Estrutura algébrica dos modelos integráveis

Pós-graduação em Física - IFT

Construção exata de sólitons de Hopf

Pós-graduação em Física - IFT

MULTI-BUMP SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON R

This paper is concerned with the existence of multi-bump solutions to a class of quasilinear Schrodinger equations in R. The proof relies on variational methods and combines some arguments given by del Pino and Felmer, Ding and Tanaka, and Sere.

On the radial expansion of tubular structures in a quark-gluon plasma

We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes. (C) 2012 Elsevier B.V. All rights reserved.

The concept of quasi-integrability for modified non-linear Schrodinger models

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an in finite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V similar to (vertical bar psi vertical bar(2))(2+epsilon), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

ATTEMPTS TO DEFINE QUASI-INTEGRABILITY

In this paper we discuss some ideas on how to define the concept of quasi-integrability. Our ideas stem from the observation that many field theory models are "almost" integrable; i.e. they possess a large number of "almost" conserved quantities. Most of our discussion will involve a certain class of models which generalize the sine-Gordon model in (1 + 1) dimensions. As will be mentioned many field configurations of these models look like those of the integrable systems and so appear to be close to those in integrable model. We will then attempt to quantify these claims looking in particular, both analytically and numerically, at field configurations with scattering solitons. We will also discuss some preliminary results obtained in other models.

Solitrons Hidrodinâmicos de Korteweg-de Vries.

Esse artigo foi escrito para alunos de graduação e pós- graduação em Física e para alunos de Engenharia. Primeiramente mostramos como construir a equação diferencial não-linear de Korteweg e de Vries a partir das equações básicas da hidrodinâmica. Em seguida mostramos como resolvê-la obtendo as ondas denominadas de solitons.

Some aspects of self-duality and generalised BPS theories

If a scalar eld theory in (1+1) dimensions possesses soliton solutions obeying rst order BPS equations, then, in general, it is possible to nd an in nite number of related eld theories with BPS solitons which obey closely related BPS equations. We point out that this fact may be understood as a simple consequence of an appropriately generalised notion of self-duality. We show that this self-duality framework enables us to generalize to higher dimensions the construction of new solitons from already known solutions. By performing simple eld transformations our procedure allows us to relate solitons with di erent topological properties. We present several interesting examples of such solitons in two and three dimensions.

A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.

Optically active photoresponsive multifunctional polymeric materials

In the last year [1], Angiolini and co-workers have synthesized and investigated methacrylic polymers bearing in the side chain the chiral cyclic (S)-3-hydroxypyrrolidine moiety interposed between the main chain and the trans-azoaromatic chromophore, substituted or not in the 4’ position by an electron-withdrawing group. In these materials, the presence of a rigid chiral moiety of one prevailing absolute configuration favours the establishment of a chiral conformation of one prevailing helical handedness, at least within chain segments of the macromolecules, which can be observed by circular dichroism (CD). The simultaneous presence of the azoaromatic and chiral functionalities allows the polymers to display both the properties typical of dissymmetric systems (optical activity, exciton splitting of dichroic absorptions), as well as the features typical of photochromic materials (photorefractivity, photoresponsiveness, NLO properties). The first part of this research was to synthesize analogue homopolymers and copolymers based on bisazoaromatic moiety and compare their properties to those of the above mentioned analogue derivatives bearing only one azoaromatic chromophore in the side chain. We focused also the attention on the effects induced on the thermal and chiroptical behaviours by the insertion of particulars achiral comonomers characterized by different side-chain mobility and grown hindrance (MMA, tert-BMA and TrMA). On the other hand carbazole containing polymers [2] have attracted much attention because of their unique features. The use of these materials in advanced micro- and nanotechnologies spreads in many different applications such as photoconductive and photorefractive polymers, electroluminescent devices, programmable optical interconnections, data storage, chemical photoreceptors, NLO, surface relief gratings, blue emitting materials and holographic memory. The second part of the work was focused on the synthesis and the characterization polymeric derivatives bearing in the side chain carbazole or phenylcarbazole moieties linked to the (S)- 2-hydroxy succinimide or the (S)-3-hydroxy pyrrolidinyl ring as chiral groups covalently linked to the main chain through ester bonds. The last objective of this research was to design, synthesize, and characterize multifunctional methacrylic homopolymers and copolymers bearing three distinct functional groups (i.e. azoaromatic, carbazole and chiral group of one single configuration) directly linked in the side chain. This polymeric derivatives could be of potential interest for several advanced application fields, such as optical storage, waveguides, chiroptical switches, chemical photoreceptors, NLO, surface relief gratings, photoconductive materials, etc.

Synthesen und Charakterisierungen Arylamin-haltiger Polymere: multifunktionelle hoch-T g-Copolymere für photorefraktive Anwendungen

Zusammenfassung Die vorliegenden Arbeit beschäftigt sich mit den Synthesen und Charakterisierungen multifunktioneller, Arylamin-haltiger Polymere, welche sich als photorefraktive(PR)-Materialien eignen. Die Glastemperaturen (Tg) der angestrebten Materialien liegen deutlich über Raumtemperatur, um so den Pockels-Mechanismus zum Aufbau des PR-Effektes zu favorisieren. Hierzu sind zwei synthetische Konzepte, basierend auf Maleinimid-Methylvinylisocyanat-Reaktiv-Polymeren und Triphenylamin-haltigen Polymeren, entwickelt worden. Im Rahmen des Reaktiv-Polymer-Konzeptes konnten PR-Materialien mit den bisher größten Beugungs-Effizienzen sowie den schnellsten Ansprechzeiten für multifunktionelle hoch-Tg-Polymere dargestellt werden. Hierfür wurden Maleinimid-Methylvinylisocyanat-Reaktiv-Polymere synthetisiert welche an der Imid-Position über Spacer-Gruppen mit Carbazol-Einheiten funktionalisiert sind. Die Tg´s der Polymere konnten zwischen 60°C und 194°C eingestellt werden. Die Isocyanat-Gruppen wurden dann polymeranlog mit hydroxyalkyl-funktionalisierten Chromophoren umgesetzt. Die Kinetik des PR-Effektes dieser Materialien wird durch die Ladungsträger-Beweglichkeiten in den Proben bestimmt. Eine Steigerung der Farbstoff-Konzentrationen erhöht die PR-Leistungen der Materialien, behindert jedoch deren Kinetik.Das Triphenylamin-Polymer-Konzept verwendet Triphenylamine als Lochleiter. Hierfür wurden die radikalischen Polymerisations-Verhalten der Monomere p-Diphenylaminostyrol (DPAS) und erstmals p-Ditoluylaminostyrol (DTAS) untersucht. Die Monomere wurden durch spontane, freie und kontrollierte radikalische Verfahren polymerisiert. Mittels eines TEMPO-Derivates gelang der Aufbau von Block-Copolymeren. Poly-DPAS konnte, im Gegensatz zu Poly-DTAS, polymeranlog tricyanovinyliert werden. Dadurch lassen sich PDPAS-block-PTPAS-Copolymere selektiv im PDPAS-Block tricyanovinylieren. Diese Materialien weisen eine Tendenzen zur Mikro-Phasen-Separation auf.Die Strukturierung von PDPAS konnte durch Photo-Polymerisation mit einer Auflösung von wenigen mm demonstriert werden. Carbazol und Triphenylamin-haltige Materialien wurden mittels Cyclo-Voltametrie untersucht.

A scanning electron microscope for ultracold quantum gases

This thesis presents a new imaging technique for ultracold quantum gases. Since the first observation of Bose-Einstein condensation, ultracold atoms have proven to be an interesting system to study fundamental quantum effects in many-body systems. Most of the experiments use optical imaging rnmethods to extract the information from the system and are therefore restricted to the fundamental limitation of this technique: the best achievable spatial resolution that can be achieved is comparable to the wavelength of the employed light field. Since the average atomic distance and the length scale of characteristic spatial structures in Bose-Einstein condensates such as vortices and solitons is between 100 nm and 500 nm, an imaging technique with an adequate spatial resolution is needed. This is achieved in this work by extending the method of scanning electron microscopy to ultracold quantum gases. A focused electron beam is scanned over the atom cloud and locally produces ions which are subsequently detected. The new imaging technique allows for the precise measurement of the density distribution of a trapped Bose-Einstein condensate. Furthermore, the spatial resolution is determined by imaging the atomic distribution in one-dimensional and two-dimensional optical lattices. Finally, the variety of the imaging method is demonstrated by the selective removal of single lattice site. rn