High-momentum tails as magnetic structure probes for strongly-correlated SU(κ)SU(\kappa) fermionic mixtures in one-dimensional traps

A universal $k^{-4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of Pagano et al. [Nat. Phys. {\bf 10}, 198 (2014)], realizing a gas with tunable $SU(\kappa)$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\kappa$ components of the gas and the Young tableaux for the $S_N$ permutation symmetry group identifying the magnetic structure of the ground-state. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-states simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components and on interaction strength. Moreover, using a virial approach in the limit of infinite interactions, we show that the contact increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in Ref.~[Nat. Phys. {\bf 10}, 198 (2014)].Comment: 13 pages, 6 figure

The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure

Symmetrien des N=2 Strings

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Increased visual sensitivity and occipital activity in patients with hemianopia following vision rehabilitation

Acknowledgements We would like to thank the participants for giving up their time to engage with the research.Peer reviewedPublisher PD

Vom Einzel- zum Krippenkind. Beziehungs- und Interaktionsprozesse eines einjährigen Kindes im Transitionsprozess zur außerfamiliären Betreuung - eine psychoanalytisch-pädagogische Einzelfallstudie

Trotz der häufig anzutreffenden gesellschaftlichen Praxis, Kinder nach Abschluss des ersten Lebensjahres in eine Krippenbetreuung einzugewöhnen, ist bisher wenig bekannt, wie die Kleinst- und Kleinkinder selbst diese meist erste Transition erleben, verarbeiten und mitgestalten. Im Mittelpunkt der psychoanalytisch-pädagogisch ausgerichteten Dissertation stehen die vielschichtigen, latenten Beziehungs- und Interaktionsprozesse im Dreieck Eltern - Kind - Kindheitspädagogin im Übergang zur Krippenbetreuung. Erstmalig zeigt die multiperspektivische Beobachtungsstudie die Besonderheiten der Eingewöhnung von Ein- bis Zweijährigen auf, die erhebliche Unterschiede von denen älterer Kinder aufweist. Aus der novellenartig gehaltenen Einzelfallstudie lässt sich ableiten, dass frühe Eingewöhnungsprozesse mit einer forcierten Selbständigkeitsentwicklung des Kindes einhergehen können. Anders als im familiären Gefüge des Aufwachsens muss das beobachtete einjährige Einzelkind vielfältige Herausforderungen im neuen, institutionellen Kontext bewältigen. Diese kommen einer Forcierung ihrer Selbständigkeit gleich. Ungeachtet dessen zeigt sich in dieser Arbeit, dass die frühe Transition mit ihrer unabdingbaren Trennungsdynamik auch progressive Entwicklungspotentiale für das Kind bereithält. Desweiteren lässt sich an diesem individuellen Einzelfall der frühe, ambivalente Übergang von einer Situation des Einzelkindes in der Familie hin zu einem Krippenkind in der institutionalisierten Kinderbetreuung untersuchen. Mit dem Einsatz der psychoanalytischen Beobachtungs- und Auswertungsmethode nach Bick/Tavistock-Konzept gelingt ein seltener Einblick in die frühe Kinderbetreuung, der belegt, dass es sich bei der frühen Krippenbetreuung um ein hoch komplexes und konfliktreiches Feld handelt.Despite of the common social practice of bringing toddlers to the day care center in their first year of life, there is just little profound knowledge of this topic. Especially the children´s feelings, experience and active participation of day care entry and their setting-in processes. This psychoanalytic-pedagogical thesis will focus on the multifaceted and complex latent interaction triangle of parents - child - childcare during adapting to day care. For the first time this multi-perspective observational study is pointing out the particular characteristics of one and two year old children, within this transition to day care process and its significant differences regarding older children. From this thesis, based on a individual case study can be deduced that an early childcare transition process correlate with forced independence and autonomy development. This work illuminates which different strains the one year old child had to challenge in the context of an institutionalized group care system compared to the family-related environment. Nevertheless the conclusions of this thesis take the progressive development potential for the child into account, that result of the interpersonal relations of the transmission and separation process. Based on one individual case study of an early, ambivalent transition from an only child in the family circle to the institutionalized day care nursery and by the methods of psychoanalytic observation and evaluation (Bick/Tavistock-Concept) this work provides a glimpse behind the scenes of the early childcare adapting process. It provides an unprecedented perspective for latent interactions and relations during this enter out-of-home-care. This clearly demonstrates the complexity, conflict-prone and controversy of the early child care topic