the layer electrons.Comment: 7 pages, 4 figures, submitted to the special issue "Fundamental
Physics with Ultra-High Fields" in The European Physical Journal
Isospin Dependence of Power Corrections in Deep Inelastic Scattering
We present results of a perturbative QCD analysis of deep inelastic
measurements of both the deuteron and proton structure functions. We evaluate
the theoretical uncertainty associated to nuclear effects in the deuteron, and
we extract simultaneously the isospin depedendence of: i)the higher twists
terms; ii) the ratio of the longitudinal to transverse cross sections; iii) the
ratio of the neutron to proton structure functions. The extraction of the
latter, in particular, has been at the center of an intense debate. Its
accurate determination is crucial both theoretically and for the interpretation
of the more precise neutrino experiments including the newly planned high
intensity 50 GeV proton synchrotron.Comment: 33 pages, 16 figure
Charge Symmetry Violation Corrections to Determination of the Weinberg Angle in Neutrino Reactions
We show that the correction to the Paschos-Wolfenstein relation associated
with charge symmetry violation in the valence quark distributions is
essentially model independent. It is proportional to a ratio of quark momenta
that is independent of Q^2. This result provides a natural explanation of the
surprisingly good agreement found between our earlier estimates within several
different models. When applied to the recent NuTeV measurement, this effect
significantly reduces the discrepancy with other determinations of the Weinberg
angle.Comment: 7 pages, no figures; expanded discussion of N.ne.Z correction
Determination of from Gross-Llewellyn Smith sum rule by accounting for infrared renormalon
We recapitulate the method which resums the truncated perturbation series of
a physical observable in a way which takes into account the structure of the
leading infrared renormalon. We apply the method to the Gross-Llewellyn Smith
(GLS) sum rule. By confronting the obtained result with the experimentally
extracted GLS value, we determine the value of the QCD coupling parameter which
turns out to agree with the present world average.Comment: invited talk by G.C. in WG3 of NuFact02, July 1-6, 2002, London; 4
pages, revte
Shadowing, Binding and Off-Shell Effects in Nuclear Deep Inelastic Scattering
We present a unified description of nuclear deep inelastic scattering (DIS)
over the whole region of the Bjorken variable. Our approach is based on
a relativistically covariant formalism which uses analytical properties of
quark correlators. In the laboratory frame it naturally incorporates two
mechanisms of DIS: (I) scattering from quarks and antiquarks in the target and
(II) production of quark-antiquark pairs followed by interactions with the
target. We first calculate structure functions of the free nucleon and develop
a model for the quark spectral functions. We show that mechanism (II) is
responsible for the sea quark content of the nucleon while mechanism (I)
governs the valence part of the nucleon structure functions. We find that the
coherent interaction of pairs with nucleons in the nucleus leads to
shadowing at small and discuss this effect in detail. In the large
region DIS takes place mainly on a single nucleon. There we focus on the
derivation of the convolution model. We point out that the off-shell properties
of the bound nucleon structure function give rise to sizable nuclear effects.Comment: 29 pages (and 10 figures available as hard copies from Authors),
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