pyfds 0.3.1 - modular field simulation tool - Claes, Leander; Webersen, Manuel

Zwischen Beutesuche und politischen Ambitionen. Die Normannen an Rhein und Maas zwischen 880 und 892 - Kamp, Hermann (Zeitschrift des Aachener Geschichtsvereins)

Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing - Delarue, Benjamin; Monclair, Daniel; Sanders, Andrew (arXiv:2403.14257)
By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique basic hyperbolic set on which the flow is conjugate to the refraction flow of Sambarino. Under the assumption of irreducibility, we utilize the work of Stoyanov to establish spectral estimates for the associated complex Ruelle transfer operators, and by way of corollary: exponential mixing, exponentially decaying error term in the prime orbit theorem, and a spectral gap for the Ruelle zeta function. With no irreducibility assumption, results of Dyatlov-Guillarmou imply the global meromorphic continuation of zeta functions with smooth weights, as well as the existence of a discrete spectrum of Ruelle-Pollicott resonances and (co)-resonant states. We apply our results to space-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds of Danciger-Gu\'eritaud-Kassel, and the Benoist-Hilbert geodesic flow for strictly convex real projective manifolds.

Quantum resonances and scattering poles of classical rank one locally symmetric spaces - Delarue, Benjamin; Hilgert, Joachim (arXiv:2403.14426)
For negatively curved symmetric spaces it is known that the poles of the scattering matrices defined via the standard intertwining operators for the spherical principal representations of the isometry group are either given as poles of the intertwining operators or as quantum resonances, i.e. poles of the meromorphically continued resolvents of the Laplace-Beltrami operator. We extend this result to classical locally symmetric spaces of negative curvature with convex-cocompact fundamental group using results of Bunke and Olbrich. The method of proof forces us to exclude the spectral parameters corresponding to singular Poisson transforms.

Error bounds for kernel-based approximations of the Koopman operator - Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl; Peitz, Sebastian; Nüske, Feliks (Applied and Computational Harmonic Analysis)
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds for the finite-data estimation error. Moreover, we derive a bound on the prediction error of observables in the RKHS using a finite Mercer series expansion. Further, assuming Koopman-invariance of the RKHS, we provide bounds on the full approximation error. Numerical experiments using the Ornstein-Uhlenbeck process illustrate our results.

Measuring collective efficacy for inclusion in a global context - Sharma , Umesh; Loreman , Tim; May , Fiona; Romano , Alessandra; Lozano , Caroline Sahli; Avramidis , Elias; Woodcock , Stuart; Subban , Pearl; Kullmann, Harry (European Journal of Special Needs Education)

Governing autonomies. Imagining responsible AI in the European armament project “Future Combat Air System” - Hälterlein, Jens (The Reality of Autonomous Weapon Systems)

Biometrische Gesichtserkennung – Technologischer Solutionismus für mehr „Sicherheit“ - Hälterlein, Jens (CILIP Bürgerrechte & Polizei)

‚Schelmische‘ Post-DDR-Romane: Ingo Schulzes „Peter Holtz“ und Lea Streisands „Hufeland, Ecke Bötzow“ - Elit, Stefan (‚Topographisches‘ Schreiben: Lea Streisand, Paderborn, Wintersemester 2022/2023)

Derivation of Miller's rule for the nonlinear optical susceptibility of a quantum anharmonic oscillator - Meyer, Maximilian Tim; Schindlmayr, Arno (Journal of Physics B: Atomic, Molecular and Optical Physics)
Miller's rule is an empirical relation between the nonlinear and linear optical coefficients that applies to a large class of materials but has only been rigorously derived for the classical Lorentz model with a weak anharmonic perturbation. In this work, we extend the proof and present a detailed derivation of Miller's rule for an equivalent quantum-mechanical anharmonic oscillator. For this purpose, the classical concept of velocity-dependent damping inherent to the Lorentz model is replaced by an adiabatic switch-on of the external electric field, which allows a unified treatment of the classical and quantum-mechanical systems using identical potentials and fields. Although the dynamics of the resulting charge oscillations, and hence the induced polarizations, deviate due to the finite zero-point motion in the quantum-mechanical framework, we find that Miller's rule is nevertheless identical in both cases up to terms of first order in the anharmonicity. With a view to practical applications, especially in the context of ab initio calculations for the optical response where adiabatically switched-on fields are widely assumed, we demonstrate that a correct treatment of finite broadening parameters is essential to avoid spurious errors that may falsely suggest a violation of Miller's rule, and we illustrate this point by means of a numerical example.