Single switch surface hopping for a model of pyrazine

The single switch trajectory surface hopping algorithm is tested for numerical simulations of a two-state three-mode model for the internal conversion of pyrazine through a conical intersection of potential energy surfaces. The algorithm is compared to two other surface hopping approaches, namely, Tully’s method of the fewest switches [J. Chem. Phys. 93, 1061 (1990)] and the method by Voronin et al. [J. Phys. Chem. A 102, 6057 (1998)] . The single switch algorithm achieves the most accurate results. Replacing its deterministic nonadiabatic branching condition by a probabilistic accept-reject criterion, one obtains the method of Voronin et al. without momentum adjustment. This probabilistic version of the single switch approach outperforms the considered algorithms in terms of accuracy, memory requirement, and runtime

Construction and validation of a rigorous surface hopping algorithm for conical crossings

This article presents and evaluates a surface hopping algorithm for time-dependent two-level Schr¨odinger systems with conically intersecting eigenvalues. The algorithm implements an asymptotic semigroup for approximating the solution’s Wigner function, that was rigorously defined and derived from the Schr¨odinger equation by two of the authors in previous work. It is applied to two-dimensional isotropic systems, which include linear Jahn-Teller Hamiltonians, and Gaussian initial data. It reproduces energy level populations and expectation values with an accuracy of two to three percent

Energy Level Crossings in Molecular Dynamics

Energy level crossings are the landmarks that separate classical from quantum mechanical modeling of molecular systems. They induce non-adiabatic transitions between the otherwise adiabatically decoupled electronic level spaces. This review covers results on the analysis of propagation through level crossings of codimension two, a mathematical justification of surface hopping algorithms, and a spectral study of a linear isotropic system

Wigner Measure Propagation and Conical Singularity for General Initial Data

We study the evolution of Wigner measures of a family of solutions of a Schr\"odinger equation with a scalar potential displaying a conical singularity. Under a genericity assumption, classical trajectories exist and are unique, thus the question of the propagation of Wigner measures along these trajectories becomes relevant. We prove the propagation for general initial data.Comment: 24 pages, 1 figur

In vivo imaging of murine endocrine islets of Langerhans with extended-focus optical coherence microscopy

Aims/hypothesis: Structural and functional imaging of the islets of Langerhans and the insulin-secreting beta cells represents a significant challenge and a long-lasting objective in diabetes research. In vivo microscopy offers a valuable insight into beta cell function but has severe limitations regarding sample labelling, imaging speed and depth, and was primarily performed on isolated islets lacking native innervations and vascularisation. This article introduces extended-focus optical coherence microscopy (xfOCM) to image murine pancreatic islets in their natural environment in situ, i.e. in vivo and in a label-free condition. Methods: Ex vivo measurements on excised pancreases were performed and validated by standard immunohistochemistry to investigate the structures that can be observed with xfOCM. The influence of streptozotocin on the signature of the islets was investigated in a second step. Finally, xfOCM was applied to make measurements of the murine pancreas in situ and in vivo. Results: xfOCM circumvents the fundamental physical limit that trades lateral resolution for depth of field, and achieves fast volumetric imaging with high resolution in all three dimensions. It allows label-free visualisation of pancreatic lobules, ducts, blood vessels and individual islets of Langerhans ex vivo and in vivo, and detects streptozotocin-induced islet destruction. Conclusions/interpretation: Our results demonstrate the potential value of xfOCM in high-resolution in vivo studies to assess islet structure and function in animal models of diabetes, aiming towards its use in longitudinal studies of diabetes progression and islet transplant

Complexity, transparency and time pressure: practical insights into science communication in times of crisis

A global crisis such as the COVID-19 pandemic that started in early 2020 poses significant challenges for how research is conducted and communicated. We present four case studies from the perspective of an interdisciplinary research institution that switched to “corona-mode” during the first two months of the crisis, focussing all its capacities on COVID-19-related issues, communicating to the public directly and via media, as well as actively advising the national government. The case studies highlight the challenges posed by the increased time pressure, high demand for transparency, and communication of complexity and uncertainty. The article gives insights into how these challenges were addressed in our research institution and how science communication in general can be managed during a crisis

Fast focus field calculations

We present a fast calculation of the electromagnetic field near the focus of an objective with a high numerical aperture (NA). Instead of direct integration, the vectorial Debye diffraction integral is evaluated with the fast Fourier transform for calculating the electromagnetic field in the entire focal region. We generalize this concept with the chirp z transform for obtaining a flexible sampling grid and an additional gain in computation speed. Under the conditions for the validity of the Debye integral representation, our method yields the amplitude, phase and polarization of the focus field for an arbitrary paraxial input field on the objective. We present two case studies by calculating the focus fields of a 40×1.20 NA water immersion objective for different amplitude distributions of the input field, and a 100×1.45 NA oil immersion objective containing evanescent field contributions for both linearly and radially polarized input fields