961 research outputs found
Generalized Nonlinear Proca Equation and its Free-Particle Solutions
We introduce a non-linear extension of Proca's field theory for massive
vector (spin ) bosons. The associated relativistic nonlinear wave equation
is related to recently advanced nonlinear extensions of the Schroedinger,
Dirac, and Klein-Gordon equations inspired on the non-extensive generalized
thermostatistics. This is a theoretical framework that has been applied in
recent years to several problems in nuclear and particle physics, gravitational
physics, and quantum field theory. The nonlinear Proca equation investigated
here has a power-law nonlinearity characterized by a real parameter
(formally corresponding to the Tsallis entropic parameter) in such a way that
the standard linear Proca wave equation is recovered in the limit . We derive the nonlinear Proca equation from a Lagrangian that,
besides the usual vectorial field , involves an
additional field . We obtain exact time dependent
soliton-like solutions for these fields having the form of a -plane wave,
and show that both field equations lead to the relativistic energy-momentum
relation for all values of . This suggests
that the present nonlinear theory constitutes a new field theoretical
representation of particle dynamics. In the limit of massless particles the
present -generalized Proca theory reduces to Maxwell electromagnetism, and
the -plane waves yield localized, transverse solutions of Maxwell equations.
Physical consequences and possible applications are discussed
Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model
A spin-1 model, appropriated to study the competition between bilinear
(J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random
interactions, both of them with zero mean, is investigated. The interactions
are infinite-ranged and the replica method is employed. Within the
replica-symmetric assumption, the system presents two phases, namely,
paramagnetic and spin-glass, separated by a continuous transition line. The
stability analysis of the replica-symmetric solution yields, besides the usual
instability associated with the spin-glass ordering, a new phase due to the
random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure
Towards an optical potential for rare-earths through coupled channels
The coupled-channel theory is a natural way of treating nonelastic channels,
in particular those arising from collective excitations, defined by nuclear
deformations. Proper treatment of such excitations is often essential to the
accurate description of reaction experimental data. Previous works have applied
different models to specific nuclei with the purpose of determining
angular-integrated cross sections. In this work, we present an extensive study
of the effects of collective couplings and nuclear deformations on integrated
cross sections as well as on angular distributions in a consistent manner for
neutron-induced reactions on nuclei in the rare-earth region. This specific
subset of the nuclide chart was chosen precisely because of a clear static
deformation pattern. We analyze the convergence of the coupled-channel
calculations regarding the number of states being explicitly coupled. Inspired
by the work done by Dietrich \emph{et al.}, a model for deforming the spherical
Koning-Delaroche optical potential as function of quadrupole and hexadecupole
deformations is also proposed. We demonstrate that the obtained results of
calculations for total, elastic and inelastic cross sections, as well as
elastic and inelastic angular distributions correspond to a remarkably good
agreement with experimental data for scattering energies above around a few
MeV.Comment: 7 pages, 6 figures. Submitted to the proceedings of the XXXVI
Reuni\~ao de Trabalho de F\'{\i}sica Nuclear no Brasil (XXXVI Brazilian
Workshop on Nuclear Physics), held in Maresias, S\~ao Paulo, Brazil in
September 2013, which should be published on AIP Conference Proceeding
Series. arXiv admin note: substantial text overlap with arXiv:1311.1115,
arXiv:1311.042
Thermostatistics of overdamped motion of interacting particles
We show through a nonlinear Fokker-Planck formalism, and confirm by molecular
dynamics simulations, that the overdamped motion of interacting particles at
T=0, where T is the temperature of a thermal bath connected to the system, can
be directly associated with Tsallis thermostatistics. For sufficiently high
values of T, the distribution of particles becomes Gaussian, so that the
classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures
of the thermal bath, the system displays a mixed behavior that follows a novel
type of thermostatistics, where the entropy is given by a linear combination of
Tsallis and Boltzmann-Gibbs entropies.Comment: 4 pages, 2 figure
Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
Generalizations of the three main equations of quantum physics, namely, the
Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear
terms, characterized by exponents depending on an index , are considered in
such a way that the standard linear equations are recovered in the limit . Interestingly, these equations present a common, soliton-like,
travelling solution, which is written in terms of the -exponential function
that naturally emerges within nonextensive statistical mechanics. In all cases,
the well-known Einstein energy-momentum relation is preserved for arbitrary
values of
Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
A general type of nonlinear Fokker-Planck equation is derived directly from a
master equation, by introducing generalized transition rates. The H-theorem is
demonstrated for systems that follow those classes of nonlinear Fokker-Planck
equations, in the presence of an external potential. For that, a relation
involving terms of Fokker-Planck equations and general entropic forms is
proposed. It is shown that, at equilibrium, this relation is equivalent to the
maximum-entropy principle. Families of Fokker-Planck equations may be related
to a single type of entropy, and so, the correspondence between well-known
entropic forms and their associated Fokker-Planck equations is explored. It is
shown that the Boltzmann-Gibbs entropy, apart from its connection with the
standard -- linear Fokker-Planck equation -- may be also related to a family of
nonlinear Fokker-Planck equations.Comment: 19 pages, no figure
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