Thermalization of Interacting Fermions and Delocalization in Fock space

By means of exact diagonalization, we investigate the onset of 'eigenstate thermalization' and the crossover to ergodicity in a system of 1D fermions with increasing interaction. We show that the fluctuations in the expectation values of the momentum distribution from eigenstate to eigenstate decrease with increasing coupling strength and system size. It turns out that these fluctuations are proportional to the inverse participation ratio of eigenstates represented in the Fock basis. We demonstrate that eigenstate thermalization should set in even for vanishingly small perturbations in the thermodynamic limit.Comment: 4 pages, 4 figure

Localized phase structures growing out of quantum fluctuations in a quench of tunnel-coupled atomic condensates

We investigate the relative phase between two weakly interacting 1D condensates of bosonic atoms after suddenly switching on the tunnel-coupling. The following phase dynamics is governed by the quantum sine-Gordon equation. In the semiclassical limit of weak interactions, we observe the parametric amplification of quantum fluctuations leading to the formation of breathers with a finite lifetime. The typical lifetime and density of the these 'quasibreathers' are derived employing exact solutions of the classical sine-Gordon equation. Both depend on the initial relative phase between the condensates, which is considered as a tunable parameter.Comment: 7 pages, 5 figure

Diophantine triples in linear recurrence sequences of Pisot type

The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence or finiteness of Diophantine triples in such sequences. Whilst the case of binary recurrence sequences is almost completely solved, not much was known about recurrence sequences of larger order, except for very specialized generalizations of the Fibonacci sequence. Now, we will prove that any linear recurrence sequence with the Pisot property contains only finitely many Diophantine triples, whenever the order is large and a few more not very restrictive conditions are met.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1602.0823

Exports: Orientation Towards Emerging Markets

Nearly 60 percent of globally traded industrial goods are R&D-intensive. Two fifths are goods with very high research intensity (cutting-edge technology), while the remaining three fifths are goods with high research intensity (high-level technology).1 Up until the 1990s, the USA was the global market leader. However, since then, the situation has changed in favor of Germany and remained so despite the recent economic crisis.2 In 2009, Germany exported R&D-intensive goods amounting to USD 670 billion. The two main competitors, the USA and Japan, exported goods worth USD 561 and 388 billion respectively. The new Central and Eastern European EU member states, which increasingly focus on the production of R&D-intensive goods, reached a value of USD 189 billion altogether. The situation on the import side is reversed: Here the US market dominates with imports worth USD 756 billion, while Germany comes second with USD 430 Billion.International Trade, country and industry studies of trade, manufacturing. - industries

Electron-Plasmon scattering in chiral 1D systems with nonlinear dispersion

We investigate systems of spinless one-dimensional chiral fermions realized, e.g., in the arms of electronic Mach-Zehnder interferometers, at high energies. Taking into account the curvature of the fermionic spectrum and a finite interaction range, we find a new scattering mechanism where high-energy electrons scatter off plasmons (density excitations). This leads to an exponential decay of the single-particle Green's function even at zero temperature with an energy-dependent rate. As a consequence of this electron-plasmon scattering channel, we observe the coherent excitation of a plasmon wave in the wake of a high-energy electron resulting in the buildup of a monochromatic sinusoidal density pattern.Comment: 5 pages, 3 figures; version as publishe

Verformungslokalisierung und Scherzonenbildung am spröd-viskosen Übergang, Cap de Creus, Spanien

#### 0 #### Title page and table of contents #### 1 #### Preamble 1 1.1 What is the dissertation about? 1 1.2 Structure of the work 2 1.3 Scientific manuscripts 2 #### 2 #### Introduction 5 2.1 Abstract 5 2.2 Kurzfassung 7 2.3 Introduction 9 2.3.1 Scientific framework of this thesis 11 #### 3 #### Networking of shear zones at the brittle-viscous transition (Cap de Creus, NE Spain) 15 3.1 Abstract 15 3.2 Introduction 16 3.3 Geological setting 17 3.4 Shear zone nucleation and growth 20 3.4.1 Strain localization within fractures 20 3.4.2 Shear zone nucleation and propagation 23 3.4.3 Shear zone interconnection and strain homoganization 27 3.5 Discussion and interpretation 33 3.5.1 Evidence for a strain-dependent BVT 33 3.5.2 A model for the formation, propagation and networking of shear zones at the BVT 35 3.5.3 Bulk kinematics and scales of strain localization 39 3.5.4 Implications for crustal strength at the BVT 41 3.6 Conclusions 42 3.7 Acknowledgements 43 #### 4 #### Strain localization at the brittle-viscous transition (Cap de Creus, NE Spain) 45 4.1 Abstract 45 4.2 Introduction 46 4.3 Geological background 48 4.4 Isolated mylonitic shear zones 49 4.4.1 Fabrics in unsheared rocks 50 4.4.2 Distributed deformation 53 4.4.3 Intragranular strain localization 55 4.4.4. Strain localization in the transgranular scale 57 4.5 Discussion 59 4.5.1 Combined fracturing and mylonitic shearing 59 4.5.2 Fracture propagation and the role of S1/2 64 4.5.3 A model for the strength evolution of a mylonitic shear zone at the BVT 67 4.6 Conclusions 69 4.7 Acknowledgements 71 #### 5 #### Interconnecting Shear Zones 73 5.1 Abstract 73 5.2 Introduction 74 5.3 Macroscale observations 76 5.3.1 F-type shear zones 76 5.3.2 UM-type shear zones 77 5.3.3 M-type shear zones 79 5.4 Microscale observations 82 5.4.1 Microscale observations from UM-type shear zones 82 5.4.2 Geothermometry of UM-type shear zones 91 5.4.3 Microscale observations from M-type shear zones 93 5.4.4 Paleopiezometric data from M-type shear zones 97 5.5 Discussion 100 5.5.1 Deformation in UM-type shear zones 100 5.5.2 Grain size-sensitive creep in step-over shear zones 102 5.6 Summary and Conclusions 107 5.7 Acknowledgements 108 #### 6 #### Multiscaling of Shear zones 109 6.1 Abstract 109 6.2 Introduction 110 6.3 Scaling parameters of shear zones 113 6.3.1 The Strain Localization Factor (LfRA) 113 6.3.2 The Strain Intensity Factor (Iloc) 115 6.4 Scaling of Cap the Creus shear zones 119 6.4.1 Geology of the shear zones 119 6.4.2 Determination of LfRA for different scales 121 6.5 Interpretation and discussion 124 6.5.1 The role of mechanical anisotropies 125 6.5.2 The effects of strain and kinematics 130 6.5.3 Do shear zones soften or harden during upscaling 134 6.6 Summary and Conclusions 136 6.7 Acknowledgements 138 #### 7 #### Summary and Implications 139 7.1 Summary 139 7.1.1 Strain Localization 139 7.1.2 The formation of decameter-wide shear zones 142 7.1.3 Multiscaling of shear zones 144 7.2 Scientific implications 146 #### 8 #### References 151 #### 9 #### Appendix 173 9.1 Terminology 173 9.2 Quantifying γmax in shear zone centers 176 9.3 Sample descriptions 178 9.4 Element distribution maps to Fig. 4.11 180 9.5 Figure- and sample locations 181 9.6 Measurement of shear zones 182 9.7 Determination of the representative area (RA) 182 9.8 Determining Φmi with ACF 183 9.9 Thresholding of ACF data 186 9.10 Robustness of RA determinations 187 9.11 Thermometry of UM-type shear zones 191 #### Danksagung 195Modes and scales of strain localization at the brittle-viscous transition were investigated in the Northern Shear Belt, Cap de Creus, NE Spain. Field and microstructural investigations revealed that the formation of decametre-wide mylonitic shear zones involved pressure- and temperature-sensitive deformation mechanisms. On the meter-scale, the formation and growth of mylonitic shear zone were characterized by precursory brittle fracturing and a strain- dependent brittle-viscous transition. Where shear zones interconnected and formed decameter-wide networks, fracturing was transitional to grain-size sensitive creep. As the shear zones that constitute these networks widened, the strain distribution was homogenized within the initial limits of the networks. Thereby decameter-wide shear zones formed, whose deformation was governed by a combination of viscous deformation mechanisms involving dislocation and diffusion creep. Multiscale analyses proofed that the scale- dependence of deformation mechanisms in combination with the scaling of pre- existing mechanical anisotropies, that characterize the country rock, control the spatial evolution of shear zones as they grow from millimeter- to kilometer scales.Diese Untersuchung beschäftigt sich mit der Art und den Maßstäben von Verformungslokalisierung innerhalb des Northern Shear Belt am Cap de Creus in NE Spanien. Feld- und mikrostrukturelle Untersuchungen haben gezeigt, dass die Entstehung von mächtigen mylonitischen Scherzonen, die den Northern Shear Belt bilden, eng mit Übergängen zwischen druck- und temperatursensitiven Verformungsmechanismen zusammenhängt. Die Entstehung und das Größenwachstum von mylonitischen Scherzonen auf dem Metermaßstab waren von initialem spröden Brechen und einem verformungsbedingten Übergang hin zu mylonitischer Scherung gekennzeichnet. Spröde Brüche stellten dort, wo sich Scherzonen verbanden und Netzwerke bildeten, Vorläufer zu Scherzonen dar, in denen Verformung von viskosem Korngrenzgleiten dominiert wurde. Mit zunehmendem Breitenwachstum der vernetzten Scherzonen homogenisierte sich die Verformungsverteilung innerhalb der initialen Grenzen des Netzwerkes. Die Deformation in den dadurch gebildeten zehnermetermächtigen Scherzonen wurde von kombiniertem Dislokations- und Diffusionskriechen kontrolliert. Multiskalenanalysen haben gezeigt, dass die räumliche Entwicklung von Scherzonen während ihres Wachstums vom Millimeter- zum Kilometermaßstab von der Maßstabsgebundenheit der Verformungsmechanismen und den Maßstäben von präexistierenden mechanischen Anisotropien im Gestein kontrolliert wurde

Designing a Tool to Assess Professional Competences: Theoretical Foundations and Potential Applications

This conceptual paper outlines the descriptive theoretical foundations or kernel theories for designing an information and communication technology (ICT) tool to assess professional competences in the Austrian trade and craft sector. Upon completion, the ICT-tool serves as a boundary object in which applicants and assessors can interact. While this paper consists of a literature review and conceptual discussion, the overall project is methodologically placed within a multidisciplinary design-science paradigm. Design science scaffolds and structures the development of a theoretical model, the generation of assessment-items and the ICT-tool itself. This paper discusses the necessary descriptive knowledge or kernel theories on which the design of the ICT-tool rests. First, we describe the validation of prior learning - a process advocated by the European Union to make professional competences visible. Second, we describe the process how professional competences come about: through formal, non-formal and informal learning. Subsequently, we outline a knowledge-driven discourse on professional competences and discuss how different definitions of professional competence afford different approaches for its assessment. By presenting a use-case, we outline how the ICT-tool may guide applicants and assessors through this process