26,734 research outputs found

    Cavity-Catalyzed Hydrogen Transfer Dynamics in an Entangled Molecular Ensemble under Vibrational Strong Coupling

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    Microcavities have been shown to influence the reactivity of molecular ensembles by strong coupling of molecular vibrations to quantized cavity modes. In quantum mechanical treatments of such scenarios, frequently idealized models with single molecules and scaled, effective molecule-cavity interactions or alternatively ensemble models with simplified model Hamiltonians are used. In this work, we go beyond these models by applying an ensemble variant of the Pauli-Fierz Hamiltonian for vibro-polaritonic chemistry and numerically solve the underlying time-dependent Schr\"odinger equation to study the cavity-induced quantum dynamics in an ensemble of thioacetylacetone (TAA) molecules undergoing hydrogen transfer under vibrational strong coupling (VSC) conditions. Beginning with a single molecule coupled to a single cavity mode, we show that the cavity indeed enforces hydrogen transfer from an enol to an enethiol configuration with transfer rates significantly increasing with light-matter interaction strength. This positive effect of the cavity on reaction rates is different from several other systems studied so far, where a retarding effect of the cavity on rates was found. It is argued that the cavity ``catalyzes'' the reaction by transfer of virtual photons to the molecule. The same concept applies to ensembles with up to N=20N=20 TAA molecules coupled to a single cavity mode, where an additional, significant, ensemble-induced collective isomerization rate enhancement is found. The latter is traced back to complex entanglement dynamics of the ensemble, which we quantify by means of von Neumann-entropies. A non-trivial dependence of the dynamics on ensemble size is found, clearly beyond scaled single-molecule models, which we interpret as transition from a multi-mode Rabi to a system-bath-type regime as NN increases.Comment: Manuscript 9 pages, 5 figures (minor changes in v2). Supplementary Information 7 pages, 5 figures (Section III rewritten in v2 after peer-review

    A Descriptive Qualitative Study Exploring Middle-School Teachers’ Perceptions of Professional Development on Technology Integration

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    Today’s teachers are being encouraged to incorporate technology into their classrooms. Technology integration became a worldwide focus for schools after remote learning was necessary to continue instruction due to the COVID-19 pandemic. Additionally, research shows that technology-infused lessons improve student achievement and increase student engagement. Despite efforts to support teachers throughout the technology integration process, concerns have developed. Preparing highly qualified teachers ready to incorporate technology into their teaching repertoire has developed additional stress factors. In this descriptive qualitative study, the researcher wanted to address the problem of teacher attrition, possibly related to stress factors associated with technology integration. The purpose of this qualitative descriptive study was to explore teachers’ perceptions of professional development opportunities that possibly improve the technology integration process. Additionally, the researcher wanted to identify stress factors associated with technology adoption and how professional development may help to reduce stress factors associated with technology integration in one middle school in New York. The researcher chose a qualitative descriptive study using Vygotsky’s social constructivist theory and Bandura’s social learning theory on self-efficacy as the theoretical framework. The researcher included an exposition of the literature sources, synthesized the research findings, and provided recommendations for practice and future research. The data collection process consisted of semistructured open-ended questions that were developed with the support of a panel of experts. There were 10 participants chosen using a snowball sampling strategy. This study’s findings were that professional development should be hands-on, continuous, and targeted to increase teachers’ personal level of engagement. Also, creating opportunities for colleague support systems reduced stress factors associated with technology integration. These peer support systems reduced the time required to research the most effective resources, digital tools, and applications as participants shared the resources with one another. Recommendations for practice included providing adequate professional development, offering appropriate infrastructure, and hands-on, targeted, continuous training for teachers to feel more comfortable developing technology-infused lessons. Recommendations for research include providing additional insight into teachers’ perceived benefits and motivation for technology integration and how stress factors associated with the technology adoption process possibly increase teacher attrition

    Rotation and vibration in tetraquarks

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    A novel approach is introduced for obtaining precise solutions of the pairing Hamiltonian for tetraquarks, which utilizes an algebraic technique in infinite dimensions. The parameters involved in the transition phase are calibrated based on potential tetraquark candidates derived from phenomenology. Our investigation shows that the rotation and vibration transitional theory delivers a more accurate explanation for heavy tetraquarks compared to other methods utilizing the same formalism. To illustrate the concept, we compute the spectra of several tetraquarks, namely charm, bottom, bottom-charm and open charm and bottom systems, and contrast them with those of other particles.Comment: 13 pages, 4 figures, 4 Tables. Invited contribution to a Special Issue of Few Body Systems: "Emergence and Structure of Baryons -- Selected Contributions from the International Conference Baryons 2022

    Continuous eigenfunctions of the transfer operator for the Dyson model

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    In this article we prove that there exists a continuous eigenfunction for the transfer operator corresponding to potentials for the classical Dyson model in the subcritical regime for which the parameter α\alpha is greater than 3/23/2, and we conjecture that this value is sharp. This is a significant improvement on previous results where the existence of a continuous eigenfunction of the transfer operator was only established for general potentials satisfying summable variations, which would correspond to the parameter range α>2\alpha > 2. Moreover, this complements as result by Bissacot, Endo, van Enter and Le Ny \cite{vanenter}, who showed that there is no continuous eigenfunction at low temperatures. Our approach to obtaining these new results involves a novel approach based on random cluster models

    On real and observable realizations of input-output equations

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    Given a single algebraic input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand sides. It has been shown that in the case where the input-output equation is of order one, rational realizations can be computed, if they exist. In this work, we focus first on the existence and actual computation of the so-called observable rational realizations, and secondly on rational realizations with real coefficients. The study of observable realizations allows to find every rational realization of a given first order input-output equation, and the necessary field extensions in this process. We show that for first order input-output equations the existence of a rational realization is equivalent to the existence of an observable rational realization. Moreover, we give a criterion to decide the existence of real rational realizations. The computation of observable and real realizations of first order input-output equations is fully algorithmic. We also present partial results for the case of higher order input-output equations

    A simplified lower bound for implicational logic

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    We present a streamlined and simplified exponential lower bound on the length of proofs in intuitionistic implicational logic, adapted to Gordeev and Haeusler's dag-like natural deduction.Comment: 31 page

    Path integrals and stochastic calculus

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    Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in the light-hearted fashion that physicists enjoy. Similar issues arise in the field of stochastic calculus, which we review to prepare the ground for a proper construction of path integrals. At the level of path integration, and in arbitrary space dimension, we not only report on existing Riemannian geometry-based approaches that render path integrals amenable to the standard rules of calculus, but also bring forth new routes, based on a fully time-discretized approach, that achieve the same goal. We illustrate these various definitions of path integration on simple examples such as the diffusion of a particle on a sphere.Comment: 96 pages, 4 figures. New title, expanded introduction and additional references. Version accepted in Advandes in Physic

    Model Diagnostics meets Forecast Evaluation: Goodness-of-Fit, Calibration, and Related Topics

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    Principled forecast evaluation and model diagnostics are vital in fitting probabilistic models and forecasting outcomes of interest. A common principle is that fitted or predicted distributions ought to be calibrated, ideally in the sense that the outcome is indistinguishable from a random draw from the posited distribution. Much of this thesis is centered on calibration properties of various types of forecasts. In the first part of the thesis, a simple algorithm for exact multinomial goodness-of-fit tests is proposed. The algorithm computes exact pp-values based on various test statistics, such as the log-likelihood ratio and Pearson\u27s chi-square. A thorough analysis shows improvement on extant methods. However, the runtime of the algorithm grows exponentially in the number of categories and hence its use is limited. In the second part, a framework rooted in probability theory is developed, which gives rise to hierarchies of calibration, and applies to both predictive distributions and stand-alone point forecasts. Based on a general notion of conditional T-calibration, the thesis introduces population versions of T-reliability diagrams and revisits a score decomposition into measures of miscalibration, discrimination, and uncertainty. Stable and efficient estimators of T-reliability diagrams and score components arise via nonparametric isotonic regression and the pool-adjacent-violators algorithm. For in-sample model diagnostics, a universal coefficient of determination is introduced that nests and reinterprets the classical R2R^2 in least squares regression. In the third part, probabilistic top lists are proposed as a novel type of prediction in classification, which bridges the gap between single-class predictions and predictive distributions. The probabilistic top list functional is elicited by strictly consistent evaluation metrics, based on symmetric proper scoring rules, which admit comparison of various types of predictions

    3d mirror symmetry of braided tensor categories

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    We study the braided tensor structure of line operators in the topological A and B twists of abelian 3d N=4\mathcal{N}=4 gauge theories, as accessed via boundary vertex operator algebras (VOA's). We focus exclusively on abelian theories. We first find a non-perturbative completion of boundary VOA's in the B twist, which start out as certain affine Lie superalebras; and we construct free-field realizations of both A and B-twist VOA's, finding an interesting interplay with the symmetry fractionalization group of bulk theories. We use the free-field realizations to establish an isomorphism between A and B VOA's related by 3d mirror symmetry. Turning to line operators, we extend previous physical classifications of line operators to include new monodromy defects and bound states. We also outline a mechanism by which continuous global symmetries in a physical theory are promoted to higher symmetries in a topological twist -- in our case, these are infinite one-form symmetries, related to boundary spectral flow, which structure the categories of lines and control abelian gauging. Finally, we establish the existence of braided tensor structure on categories of line operators, viewed as non-semisimple categories of modules for boundary VOA's. In the A twist, we obtain the categories by extending modules of symplectic boson VOA's, corresponding to gauging free hypermultiplets; in the B twist, we instead extend Kazhdan-Lusztig categories for affine Lie superalgebras. We prove braided tensor equivalences among the categories of 3d-mirror theories. All results on VOA's and their module categories are mathematically rigorous; they rely strongly on recently developed techniques to access non-semisimple extensions.Comment: 158 pages, comments welcome
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