Generalized Nonlinear Proca Equation and its Free-Particle Solutions

We introduce a non-linear extension of Proca's field theory for massive vector (spin $1$) 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 $q$ (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit $q \rightarrow 1$. We derive the nonlinear Proca equation from a Lagrangian that, besides the usual vectorial field $\Psi^{\mu}(\vec{x},t)$, involves an additional field $\Phi^{\mu}(\vec{x},t)$. We obtain exact time dependent soliton-like solutions for these fields having the form of a $q$-plane wave, and show that both field equations lead to the relativistic energy-momentum relation $E^{2} = p^{2}c^{2} + m^{2}c^{4}$ for all values of $q$. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present $q$-generalized Proca theory reduces to Maxwell electromagnetism, and the $q$-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

Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields

The behavior of the nonlinear susceptibility $\chi_3$ and its relation to the spin-glass transition temperature $T_f$, in the presence of random fields, are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue $\lambda_{\rm AT}$ (replicon) on the random fields is analyzed. Particularly, in absence of random fields, the temperature $T_f$ can be traced by a divergence in the spin-glass susceptibility $\chi_{\rm SG}$, which presents a term inversely proportional to the replicon $\lambda_{\rm AT}$. As a result of a relation between $\chi_{\rm SG}$ and $\chi_3$, the latter also presents a divergence at $T_f$, which comes as a direct consequence of $\lambda_{\rm AT}=0$ at $T_f$. However, our results show that, in the presence of random fields, $\chi_3$ presents a rounded maximum at a temperature $T^{*}$, which does not coincide with the spin-glass transition temperature $T_f$ (i.e., $T^* > T_f$ for a given applied random field). Thus, the maximum value of $\chi_3$ at $T^*$ reflects the effects of the random fields in the paramagnetic phase, instead of the non-trivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that $\chi_3$ still maintains a dependence on the replicon $\lambda_{\rm AT}$, although in a more complicated way, as compared with the case without random fields. These results are discussed in view of recent observations in the LiHo$_x$Y$_{1-x}$F$_4$ compound.Comment: accepted for publication in PR

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

Multispecies effects in the equilibrium and out-of-equilibrium thermostatistics of overdamped motion

Progress has been recently made, both theoretical and experimental, regarding the thermostatistics of complex systems of interacting particles or agents (species) obeying a nonlinear Fokker-Planck dynamics. However, major advances along these lines have been restricted to systems consisting of only one type of species. The aim of the present contribution is to overcome that limitation, going beyond single-species scenarios. We investigate the dynamics of overdamped motion in interacting and confined many-body systems having two or more species that experience different intra- A nd interspecific forces in a regime where forces arising from standard thermal noise can be neglected. Even though these forces are neglected, the behavior of the system can be analyzed in terms of an appropriate thermostatistical formalism. By recourse to a mean-field treatment, we derive a set of coupled nonlinear Fokker-Planck equations governing the behavior of these systems. We obtain an H theorem for this Fokker-Planck dynamics and discuss in detail an example admitting an exact, analytical stationary solution.Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nobre, F. D.. Centro Brasileiro de Pesquisas Físicas; BrasilFil: Wedemann, R. S.. Universidade do Estado de Rio do Janeiro; Brasi