Rotational dynamics of magnetic particles in suspensions
- Scherer, Claudio; Matuttis, Hans-Georg
An approach for the rotational dynamics of magnetic particles and their magnetic moments, in fluid suspensions, is developed. A possible application is to magnetic resonance in ferrofluids. Based on a generalized Lagrangian formulation for the equations of motion of the particle, we introduce its interaction with the solvent fluid via dissipative and random noise torques, as well as the interaction between the particle and its magnetic moment, treated as an independent physical entity and characterized by three generalized coordinates: its two polar angles and its modulus. In the appropriate limits, it reduces to the cases of superparamagnetic particles or nonsuperparamagnetic...
Infinite hierarchies of nonlinearly dependent periodic orbits
- Gallas, Jason Alfredo Carlson
Quadratic maps are used to show explicitly that the skeleton of unstable periodic orbits underlying classical and quantum dynamics is stratified into a doubly infinite hierarchy of orbits inherited from a set of basic ‘‘seeds’’ through certain nonlinear transformations Tα(x). The hierarchy contains nonunique substructurings which arise from the different possibilities of sequencing the transformations Tα(x). The structuring of the orbital skeleton is shown to be generic for Abelian equations, i.e., for all dynamical systems generated by iterating rational functions.
Optimally adapted multistate neural networks trained with noise
- Erichsen Junior, Rubem; Theumann, Walter Karl
The principle of adaptation in a noisy retrieval environment is extended here to a diluted attractor neural network of Q-state neurons trained with noisy data. The network is adapted to an appropriate noisy training overlap and training activity, which are determined self-consistently by the optimized retrieval attractor overlap and activity. The optimized storage capacity and the corresponding retriever overlap are considerably enhanced by an adequate threshold in the states. Explicit results for improved optimal performance and new retriever phase diagrams are obtained for Q=3 and Q=4, with coexisting phases over a wide range of thresholds. Most of the interesting results...
Nonintegrable interaction of ion acoustic and electromagnetic waves in a plasma
- Rizzato, Felipe Barbedo; Lopes, Sergio Roberto; Chian, Abraham Chian-Long
In this paper we reexamine the one-dimensional interaction of electromagnetic and ion acoustic waves in a plasma. Our model is similar to one solved by Rao et al. [Phys. Fluids 26, 2488 (1983)] under a number of analytical approximations. Here we perform a numerical investigation to examine the stability of the model. We find that for slightly overdense plasmas, the propagation of stable solitary modes can occur in an adiabatic regime where the ion acoustic electric-field potential is enslaved to the electromagnetic field of a laser. However, if the laser intensity or plasma density increases or the laser frequency decreases,...
Quasilinear evolution of cyclotron maser instability
- Yoon, Peter H.; Ziebell, Luiz Fernando
A quasilinear analysis of the relativistic electron cyclotron maser instability is presented. A background plasma is assumed to support the wave motion, while the instability is driven by a tenuous population of energetic electrons possessing a loss-cone feature. The analysis makes use of an efBcient moment method. In this approach, evolution equations for the moments of particle distribution function are derived from the particle kinetic equation. Then, a self-similar model of the loss-cone electron distribution function is imposed. Simultaneously, the wave kinetic equation is solved. The resulting fully self-consistent set of equations that governs the evolution of the particles and...
Microemulsion model with oil-water anisotropy
- Barbosa, Marcia Cristina Bernardes; Frichembruder, Marcos
We consider a spin model for applications to oil-water-amphiphilic-surfactant mixtures near the region where those phases coexist. We analyze this model assuming that oil and water molecules cannot be treated symmetrically, given that they do exhibit different chemical potentials. Using a mean-field approximation, we find that the modulated phase assumes two possible arrangements, such as sheets (lamellar phase) or rods (hexagonal phase). Due to fluctuations, the lamellar phase is present when the difference between the chemical potential of oil and the chemical potential of water is not too high. Both lamellar and hexagonal phases are present when this difference exceeds...
Self-consistent chaos and Arnold diffusion in a cyclotron-maser wave-particle system
- Pakter, Renato; Couto, Flavia de Oliveira; Rizzato, Felipe Barbedo
In this work, we search for the presence of chaos in a self-consistent model for the cyclotronresonance maser accelerator. Two characteristic regimes are identified. If the initial action variable of the accelerating particles is small, rapid phase bunching occurs and the particle population is condensed into a single macroparticle in phase space. As a result, this low-dimensional state is predominantly regular. For larger energies, on the other hand, there is no macroparticle formation. The system is high dimensional, and chaos is found. Arnold difFusion appears to occur in these chaotic states.
Space of interactions with definite symmetry in neural networks with biased patterns as a spin-glass problem
- Theumann, Alba Graciela Rivas de
We study the space of interactions of a connected neural network with biased patterns, when the synaptic interactions satisfy a symmetry constraint. We show that the solution to the problem requires the calculation of a quantity NΩμ analogous to the thermodynamic potential of a multiply connected Ising model with site dependent interactions, which maps the present problem into the spin-glass problem. By using a diagrammatic expansion, we express NΩμ formally as a functional of renormalized site dependent ‘‘propagators’’ Gij and local ‘‘magnetizations’’ mi , which are determined from a variational principle. Calculating NΩμ in the single site or Brout approximation...
Low-dimensional phase-locked states in the zakharov equations
- Oliveira, Glaucius Iahnke de; Oliveira, Luiz Paulo Luna de; Rizzato, Felipe Barbedo
In this paper we identify phase-locked states among the solutions of the Zakharov equations. Locked states appear as resonant island chains in the appropriate Poincaré plots, with the relevant surface of section obtained by projecting out the full dynamical set on a subspace defined in terms of a pair of center-manifold variables. This pair allows an accurate canonical description of the system immediately after an inverse pitchfork bifurcation destabilizes an initial homogeneous steady state. If one is very close to the bifurcation point, nonlinear saturation of the initial instability is provided by quasistatic integrable ion-acoustic fluctuations, but as one proceeds...
Chaotic dynamics induced by space-charge waves in cyclotron resonance accelerators
- Pakter, Renato; Caldas, Ibere Luiz; Couto, Flavia de Oliveira; Caetano, Tiberio Silva; Rizzato, Felipe Barbedo
In this work, we analyze the effects produced by the inclusion of space-charge waves in a Hamiltonian model for a cyclotron resonant accelerator. We find that space charges impose limits on acceleration and that these limits appear as bounding curves on the appropriate stroboscopic phase spaces. In addition, space charges create nonlinearly locked states which undergo not only the period doubling bifurcations preceding chaos, but saddle-node inverse bifurcations as well.
Neutral polyampholyte in an ionic solution
- Diehl, Alexandre; Barbosa, Marcia Cristina Bernardes; Levin, Yan
The behavior of a neutral polyampholyte (PA) chain with N monomers, in an ionic solution, is analyzed in the framework of the full Debye-Hückel-Bjerrum-Flory (DHBjF) theory. A PA chain, that in addition to the neutral monomers, also contains an equal number of positively and negatively charged monomers, is dissolved in an ionic solution. For high concentrations of salt and at high temperatures, the PA exists in an extended state. As the temperature is decreased, the electrostatic energy becomes more relevant and at a T=Tθ the system collapses into a dilute globular state, or microelectrolyte. This state contains a concentration of...
Compatibility of the nuclear shell and nucleon bag models
- Krein, Gastao Inacio; Maris, Theodor August Johannes
It is shown that the standard self-consistency argument, reconciling the nuclear independentparticle model with the large low-energy nucleon-nucleon cross sections, loses its validity for nucleon bags with a radius larger than about 1 fm.
Canonical quantization of a two-dimensional model with anomalous breaking of gauge invariance
- Girotti, Horacio Oscar; Rothe, Heinz J.; Rothe, Klaus D.
We investigate in detail the operator quantum dynamics of a two-dimensional model exhibiting anomalous breaking of gauge invariance. The equal-time algebra is systematically obtained by using the Dirac-bracket formalism for constrained systems. For certain values of the regularization parameter the system is shown to undergo drastic changes. For the value of the parameter corresponding to the chiral Schwinger model no operator solutions are found to exist.
Renormalization and phase transitions in Potts [fi]/sup 3/-field theory with quadratic and trilinear symmetry breaking
- Barbosa, Marcia Cristina Bernardes; Gusmao, Miguel Angelo Cavalheiro; Theumann, Walter Karl
Renormalized perturbation theory with generalized minimal subtraction is used as an appropriate renormalization-group procedure for the study of crossover behavior in the continuum version of the p-state Potts model with quadratic and trilinear symmetry breaking, within the representation of Priest and Lubensky, by means of a two-loop-order calculation in d =6-€ dimensions. The boundary between first- and second-order phase transitions is studied for longitudinal and transverse ordering as a function of p. A fixed-point runaway for longitudinal ordering is consistent with a mean-field interpretation of a first-order transition for p >p*, where p* >/2 but not with a secondorder transition...
Canonical derivation of the gluon propagator in the temporal gauge
- Girotti, Horacio Oscar; Rothe, Heinz J.
We reexamine the problem of obtaining, within the operator approach, an unambiguous expression for the longitudinal gluon propagator in the temporal gauge. A regularization procedure respecting Gauss's law and the Hermiticity of the gauge fields is proposed. We thereby obtain a definite expression for the longitudinal propagator which agrees with that proposed by Caracciolo, Curci, and Menotti.
Quantum dynamics of chiral fermions in a model with anomalous breaking of gauge invariance
- Girotti, Horacio Oscar; Rothe, Heinz J.; Rothe, Klaus D.
We study the quantum dynamics of chiral fermion fields minimally coupled to a gauge field. The model, originally proposed by Jackiw and Rajaraman, is known to exhibit the anomalous breaking of gauge invariance, which leads to the appearance of an arbitrary parameter a. Both functional and operator techniques are used to obtain the two-point fermion Green's functions for a > 1 and a =1. In both cases clustering holds, and the theory contains asymptotically free fermions. The quantum equation of motion for the field tensor resembles formally that of the Proca theory, but with a dynamically generated mass and a...
Quantum spin glass : a replica-symmetric theory with positive entropy
- Theumann, Alba Graciela Rivas de
In the present paper we present a detailed analysis of quantum effects in the spin-glass transition as described by a quantum Heisenberg analogue of the Sherrington-Kirkpatrick model. The spin operators are represented in terms of two fermion fields and the problem is reduced to that of n fermion leveis at one site in a random time-dependent field and with an interaction delocalized in time. It is shown that within a Hartree-Fock approximation in a replica-symmetric theory one obtains a mean-field description of the transition with satisfactory zero-temperature properties. The transition is described by two order parameters: the static magnetic susceptibility...
Excitation rates of heavy quarks
- Canal, Carlos Alberto Garcia; Santangelo, Eve Mariel; Gay Ducati, Maria Beatriz
We obtain the production rates for c, b, and t quarks in deep-inelastic neutrino- (antineutrino-) nucleon interactions, in the standard six-quark model with left-handed couplings. ,The results are obtained with the most recent mixing parameters and we include a comparison between quark parametrizations. The excitations are calculated separately for each flavor, allowing the understanding of the role of threshold effects when considered through different rescaling variables.
Simple approximation for the bethe ansatz solution of the one-dimensional fermi gas
- Gusmao, Miguel Angelo Cavalheiro
We present a simple approximation scheme for the solution of the integral equations resulting from the Bethe-ansatz diagonalization of the one-dimensional Fermi gas with ô-function attraction. These equations arise for the Hubbard model with attractive interaction in the limit of weak coupling and low density. We obtain the ground-state energy as a function of coupling and density in very good agreement with numerical solutions, as well as a value for the parameter determining the gap in the magnetic excitation spectrum which strongly supports a conjecture of Larkin and Sak.
Phase transitions in asymmetric potts models : breakdown of classical mean-field picture
- Gusmao, Miguel Angelo Cavalheiro
It is shown that mean-field theory fails to give a correct qualitative picture of the thermodynamic behavior of the q-state Potts model when the exchange interaction is anisotropic in spin space. The correct picture is recovered either by introducing a single-particle anisotropy or by taking correlations into account via a Bethe-Peierls approximation. This analysis helps the interpretation of previous renormalization-group results for asymmetric Potts models.