Large amplitude behavior of the Grinfeld instability: a variational approach

In previous work, we have performed amplitude expansions of the continuum equations for the Grinfeld instability and carried them to high orders. Nevertheless, the approach turned out to be restricted to relatively small amplitudes. In this article, we use a variational approach in terms of multi-cycloid curves instead. Besides its higher precision at given order, the method has the advantages of giving a transparent physical meaning to the appearance of cusp singularities and of not being restricted to interfaces representable as single-valued functions. Using a single cycloid as ansatz function, the entire calculation can be performed analytically, which gives a good qualitative overview of the system. Taking into account several but few cycloid modes, we obtain remarkably good quantitative agreement with previous numerical calculations. With a few more modes taken into consideration, we improve on the accuracy of those calculations. Our approach extends them to situations involving gravity effects. Results on the shape of steady-state solutions are presented at both large stresses and amplitudes. In addition, their stability is investigated.Comment: subm. to EPJ

Observation of many-body localization in a one-dimensional system with single-particle mobility edge

We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL, when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-Andr\'{e} model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase

Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice

A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, if correlations are present in the disorder potential, the localization transition can occur at a finite disorder strength and SPMEs become possible. In this work, we find experimental evidence for the existence of such a SPME in a one-dimensional quasi-periodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime

Probing weak ergodicity breaking in the one-dimensional Fermi-Hubbard model

We employ an analog quantum simulator with ultracold fermionic K-40 atoms in an optical lattice confined to one dimension to probe the dynamics of a given initial state far from equilibrium. While generic closed quantum systems are expected to behave ergodically and thus reach thermal equilibrium as predicted by the eigenstate thermalization hypothesis, there are well-known exceptions to this paradigm. Above all, integrability and many-body localization avoid thermalization through an extensive set of conserved quantities. However, recently new types of systems that can neither be classified uniquely as thermal or integrable and that are commonly summarized as weakly ergodicity breaking, attracted considerable interest. In this thesis we investigate two such classes, mobility edges and Hilbert space fragmentation, experimentally and support our findings with complementary theoretical insights. In the first project we realize a lattice model with quasiperiodic on-site detuning with a single-particle mobility edge such that the non-interacting system can be prepared in a coexistence of localized and extended eigenstates. Upon the addition of local interactions two central questions that are in the focus of a current theoretical debate, arise: Does many-body localization occur in the presence of a single-particle mobility edge? Does a many-body intermediate phase characterized by a coexistence of localized and extended many-body states emerge? In our work we establish the existence of many-body localization in such a model in a regime where all single-particle states are localized. Further, we observe that the presence of extended states does not lead to a faster relaxation of the system to a thermal ensemble such that extended many-body states do not serve as an efficient heat bath. This does not explicitly exclude the existence of a many-body intermediate phase. The second project is dedicated to the one-dimensional Fermi-Hubbard model in the presence of a strong linear external potential, the so-called tilt. This model is the ideal setting to probe the physics of Hilbert space fragmentation, a recently discovered mechanism that avoids thermalization with only few conserved quantities. We probe the dynamics of various initial states that differ by the fraction of doubly occupied sites. Herein we employ new experimental methods to characterize the initial state by means of microwave spectroscopy and to tune the spin-dependent tilt via radio-frequency dressing. We observe a strong dependence on the initial conditions, a characteristic property of weakly ergodicity-breaking systems. Together with numerical simulations of a leading-order effective Hamiltonian we can provide evidence that our experimental observations are in agreement with this effective description such that we can indeed implement a fragmented model in our system.Wir benutzen einen analogen Quantensimulator mit ultrakalten fermionischen K-40-Atomen in einem eindimensionalen optischen Gitter, um die Dynamik eines Anfangszustandes fernab des Gleichgewichts zu untersuchen. Während sich generische abgeschlossene Quantensysteme ergodisch verhalten und ihr thermisches Gleichgewicht erreichen - eine Vorhersage der Hypothese der Eigenzustandsthermalisierung - gibt es bekannte Ausnahmen von diesem Grundsatz. Insbesondere Integrabilität und Vielteilchenlokalisierung führen zu nicht-thermischem Verhalten aufgrund einer extensiven Zahl von Erhaltungsgrößen. Zuletzt sind hingegen weitere Systeme in den wissenschaftlichen Fokus gerückt, die weder eindeutig als thermisch noch als integrabel klassifiziert und typischerweise als schwach ergodizitätsverletzend zusammengefasst werden können. In dieser Doktorarbeit betrachten wir mit Vielteilchen-Mobilitätskanten und Hilbertraumfragmentierung zwei Vertreter dieser neuen Klassen von der experimentellen Seite und unterstützen die Ergebnisse mit komplementären theoretischen Resultaten. Im ersten Projekt realisieren wir ein Gittermodell mit quasiperiodischer Unordnung und einer Einteilchen-Mobilitätskante. Dieses nicht-wechselwirkende System können wir dadurch in einer Koexistenz aus lokalisierten und ausgedehnten Zuständen präparieren. Die Einführung lokaler Wechselwirkungen motiviert in diesem Kontext zwei zentrale Fragen, die Gegenstand aktueller theoretischer Debatten sind: Kann Vielteilchenlokalisierung in einem System mit einer Mobilitätskante überhaupt vorkommen? Existiert dazwischen eine neue Vielteilchenphase, die durch eine Koexistenz lokalisierter und ausgedehnter Vielteilchenzustände definiert ist? In dieser Arbeit demonstrieren wir Vielteilchenlokalisierung in einem Parameterbereich, in dem alle zugehörigen Einteilchenzustände lokalisiert sind. Weiterhin beobachten wir, dass nicht-lokalisierte Zustände nicht zu einer beschleunigten Relaxation des Systems hin zu einem thermischen Zustand führen und somit kein effizientes Bad darstellen. Dies schließt die Möglichkeit einer neuen (intermediären) Vielteilchenphase nicht explizit aus. Das zweite Projekt untersucht das eindimensionale Fermi-Hubbard-Modell in der Gegenwart eines starken linearen externen Potentials, des sogenannten Tilts. Dieses Modell dient als ideales Versuchsfeld, um die Physik fragmentierter Hilberträume zu untersuchen. Dabei handelt es sich um einen neu entdeckten Mechanismus, der in der Gegenwart nur weniger Erhaltungsgrößen zu nicht-thermischen Eigenschaften führt. Wir untersuchen die Dynamik verschiedener Anfangszustände, die sich durch den Anteil doppelt besetzter Gitterplätze unterscheiden. Dabei kommen neue experimentelle Methoden zur Charakterisierung des Anfangszustands mittels Mikrowellenspektroskopie und zur Kontrolle des spinabhängigen Tilts durch Radiofrequenz-Dressing zum Einsatz. Wir beobachten eine starke Abhängigkeit der Dynamik von den jeweiligen Anfangsbedingungen, was ein charakteristisches Merkmal schwacher Ergodizitätsverletzung darstellt. Zusammen mit numerischen Simulationen des effektiven Hamiltonians führender Ordnung in Störungstheorie können wir Beweise liefern, dass unsere experimentellen Befunde mit dieser effektiven Beschreibung übereinstimmen und wir daher ein fragmentiertes Modell in unserem System implementieren können

Benchmarking a Novel Efficient Numerical Method for Localized 1D Fermi-Hubbard Systems on a Quantum Simulator

Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While state-of-the-art quantum simulators are in principle able to simulate quantum dynamics well outside the domain of classical computers, they are noisy and limited in the variability of the initial state of the dynamics and the observables that can be measured. Despite these limitations, here we show that such a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We develop an efficient numerical technique that facilitates classical simulations in regimes not accessible to exact calculations or other established numerical techniques. The method is based on approximations that are well suited to describe localized one-dimensional Fermi-Hubbard systems. Since this new method does not have an error estimate and the approximations do not hold in general, we use a neutral-atom Fermi-Hubbard quantum simulator with $L_{\text{exp}}\simeq290$ lattice sites to benchmark its performance in terms of accuracy and convergence for evolution times up to $700$ tunnelling times. We then use these approximations in order to derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems, which we show to be in quantitative agreement with experimental results. Finally, we demonstrate that the convergence of our method is the slowest when the entanglement depth developed in the many-body system we consider is neither too small nor too large. This represents a promising regime for near-term applications of quantum simulators.Comment: 24 pages, 10 figure

Quantitative cross-species extrapolation between humans and fish: The case of the anti-depressant fluoxetine

This article has been made available through the Brunel Open Access Publishing Fund.Fish are an important model for the pharmacological and toxicological characterization of human pharmaceuticals in drug discovery, drug safety assessment and environmental toxicology. However, do fish respond to pharmaceuticals as humans do? To address this question, we provide a novel quantitative cross-species extrapolation approach (qCSE) based on the hypothesis that similar plasma concentrations of pharmaceuticals cause comparable target-mediated effects in both humans and fish at similar level of biological organization (Read-Across Hypothesis). To validate this hypothesis, the behavioural effects of the anti-depressant drug fluoxetine on the fish model fathead minnow (Pimephales promelas) were used as test case. Fish were exposed for 28 days to a range of measured water concentrations of fluoxetine (0.1, 1.0, 8.0, 16, 32, 64 μg/L) to produce plasma concentrations below, equal and above the range of Human Therapeutic Plasma Concentrations (HTPCs). Fluoxetine and its metabolite, norfluoxetine, were quantified in the plasma of individual fish and linked to behavioural anxiety-related endpoints. The minimum drug plasma concentrations that elicited anxiolytic responses in fish were above the upper value of the HTPC range, whereas no effects were observed at plasma concentrations below the HTPCs. In vivo metabolism of fluoxetine in humans and fish was similar, and displayed bi-phasic concentration-dependent kinetics driven by the auto-inhibitory dynamics and saturation of the enzymes that convert fluoxetine into norfluoxetine. The sensitivity of fish to fluoxetine was not so dissimilar from that of patients affected by general anxiety disorders. These results represent the first direct evidence of measured internal dose response effect of a pharmaceutical in fish, hence validating the Read-Across hypothesis applied to fluoxetine. Overall, this study demonstrates that the qCSE approach, anchored to internal drug concentrations, is a powerful tool to guide the assessment of the sensitivity of fish to pharmaceuticals, and strengthens the translational power of the cross-species extrapolation

CampusAnalyst - räumliche Analysewerkzeuge zur innovativen Hochschulplanung

Hochschulanlagen sind wesentliche Elemente einer Wissensstadt und haben einen großen Einfluss auf die urbane Entwicklung. Daneben ist wissenschaftlich erwiesen, dass ihre räumliche Struktur den "Flow of Technology" maßgeblich beeinflußt (ALLEN, 1984). Diese Erkenntnisse kommen jedoch im Entwurf von Hochschulen noch kaum zur Anwendung. Dieser Artikel stellt eine umfassende Methode der räumlichen Analyse vor, die diese Lücke schließen kann. Sie basiert auf den Forschungsergebnissen der Space Group am University College London (HILLIER & HANSON, 1984; HILLIER, 1996). Die beiden neuen Campus der Hochschule Hamm-Lippstadt dienen dabei als Fallstudie. Während der Entwurfsphase wurde eine räumliche Analyse durchgeführt, die wertvolle Erkenntnisse für die weitere Planung lieferte. Beide Campus werden auch im laufenden Betrieb weiter untersucht, um Rückschlüsse auf den Erfolg der Planungskonzepte ziehen zu können. 13.01.2012 | Christian Schwander, Christine Kohlert (München) & Eva Friedrich (London