Um estudo sobre transições de fase dinâamicas e equações estocásticas de Ginzburg-Landau-Langevin

Pós-graduação em Física - IFT

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

Ginzburg-Landau turbulence in quasi-CW Raman fiber lasers

Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers. Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers.

Vortex dynamics and upper critical fields in ultrathin Bi films

Current-voltage (I-V) characteristics of quench condensed, superconducting, ultrathin Bi films in a magnetic field are reported. These I-V's show hysteresis for all films, grown both with and without thin Ge underlayers. Films on Ge underlayers, close to superconductor-insulator transition, show a peak in the critical current, indicating a structural transformation of the vortex solid. These underlayers, used to make the films more homogeneous, are found to be more effective in pinning the vortices. The upper critical fields (B-c2) of these films are determined from the resistive transitions in perpendicular magnetic field. The temperature dependence of the upper critical field is found to differ significantly from Ginzburg-Landau theory, after modifications for disorder.

Magnetic Field Dependence of Entropy And Specific Heat of YBa2Cu3O7-delta Superconductors

The change in thermodynamic quantities (e. g., entropy, specific heat etc.) by the application of magnetic field in the case of the high-T-c superconductor YBCO system is examined phenomenological by the Ginzburg-Landau theory of anisotropic type-II superconductors. An expression for the change in the entropy (Delta S) and change in specific heat (Delta C) in a magnetic field for any general orientation of an applied magnetic field B-a with respect to the crystallographic c-axis is obtained. The observed large reduction of specific heat anomaly just below the superconducting transition and the observed variation of entropy with magnetic field are explained quantitatively.

Radio frequency studies of surface resistance and critical magnetic field of type I and type II superconductors

The surface resistance and the critical magnetic field of lead electroplated on copper were studied at 205 MHz in a half-wave coaxial resonator. The observed surface resistance at a low field level below 4.2°K could be well described by the BCS surface resistance with the addition of a temperature independent residual resistance. The available experimental data suggest that the major fraction of the residual resistance in the present experiment was due to the presence of an oxide layer on the surface. At higher magnetic field levels the surface resistance was found to be enhanced due to surface imperfections.

The attainable rf critical magnetic field between 2.2°K and T_c of lead was found to be limited not by the thermodynamic critical field but rather by the superheating field predicted by the one-dimensional Ginzburg-Landau theory. The observed rf critical field was very close to the expected superheating field, particularly in the higher reduced temperature range, but showed somewhat stronger temperature dependence than the expected superheating field in the lower reduced temperature range.

The rf critical magnetic field was also studied at 90 MHz for pure tin and indium, and for a series of SnIn and InBi alloys spanning both type I and type II superconductivity. The samples were spherical with typical diameters of 1-2 mm and a helical resonator was used to generate the rf magnetic field in the measurement. The results of pure samples of tin and indium showed that a vortex-like nucleation of the normal phase was responsible for the superconducting-to-normal phase transition in the rf field at temperatures up to about 0.98-0.99 T_c' where the ideal superheating limit was being reached. The results of the alloy samples showed that the attainable rf critical fields near T_c were well described by the superheating field predicted by the one-dimensional GL theory in both the type I and type II regimes. The measurement was also made at 300 MHz resulting in no significant change in the rf critical field. Thus it was inferred that the nucleation time of the normal phase, once the critical field was reached, was small compared with the rf period in this frequency range.

Current dependence of the energy gap in superconductors : a direct measurement

From the tunneling characteristics of a tin-tin oxide-lead junction, a direct measurement has been made of the energy-gap variation for a superconductor carrying a current in a compensated geometry. Throughout the region investigated – several temperatures near T_c and down to a reduced temperature t = 0.8 –the observed current dependence agrees quite well with predictions based on the Ginzburg-Landau-Gor’kov theory. Near T_c the predicted temperature dependence is also well verified, though deviations are observed at lower temperatures; even for the latter, the data are internally consistent with the temperature dependence of the experimental critical current. At the lowest temperature investigated, t = 0.8, a small “Josephson” tunneling current allowed further a direct measurement of the electron drift velocity at low current densities. From this, a preliminary experimental value of the critical velocity, believed to be the first reported, can be inferred in the basis of Ginzburg-Landau theory. For tin at t = 0.8, we find v_c = 87 m/sec. This value does not appear fully consistent with those predicted by recent theories for superconductors with short electronic mean-free-paths.

Topological objects in two-gap superconductor

We discuss the non-Abelian topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. We prove that these non-Abrikosov vortices can have either integral or fractional magnetic flux, depending on the interaction potential. We show that they are described by the non-Abelian topology pi(2)(S-2) and pi(1)(S-1), in addition to the well-known Abelian topology pi(1)(S-1). Furthermore, we discuss the possibility to construct a stable magnetic knot in two-gap superconductor by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology pi(3)(S-2) is described by the Chern-Simon index of the electromagnetic potential. We argue that similar topological objects may exist in multi-gap or multi-layer superconductors and multi-component Bose-Einstein condensates and superfluids, and discuss how these topological objects can be constructed in MgB2, Sr2RuO4, He-3, and liquid metallic hydrogen.

Stress correlations in granular materials: An entropic formulation

We study the response of dry granular materials to external stress using experiment, simulation, and theory. We derive a Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the nature of the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively. © 2009 The American Physical Society.

Studies on High- Tc Superconductors with Inequivalent Conducting Layers

The thesis deals with the study of super conducting properties of layered cuprates within the frame work of a modified Lawrence-Doniach (LD) model. The thesis is organized in seven chapters. Chapter I is a survey of the phenomena and theories of conventional superconductivity which can serve as a springboard for launching the study of the new class of oxide superconductors and it also includes a chronological description of the efforts made to overcome the temperature barrier. Chapter II deals with the structure and properties of the copper oxide superconductors and also the experimental constraints on the theories of high te:::nperature superconductivity. A modified Lawrence-Doniach type of phenomenological model which forms the basis of the presnt study is also discussed. In chapter III~ the temperature dependence of the upper critical field both parallel and perpendicular to the layers is determined and the results are compared with d.c. magnetization measurements on different superconducting compoilllds. The temperature and angular dependence of the lower critical field both parallel and perpendicular to the layers is also discussed. Chapters IV, V and VI deal with thermal fluctuation effects on superconducting properties. Fluctuation specific heat is studied in chapter IV. Paraconductivity both parallel and perpendicular to the layers is discussed in chapter V. Fluctuation diamagnetism is dealt with in chapter VI. Dimensional cross over in the fluctuation regime of all these quantities is also discussed. Chapter VII gives a summary of the results and the conclusions arrived at.

Vortex-Antivortex Dynamics in a Mesoscopic Superconducting Prism with a Centered Antidot

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Vortex-antivortex annihilation dynamics in a square mesoscopic superconducting cylinder

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Magnetic field profile of a mesoscopic SQUID-shaped superconducting film

Using a genuinely tridimensional approach to the time-dependent Ginzburg-Landau theory, we have studied the local magnetic field profile of a mesoscopic superconductor in the so-called SQUID geometry, i.e., a square with a hole at the center connected to the outside vacuum through a very thin slit. Our investigation was carried out in both the Meissner and the mixed state. We have also studied the influence of the temperature on the space distribution of the local magnetic field. © 2013 IOP Publishing Ltd.

Linear arrangement of metallic and superconducting defects in a thin superconducting sample

The vortex matter in a superconducting disk with a linear configuration of metallic and superconducting defects is studied. Effects associated to the pinning (anti-pinning) force of the metallic (superconducting) defect on the vortex configuration and on the thermodynamic critical fields are analyzed in the framework of the Ginzburg Landau theory. We calculate the loop of the magnetization, vorticity and free energy curves as a function of the magnetic field for a thin disk. Due to vortex-defect attraction for a metallic defect (repulsion for a superconducting defect), the vortices always (never) are found to be sitting on the defect position. © 2013.