Eocene nappe tectonics and late Alpine extension in the Central Anatolide belt, western Turkey

Strukturgeologische Untersuchungen belegen, daß die Anatoliden der Westtürkei im Eozän durch die Plazierung der Kykladischen Blauschiefereinheit entlang einer durchbrechenden Überschiebung auf die Menderes-Decken unter grünschieferfaziellen Metamorphosebedingungen entstanden.Die kykladischen Blauschiefer in der Westtürkei enthalten Relikte eines prograden alpinen Gefüges (DA1), welches hochruckmetamorph von Disthen und Chloritoid poikiloblastisch überwachsen wurde. Dieses Mineralstadium dauerte noch während des Beginns des nachfolgenden Deformationsereignisses (DA2) an, welches durch NE-gerichtete Scherung und Dekompression charakterisiert ist. Die nachfolgende Deformation (DA3) war das erste Ereignis, das beide Einheiten, sowohl die kykladische Blauschifereinheit als auch die Menderes-Decken, gemeinsam erfaßte. Der Überschiebungskontakt zwischen der kykladischen Blauschiefereinheit und den Menderes-Decken ist eine DA3-Scherzone: die ‘Cycladic-Menderes Thrust’ (CMT). Entlang der CMT-Überschiebungsbahn wurden die kykladischen Blauschiefer gegen veschiedene Einheiten der MN plaziert. Die CMT steigt nach S zum strukturell Hangenden hin an und kann daher als eine durchbrechende Überschiebung entlang einer nach S ansteigenden Rampe betrachtet werden. In den kykladischen Blauschiefern überprägen DA3-Strukturen, die im Zusammenhang mit der CMT stehen, hochdruckmentamorphe Gefüge.In den Menderes-Decken, dem Liegenden der CMT, wird DA3 durch regional vebreitete Gefügeelemente dokumentiert, die im Zusammenhang mit S-gerichteten Schersinnindikatoren stehen. DA3-Gefüge haben die Decken intern deformiert und bilden jene Scherzonen, welche die Decken untereinander abgrenzen. In der Çine-Decke können granitische Gesteine in Orthogneise und Metagranite unterteilt werden. Die Deformationsgeschichte dieser Gesteine dokumentiert zwei Ereignisse. Ein frühes amphibolitfazielles Ereignis erfaßte nur die Orthogneise, in denen vorwiegend NE-SW orientierte Lineare und NE-gerichtete Schersinnindikatoren entstanden. Die jüngeren Metagranite wurden sowohl durch vereinzelte DA3-Scherzonen, als auch in einer großmaßstäblichen DA3-Scherzone am Südrand des Çine-Massivs deformiert. In DA3-Scherzonen sind die Lineare N-S orientiert und die zugehörigen Schersinnindikatoren zeigen S-gerichtete Scherung unter grünschieferfaziellen Bedingungen an. Diese grünschieferfaziellen Scherzonen überprägen die amphibolitfaziellen Gefüge in den Orthogneisen. Magmatische Zirkone aus einem Metagranit, der einen Orthogneiss mit Top-NE Gefügen durchschlägt, ergaben ein 207Pb/206Pb-Alter von 547,2±1,0 Ma. Dies deutet darauf hin, daß DPA proterozoischen Alters ist. Dies wird auch durch die Tatsache gestützt, daß triassische Granite in der Çine- und der Bozdag-Decke keine DPA-Gefüge zeigen. Die jüngeren Top-S-Gefüge sind wahrscheinlich zur gleichen Zeit entstanden wie die ältesten Gefüge der Bayindir-Decke.Das Fehlen von Hochdruck-Gefügen im Liegenden der CMT impliziert eine Exhumierung der kykladischen Blauschiefer von mehr ca. 35 km, bevor diese im Eozän auf die Menderes-Decken aufgeschoben wurden. Die substantiellen Unterschiede bezüglich in der tektonometamorphen Geschichte der kykladischen Blauschiefer und der Menderes-Decken widersprechen der Modellvorstellung eines lateral kontinuierlichen Orogengürtels, nach der die Menderes-Decken als östliche Fortsezung der kykladischen Blauschiefer angesehen werden.Die Analyse spröder spätalpiner Deformationsstrukturen und das regionale Muster mit Hilfe von Spaltspurdatierung modellierter Abkühlalter deuten darauf hin, daß die Struktur des Eozänen Deckenstapels durch miozäne bis rezente Kernkomplex-Bildung stark modifiziert wurde. Eine großmaßstäbliche Muldenstruktur im zentralen Teil der Anatoliden hat sich als Folge zweier symmetrisch angeordneter Detachment-Systeme von initial steilen zu heute flachen Orientierungen im Einflußbreich von ’Rolling Hinges’ gebildet. Die Detachment-Störungen begrenzen den ‘Central Menderes metamorphic core complex’ (CMCC). Das Muster der Apatit-Spaltspuralter belegt, daß die Bildung des CMCC im Miozän begann. Durch die Rück-Deformierung von parallel zur Foliation konstruierten Linien gleicher Abkühlalter kann gezeigt werden, daß die Aufwölbung im Liegenden der Detachments zur Entstehung der Muldenstruktur führte. Das hohe topographische Relief im Bereich des CMCC ist eine Folge der Detachment-Störungen, was darauf hindeutet daß der obere Mantel in den Prozeß mit einbezogen gewesen ist.

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.