Uma abordagem de potencial e massa efetiva e a descrição de espaço de fase quântico para tratar sistemas de spins: Caracterizando o tunelamento de spin e propriedades da molécula de Fe8

Pós-graduação em Física - IFT

Monte Carlo simulations of Potts glasses

A complete understanding of the glass transition isstill a challenging problem. Some researchers attributeit to the (hypothetical) occurrence of a static phasetransition, others emphasize the dynamical transitionof mode coupling-theory from an ergodic to a non ergodicstate. A class of disordered spin models has been foundwhich unifies both scenarios. One of these models isthe p-state infinite range Potts glass with p>4, whichexhibits in the thermodynamic limit both a dynamicalphase transition at a temperature T_D, and a static oneat T_0 < T_D. In this model every spins interacts withall the others, irrespective of distance. Interactionsare taken from a Gaussian distribution.In order to understand better its behavior forfinite number N of spins and the approach to thethermodynamic limit, we have performed extensive MonteCarlo simulations of the p=10 Potts glass up to N=2560.The time-dependent spin-autocorrelation function C(t)shows strong finite size effects and it does not showa plateau even for temperatures around the dynamicalcritical temperature T_D. We show that the N-andT-dependence of the relaxation time for T > T_D can beunderstood by means of a dynamical finite size scalingAnsatz.The behavior in the spin glass phase down to atemperature T=0.7 (about 60% of the transitiontemperature) is studied. Well equilibratedconfigurations are obtained with the paralleltempering method, which is also useful for properlyestablishing static properties, such as the orderparameter distribution function P(q). Evidence is givenfor the compatibility with a one step replica symmetrybreaking scenario. The study of the cumulants of theorder parameter does not permit a reliable estimation ofthe static transition temperature. The autocorrelationfunction at low T exhibits a two-step decay, and ascaling behavior typical of supercooled liquids, thetime-temperature superposition principle, is observed. Inthis region the dynamics is governed by Arrheniusrelaxations, with barriers growing like N^{1/2}.We analyzed the single spin dynamics down to temperaturesmuch lower than the dynamical transition temperature. We found strong dynamical heterogeneities, which explainthe non-exponential character of the spin autocorrelationfunction. The spins seem to relax according to dynamicalclusters. The model in three dimensions tends to acquireferromagnetic order for equal concentration of ferro-and antiferromagnetic bonds. The ordering has differentcharacteristics from the pure ferromagnet. The spinglass susceptibility behaves like chi_{SG} proportionalto 1/T in the region where a spin glass is predicted toexist in mean-field. Also the analysis of the cumulantsis consistent with the absence of spin glass orderingat finite temperature. The dynamics shows multi-scalerelaxations if a bimodal distribution of bonds isused. We propose to understand it with a model based onthe local spin configuration. This is consistent with theabsence of plateaus if Gaussian interactions are used.

Complex higher spins, Weyl invariance and tractors

In this thesis work I analyze higher spin field theories from a first quantized perspective, finding in particular new equations describing complex higher spin fields on Kaehler manifolds. They are studied by means of worldline path integrals and canonical quantization, in the framework of supersymmetric spinning particle theories, in order to investigate their quantum properties both in flat and curved backgrounds. For instance, by quantizing a spinning particle with one complex extended supersymmetry, I describe quantum massless (p,0)-forms and find a worldline representation for their effective action on a Kaehler background, as well as exact duality relations. Interesting results are found also in the definition of the functional integral for the so called O(N) spinning particles, that will allow to study real higher spins on curved spaces. In the second part, I study Weyl invariant field theories by using a particular mathematical framework known as tractor calculus, that enable to maintain at each step manifest Weyl covariance.

Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases

In this thesis several models are treated, which are relevant for ultracold fermionic quantum gases loaded onto optical lattices. In particular, imbalanced superfluid Fermi mixtures, which are considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states experimentally, and antiferromagnetic states, whose experimental realization is one of the next major goals, are examined analytically and numerically with the use of appropriate versions of the Hubbard model.rnrnThe usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in a magnetic field with a strength exceeding the size of the superfluid gap. A spatially inhomogeneous spin-imbalanced superconductor with a complex order parameter known as FFLO-state is predicted to occur in translationally invariant systems. Since in ultracold quantum gases the experimental setups have a limited size and a trapping potential, we analyze the realistic situation of a non-translationally invariant finite sized Hubbard model for this purpose. We first argue analytically, why the order parameter should be real in a system with continuous coordinates, and map our statements onto the Hubbard model with discrete coordinates defined on a lattice. The relevant Hubbard model is then treated numerically within mean field theory. We show that the numerical results agree with our analytically derived statements and we simulate various experimentally relevant systems in this thesis.rnrnAnalogous calculations are presented for the situation at repulsive interaction strength where the N'eel state is expected to be realized experimentally in the near future. We map our analytical results obtained for the attractive model onto corresponding results for the repulsive model. We obtain a spatially invariant unit vector defining the direction of the order parameter as a consequence of the trapping potential, which is affirmed by our mean field numerical results for the repulsive case. Furthermore, we observe domain wall formation, antiferromagnetically induced density shifts, and we show the relevant role of spin-imbalance for antiferromagnetic states.rnrnSince the first step for understanding the physics of the examined models was the application of a mean field approximation, we analyze the effect of including the second order terms of the weak coupling perturbation expansion for the repulsive model. We show that our results survive the influence of quantum fluctuations and show that the renormalization factors for order parameters and critical temperatures lead to a weaker influence of the fluctuations on the results in finite sized systems than on the results in the thermodynamical limit. Furthermore, in the context of second order theory we address the question whether results obtained in the dynamical mean field theory (DMFT), which is meanwhile a frequently used method for describing trapped systems, survive the effect of the non-local Feynman diagrams neglected in DMFT.

Modellkomplexe zur Untersuchung der Radikal-Metall-Wechselwirkung innerhalb des wasseroxidierenden Zentrums im Photosystem II

Im Rahmen dieser Arbeit wurden zweikernige Modellkomplexe zur Untersuchung der Radikal-Metallwechselwirkung innerhalb des wasseroxidierenden Zentrums des Photo¬systems II synthetisiert und eine magneto-strukturelle Korrelation dieser Komplexe erstellt. Als Liganden wurden diverse sechs- bis siebenzähnige Chelatliganden verwendet, welche über zwei Koordinationstaschen und eine verbrückende Phenolatgruppe verfügen. Zwei daran gebundene Manganionen liegen in einer wohl definierten Umgebung nicht koordinativ gesättigt vor. An die freien Koordinationsstellen können weitere ein bis zwei Brückenliganden binden, bei denen es sich in dieser Arbeit hauptsächlich um Carboxylate handelt. Durch die Verwendung eines diamagnetischen Brückenliganden konnte die magnetische Spin-Spin-Austauschwechselwirkung zwischen den spintragenden Manganionen über die verbrücken¬de Phenolatgruppe bestimmt werden. Komplexe, welche über Manganionen in den gleichen Oxidationsstufen, aber über unterschiedliche Carboxylatbrückenliganden verfügen, weisen ähnliche magnetische Austauschwechselwirkungen zwischen den Metallzentren auf. Diese Beobachtung konnte durch eine strukturelle Ähnlichkeit dieser Komplexe erklärt werden. Mittels Aufsummieren der Bindungslängen der verbrückenden Phenolateinheit zu beiden Zentralionen kann innerhalb dieser Komplexe jeweils die Länge des Wechselwirkungspfades erhalten werden, welcher die magnetische Austauschwechselwirkung maßgeblich beein¬flusst. Je länger der Wechselwirkungspfad ist, desto kleiner ist die Austausch¬wechsel¬wirkung. Durch Austausch der diamagnetischen Carboxylate durch paramagnetische benzoat¬substituierte Nitronyl Nitroxid Radikale wurden den Komplexen ein bis zwei weitere Spinzentren hinzugefügt, welche mit den Spins der Zentralionen wechselwirken können. Simulationen der magnetischen Suszeptibilitätsmessungen liefern Werte für die magneti¬schen Austausch¬wechselwirkungen zwischen den Nitronyl Nitroxid Radikalen und den Manganionen, die in allen Fällen schwach ferromagnetisch zwischen 0 und 4,7 cm-1 sind. In einer Auftragung dieser Austauschwechselwirkungen gegen die Mangan-Carboxylat-Bindungs¬längen von strukturell charakterisierten äquivalenten acetatverbrückten Komplexen, kann eine lineare Abhängigkeit gezeigt werden.

Zweikernige 3d-Übergangsmetall-Komplexe mit Derivaten des para-Phenylendiamins als redoxaktive Brückenliganden

Die vorliegende Arbeit beschäftigt sich mit der Darstellung zweikerniger Koordinationsverbindungen, bei denen zweiwertige Ionen der 3d-Übergangsmetalle über einen bestimmten Liganden verbrückt sind. Dieser Brückenligand, das N,N,N‘,N‘-Tetrakis-(2-methylpyridyl)-benzol-1,4-diamin (TPBD), besteht aus einem p-Phenylendiamin-Gerüst, an dessen Stickstoffe je zwei Methylpyridin-Gruppen gebunden sind. In diesen zwei jeweils dreizähnigen Bindungstaschen wurden 3d-Übergangsmetallionen komplexiert, wobei deren Koordinationssphäre mit einem zweizähnigen capping-Liganden vom Typ des 1,10-Phenanthrolins und einem einzähnigen dritten Liganden abgesättigt wird. Die strukturellen, magnetischen und elektronischen Eigenschaften der so erhaltenen homometallischen Komplexe mit Mn(II), Fe(II), Co(II), Ni(II), Cu(II) und Zn(II) wurden untersucht. Dabei wurde besonderes Augenmerk auf die Veränderung dieser Eigenschaften bei dem Einsatz unterschiedlicher capping- und dritter Liganden gerichtet. Die schwach antiferromagnetische Wechselwirkung der metallzentrierten Spins über den Brückenliganden führt dabei stets zu einem diamagnetischen Grundzustand, was diese als mögliche Einzelmolekülmagnete ausschließt. Mit der Oxidierbarkeit des Liganden zu seiner radikalischen Spezies besteht die Möglichkeit, einen zusätzlichen Spin in dem System zu erzeugen, woraus ein Spingrundzustand von ungleich null resultiert. Es zeigte sich, dass die Lebensdauer der radikalischen Spezies eine starke Abhängigkeit sowohl von den eingesetzten Metallionen als auch den weiteren Liganden besitzt. Auch vier Derivate des ursprünglichen Brückenliganden konnten synthetisiert und deren Oxidierbarkeit zu den entsprechenden Radikalformen gezeigt werden. Neben der Darstellung homometallischer Komplexe gelang zudem die Synthese und Strukturaufklärung dreier heterometallischer zweikerniger Komplexe mit Mn(II), Co(II) und Ni(II) als Metallionen. Es konnte gezeigt werden, dass diese auch ohne die Oxidation des Brückenliganden bei schwacher antiferromagnetischer Wechselwirkung der Spins einen paramagnetischen Spingrundzustand besitzen.

Spins, moments and radii of cd isotopes

The complex nature of the nucleon-nucleon interaction and the wide range of systems covered by the roughly 3000 known nuclides leads to a multitude of effects observed in nuclear structure. Among the most prominent ones is the occurence of shell closures at so-called ”magic numbers”, which are explained by the nuclear shell model. Although the shell model already is on duty for several decades, it is still constantly extended and improved. For this process of extension, fine adjustment and verification, it is important to have experimental data of nuclear properties, especially at crucial points like in the vicinity of shell closures. This is the motivation for the work performed in this thesis: the measurement and analysis of nuclear ground state properties of the isotopic chain of 100−130Cd by collinear laser spectroscopy.rnrnThe experiment was conducted at ISOLDE/CERN using the collinear laser spectroscopy apparatus COLLAPS. This experiment is the continuation of a run on neutral atomic cadmium from A = 106 to A = 126 and extends the measured isotopes to even more exotic species. The required gain in sensitivity is mainly achieved by using a radiofrequency cooler and buncher for background reduction and by using the strong 5s 2S1/2 → 5p 2P3/2 transition in singly ionized Cd. The latter requires a continuous wave laser system with a wavelength of 214.6 nm, which has been developed during this thesis. Fourth harmonic generation of an infrared titanium sapphire laser is achieved by two subsequent cavity-enhanced second harmonic generations, leading to the production of deep-UV laser light up to about 100 mW.rnrnThe acquired data of the Z = 48 Cd isotopes, having one proton pair less than the Z = 50 shell closure at tin, covers the isotopes from N = 52 up to N = 82 and therefore almost the complete region between the neutron shell closures N = 50 and N = 82. The isotope shifts and the hyperfine structures of these isotopes have been recorded and the magnetic dipole moments, the electric quadrupole moments, spins and changes in mean square charge radii are extracted. The obtained data reveal among other features an extremely linear behaviour of the quadrupole moments of the I = 11/2− isomeric states and a parabolic development in differences in mean square nuclear charge radii between ground and isomeric state. The development of charge radii between the shell closures is smooth, exposes a regular odd-even staggering and can be described and interpreted in the model of Zamick and Thalmi.

Analysis of the spectrum of the spin-1 biquadratic antiferromagnetic chain

In questo elaborato vengono discusse le catene di spin-1, modelli quantistici definiti su un reticolo unidimensionale con interazione tra siti primi vicini. Fra la ricca varietà di tipologie esistenti è stato scelto di porre attenzione primariamente sul modello antiferromagnetico con interazione puramente biquadratica. Vengono presentati diversi metodi di classificazione degli autostati di tale modello, a partire dalle simmetrie che ne caratterizzano l’Hamiltoniana. La corrispondenza con altri modelli noti, quali il modello XXZ di spin 1/2, la catena di Heisenberg SU (3) ed i modelli di Potts, è utile ad individuare strutture simmetriche nascoste nel formalismo di spin-1, le quali consentono di ricavare informazioni sullo spettro energetico. Infine, vengono presentati risultati numerici accompagnati da alcune considerazioni sulle modifiche dello spettro quando si aggiunge un termine bilineare alla Hamiltoniana biquadratica.

Two-Dimensional Manganese(II) Coordination Polymer Based on Phthalate and Pyrazine Bridges Exhibiting Antiferromagnetic Porperties

Benzodifuran-functionalised pyrene and anthracene fluorophores 1 and 2 were obtained in reasonable yields. Their single crystal structures, electrochemical, optical absorption, and fluorescence characteristics have been described. They show strong luminescence with high quantum yields of 0.53 for 1 and 0.48 for 2. Magnetic measurements for the 2D coordination polymer [Mn(Pht(Pyz(H2O)2]n (1), in which metal centres are linked together by pyrazine (Pyz) and 1,6-bridging o-phthalate ligand (Pht2-), revealed antiferromagnetic interactions between Mn(II) ions.