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Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC literature, which is given by the linear interpolation in the space of energies. Inspired by Sequential Monte Carlo, we alternate between deterministic time steps from the TT representation of the flow field and stochastic steps, which include Langevin and resampling steps. These adjust the relative weights of the different modes of the target distribution and anneal to the correct path distribution. We showcase the efficiency of our method on multiple numerical examples.

Accurate 3D object detection is vital for automated driving. While lidar sensors are well suited for this task, they are expensive and have limitations in adverse weather conditions. 3+1D imaging radar sensors offer a cost-effective, robust alternative but face challenges due to their low resolution and high measurement noise. Existing 3+1D imaging radar datasets include radar and lidar data, enabling cross-modal model improvements. Although lidar should not be used during inference, it can aid the training of radar-only object detectors. We explore two strategies to transfer knowledge from the lidar to the radar domain and radar-only object detectors: 1. multi-stage training with sequential lidar point cloud thin-out, and 2. cross-modal knowledge distillation. In the multi-stage process, three thin-out methods are examined. Our results show significant performance gains of up to 4.2 percentage points in mean Average Precision with multi-stage training and up to 3.9 percentage points with knowledge distillation by initializing the student with the teacher's weights. The main benefit of these approaches is their applicability to other 3D object detection networks without altering their architecture, as we show by analyzing it on two different object detectors. Our code is available at https://github.com/rst-tu-dortmund/lerojd, Comment: Accepted for publication as ECCV 2024

A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling best-in-class methods such as low-rank tensor regression in terms of accuracy and complexity. The neural network is trained with data on adaptively refined finite element meshes, thus reducing data complexity significantly. Error control is achieved by using a reliable finite element a posteriori error estimator, which is also provided as input to the neural network. The proposed U-Net architecture with CNN layers mimics a classical finite element multigrid algorithm. It can be shown that the CNN efficiently approximates all operations required by the solver, including the evaluation of the residual-based error estimator. In the CNN, a culling mask set-up according to the local corrections due to refinement on each mesh level reduces the overall complexity, allowing the network optimization with localized fine-scale finite element data. A complete convergence and complexity analysis is carried out for the adaptive multilevel scheme, which differs in several aspects from previous non-adaptive multilevel CNN. Moreover, numerical experiments with common benchmark problems from Uncertainty Quantification illustrate the practical performance of the architecture.

This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number.

This paper is concerned with collective variables, or reaction coordinates, that map a discrete-in-time Markov process $X_n$ in $\mathbb{R}^d$ to a (much) smaller dimension $k \ll d$. We define the effective dynamics under a given collective variable map $\xi$ as the best Markovian representation of $X_n$ under $\xi$. The novelty of the paper is that it gives strict criteria for selecting optimal collective variables via the properties of the effective dynamics. In particular, we show that the transition density of the effective dynamics of the optimal collective variable solves a relative entropy minimization problem from certain family of densities to the transition density of $X_n$. We also show that many transfer operator-based data-driven numerical approaches essentially learn quantities of the effective dynamics. Furthermore, we obtain various error estimates for the effective dynamics in approximating dominant timescales / eigenvalues and transition rates of the original process $X_n$ and how optimal collective variables minimize these errors. Our results contribute to the development of theoretical tools for the understanding of complex dynamical systems, e.g. molecular kinetics, on large timescales. These results shed light on the relations among existing data-driven numerical approaches for identifying good collective variables, and they also motivate the development of new methods.

Recent discussions on enrollment in higher education have centered around the "Enrollment Cliff." The notion holds that due to changing demographics, colleges and universities across the U.S. will see a dramatic decline in enrollment starting in 2025. The enrollment cliff poses legitimate challenges to schools around the country. Schools who are savvy in their response to the cliff can better position themselves for student population decreases and increased competition. Prioritizing student success may help the schools most vulnerable to shifting demographics navigate the years ahead.

The generation of terawatt (TW) near-single-cycle laser pulses is of high interest for applications including attosecond science. Here we demonstrate a three-stage post-compression scheme in a non-guided geometry using He as the nonlinear medium, resulting in the generation of multi-mJ pulses with a duration of 3.7 fs. Key features of this approach are its simplicity, robustness and high stability, making it ideally suited for highly demanding applications such as attosecond-pump attosecond-probe spectroscopy (APAPS). This is demonstrated by performing two-color APAPS in Ar and Ne, where both simultaneous and sequential two-photon absorption are observed. Our approach is scalable to multi-TW powers., Comment: 9 pages, 4 figures

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve training efficiency and to enable control of the approximation error, the network mimics an adaptive finite element method (AFEM). It outputs a coarse grid solution and a series of corrections as produced in an AFEM, allowing a tracking of the error decay over successive layers of the network. The observed errors are measured by a reliable residual based a posteriori error estimator, enabling the reduction to only few parameters for the approximation in the output of the network. This leads to a problem adapted representation of the solution on locally refined grids. Furthermore, each solution of the AFEM is discretized in a hierarchical basis. For the architecture, convolutional neural networks (CNNs) are chosen. The hierarchical basis then allows to handle sparse images for finely discretized meshes. Additionally, as corrections on finer levels decrease in amplitude, i.e., importance for the overall approximation, the accuracy of the network approximation is allowed to decrease successively. This can either be incorporated in the number of generated high fidelity samples used for training or the size of the network components responsible for the fine grid outputs. The architecture is described and preliminary numerical examples are presented.

We determine the uncorrelated modes that characterize the fluctuations in a semi-realistic model for the initial state of high-energy nuclear collisions, consisting of hot spots whose positions are distributed independently. Varying the number of hot spots, their size, and the weights with which they contribute to the initial state, we find that the parameter that has the largest influence on the relative importance of the fluctuation modes is the source size, with more extended hot spots leading to a more marked predominance of the principal modes., Comment: v2: published version (16 pages, 10 figures) + supplemental material: 16 figures on 15 pages

The thermal plasma filling the early universe generated a stochastic gravitational wave background that peaks in the microwave frequency range today. If the graviton production rate is expressed as a series in a fine-structure constant, $\alpha$, and the temperature over the Planck mass, $T^2_{ } / m_{\rm pl}^2$, then the lowest-order contributions come from single ($\sim \alpha T^2_{ }/m_{\rm pl}^2$) and double ($\sim T^4_{ }/m_{\rm pl}^4$) graviton production via $2\to 2$ scatterings. We show that in the Standard Model, single-graviton production dominates if the maximal temperature is smaller than $4\times 10^{18}_{ }$ GeV. This justifies previous calculations which relied solely on single-graviton production. We mention Beyond the Standard Model scenarios in which the single and double-graviton contributions could be of comparable magnitudes. Finally, we elaborate on what these results imply for the range of applicability of General Relativity as an effective theory., Comment: 16 pages. v2: clarifications added

We report on the mechanism of energy transfer in van der Waals heterostructures of the two-dimensional semiconductor WS$_2$ and graphene with varying interlayer distances, achieved through spacer layers of hexagonal boron nitride (hBN). We record photoluminescence and reflection spectra at interlayer distances between 0.5 nm and 5.8 nm (0-16 hBN layers). We find that the energy transfer is dominated by states outside the light cone, indicative of a F\"orster transfer process, with an additional contribution from a Dexter process at 0.5 nm interlayer distance. We find that the measured dependence of the luminescence intensity on interlayer distances above 1 nm can be quantitatively described using recently reported values of the F\"orster transfer rates of thermalized charge carriers. At smaller interlayer distances, the experimentally observed transfer rates exceed the predictions and furthermore depend on excess energy as well as on excitation density. Since the transfer probability of the F\"orster mechanism depends on the momentum of electron-hole pairs, we conclude that at these distances, the transfer is driven by non-thermalized charge carrier distributions.

The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method's learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available.

We sample from a given target distribution by constructing a neural network which maps samples from a simple reference, e.g. the standard normal distribution, to samples from the target. To that end, we propose using a neural network architecture inspired by the Langevin Monte Carlo (LMC) algorithm. Based on LMC perturbation results, we show approximation rates of the proposed architecture for smooth, log-concave target distributions measured in the Wasserstein-$2$ distance. The analysis heavily relies on the notion of sub-Gaussianity of the intermediate measures of the perturbed LMC process. In particular, we derive bounds on the growth of the intermediate variance proxies under different assumptions on the perturbations. Moreover, we propose an architecture similar to deep residual neural networks and derive expressivity results for approximating the sample to target distribution map.

The homogeneous precession domain (HPD) of superfluid $^{3}$He has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling $g_{aNN}$ competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a non-stationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching $g_{aNN} \sim 10^{-12}$ GeV$^{-1}$ across a decade in axion mass., Comment: 15+7 pages, 9 figures; v2: schematic illustration added, specified details of measurement scheme. Version published in PRD

We present a numerical algorithm for the computation of invariant Ruelle distributions on convex co-compact hyperbolic surfaces. This is achieved by exploiting the connection between invariant Ruelle distributions and residues of meromorphically continued weighted zeta functions established by the authors together with Barkhofen (2021). To make this applicable for numerics we express the weighted zeta as the logarithmic derivative of a suitable parameter dependent Fredholm determinant similar to Borthwick (2014). As an additional difficulty our transfer operator has to include a contracting direction which we account for with techniques developed by Rugh (1992). We achieve a further improvement in convergence speed for our algorithm in the case of surfaces with additional symmetries by proving and applying a symmetry reduction of weighted zeta functions., Comment: 52 pages, 25 figures

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios., Comment: 16 pages + 2 pages appendix, 5 figures. Submitted to Mathematical Biosciences

High-dimensional metastable molecular system can often be characterised by a few features of the system, i.e. collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of infinitesimal generator or transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples., Comment: revised version, 14 pages; This is an extended version of the paper submitted to Proceedings in Applied Mathematics and Mechanics (PAMM) 2023

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.

The ability to perform attosecond-pump attosecond-probe spectroscopy (APAPS) is a longstanding goal in ultrafast science. While first pioneering experiments demonstrated the feasibility of APAPS, the low repetition rates (10-120 Hz) and the large footprints of existing setups have so far hindered the widespread exploitation of APAPS. Here we demonstrate two-color APAPS using a commercial laser system at 1 kHz, straightforward post-compression in a hollow-core fiber and a compact high-harmonic generation (HHG) setup. The latter enables the generation of intense extreme-ultraviolet (XUV) pulses by using an out-of-focus HHG geometry and by exploiting a transient blueshift of the driving laser in the HHG medium. Near-isolated attosecond pulses are generated, as demonstrated by one-color and two-color XUV-pump XUV-probe experiments. Our concept allows selective pumping and probing on extremely short timescales and permits investigations of fundamental processes that are not accessible by other pump-probe techniques., Comment: 8 pages, 5 figures

The most widely used method for obtaining high-quality two-dimensional materials is through mechanical exfoliation of bulk crystals. Manual identification of suitable flakes from the resulting random distribution of crystal thicknesses and sizes on a substrate is a time-consuming, tedious task. Here, we present a platform for fully automated scanning, detection, and classification of two-dimensional materials, the source code of which we make openly available. Our platform is designed to be accurate, reliable, fast, and versatile in integrating new materials, making it suitable for everyday laboratory work. The implementation allows fully automated scanning and analysis of wafers with an average inference time of 100 ms for images of 2.3 Mpixels. The developed detection algorithm is based on a combination of the flakes' optical contrast toward the substrate and their geometric shape. We demonstrate that it is able to detect the majority of exfoliated flakes of various materials, with an average recall (AR50) between 67% and 89%. We also show that the algorithm can be trained with as few as five flakes of a given material, which we demonstrate for the examples of few-layer graphene, WSe$_2$, MoSe$_2$, CrI$_3$, 1T-TaS$_2$ and hexagonal BN. Our platform has been tested over a two-year period, during which more than $10^6$ images of multiple different materials were acquired by over 30 individual researchers.

A direct detection of black hole formation in neutron star mergers would provide invaluable information about matter in neutron star cores and finite temperature effects on the nuclear equation of state. We study black hole formation in neutron star mergers using a set of 190 numerical relativity simulations consisting of long-lived and black-hole-forming remnants. The postmerger gravitational-wave spectrum of a long-lived remnant has greatly reduced power at a frequency $f$ greater than $f_{\rm peak}$, for $f \gtrsim 4\,\rm kHz$, with $f_{\rm peak} \in [2.5, 4]\,\rm kHz$. On the other hand, black-hole-forming remnants exhibit excess power in the same large $f$ region and manifest exponential damping in the time domain characteristic of a quasinormal mode. We demonstrate that the gravitational-wave signal from a collapsed remnant is indeed a quasinormal ringing. We report on the opportunity for direct detections of black hole formation with next-generation gravitational-wave detectors such as Cosmic Explorer and Einstein Telescope and set forth the tantalizing prospect of such observations up to a distance of 100 Mpc for an optimally oriented and located source with an SNR of 4.

Optical micro-spectroscopy is an invaluable tool for studying and characterizing samples ranging from classical semiconductors to low-dimensional materials and heterostructures. To date, most implementations are based on point-scanning techniques, which are flexible and reliable, but slow. Here, we describe a setup for highly parallel acquisition of hyperspectral reflection and photoluminescence microscope images using a push-broom technique. Spatial as well as spectral distortions are characterized and their digital corrections are presented. We demonstrate close-to diffraction-limited spatial imaging performance and a spectral resolution limited by the spectrograph. The capabilities of the setup are demonstrated by recording a hyperspectral photoluminescence map of a CVD-grown MoSe$_2$-WSe$_2$ lateral heterostructure, from which we extract the luminescence energies, intensities and peak widths across the interface.

In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence X-Ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results., Comment: Submitted to Metrologia Focus Issue on MATHMET 2023 conference

The problem of robust controller synthesis for plants affected by structured uncertainty, captured by integral quadratic constraints, is discussed. The solution is optimized towards a worst-case white noise rejection specification, which is a generalization of the standard $\mathcal{H}_2$-norm to the robust setting including possibly non-LTI uncertainty. Arbitrary structural constraints can be imposed on the control solution, making this method suitable for distributed systems. The nonsmooth optimization algorithm used to solve the robust synthesis problem operates directly in the frequency domain, eliminating scalability issues for complex systems and providing local optimality certificates. The method is evaluated using a literature example and a real-world system using a novel implementation of a robust $\mathcal{H}_2$-performance bound., Comment: 6 pages, 4 figures, accepted for IFAC World Congress 2023. Shortened to satisfy submission page limit (removed one numerical example and compressed remaining text)

Superconducting cavities can operate analogously to Weber bar detectors of gravitational waves, converting mechanical to electromagnetic energy. The significantly reduced electromagnetic noise results in increased sensitivity to high-frequency signals well outside the bandwidth of the lowest mechanical resonance. In this work, we revisit such signals of gravitational waves and demonstrate that a setup similar to the existing "MAGO" prototype, operating in a scanning or broadband manner, could have sensitivity to strains of $\sim 10^{-22} - 10^{-18}$ for frequencies of $\sim 10 \ \text{kHz} - 1 \ \text{GHz}$., Comment: 23 pages + 11 pages of appendices

At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotransmission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate-limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient changes leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior and asymptotic periodicity of the ODE-solution., Comment: 30 pages, 12 Figures

Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel opinion dynamics model that accounts for these different roles, namely that media and influencers change their own positions on slower time scales than individuals, while influencers dynamically gain and lose followers. Numerical simulations show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. Mean-field approximations by partial differential equations reproduce this dynamic. Based on the mean-field model, we study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, we demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to better understanding the different roles and strategies in the increasingly complex information ecosystem and their impact on public opinion formation.

The environment contributes to the screening of Coulomb interactions in two-dimensional semiconductors. This can potentially be exploited to tailor material properties as well as for sensing applications. Here, we investigate the tuning of the band gap and the exciton binding energy in the two-dimensional semiconductor WS$_2$ via the external dielectric screening. Embedding WS$_2$ in van der Waals heterostructures with graphene and hBN spacers of thicknesses between one and 16 atomic layers, we experimentally determine both energies as a function of the \WS-to-graphene interlayer distance. We find that the modification to the band gap as well as the exciton binding energy are well described by a one-over-distance dependence, with a significant effect remaining at several nm distance, at which the two layers are electrically well isolated. This observation is explained by a screening arising from an image charge induced by the graphene layer. Furthermore, we find that the effectiveness of graphene to screen Coulomb interactions in nearby WS$_2$ depends on its doping level and can therefore be controlled via the electric field effect. We determine that, at room temperature, it is modified by approximately 20\% for charge carrier densities of $2\times10^{12}$ cm$^{-2}$.

The thermal plasma in the early universe produced a stochastic gravitational wave (GW) background, which peaks today in the microwave regime and was dubbed the cosmic gravitational microwave background (CGMB). In previous works only single graviton production processes that contribute to the CGMB have been considered. Here we also investigate graviton pair production processes and show that these can lead to a significant contribution if the ratio between the maximum temperature and the Planck mass, $T_{\rm max}/m_{\rm p}$, divided by the internal coupling in the heat bath is large enough. As the dark matter freeze-in production mechanism is conceptually very similar to the GW production mechanism from the primordial thermal plasma, we refer to the latter as ``GW freeze-in production''. We show that quantum gravity effects appear in single graviton production and are smaller by a factor $(T_{\rm max}/m_{\rm p})^2$ than the leading order contribution. In our work we explicitly compute the CGMB spectrum within a scalar model with quartic interaction., Comment: 18 pages, 6 figures (matches version published in Phys. Rev. D)

In the presence of a background magnetic field, axion dark matter induces an electric field and can thus excite phonon-polaritons in suitable materials. We revisit the calculation of the axion-photon conversion power output from such materials, accounting for finite volume effects, and material losses. Our calculation shows how phonon-polaritons can be converted to propagating photons at the material boundary, offering a route to detecting the signal. Using the dielectric functions of GaAs, Al$_2$O$_3$, and SiO$_2$, a fit to our loss model leads to a signal of lower magnitude than previous calculations. We demonstrate how knowledge of resonances in the dielectric function can directly be used to calculate the sensitivity of any material to axion dark matter. We argue that a combination of low losses encountered at $\mathcal{O}(1)$ K temperatures and near future improvements in detector dark count allow one to probe the QCD axion in the mass range $m_a\approx 100$ meV. This provides further impetus to examine novel materials and further develop detectors in the THz regime. We also discuss possible tuning methods to scan the axion mass., Comment: 13 pages, 2 figures, 1 table, comments welcome. Updated journal version

Axions and axion-like particles may couple to nuclear spins like a weak oscillating effective magnetic field, the "axion wind." Existing proposals for detecting the axion wind sourced by dark matter exploit analogies to nuclear magnetic resonance (NMR) and aim to detect the small transverse field generated when the axion wind resonantly tips the precessing spins in a polarized sample of material. We describe a new proposal using the homogeneous precession domain (HPD) of superfluid helium-3 as the detection medium, where the effect of the axion wind is a small shift in the precession frequency of a large-amplitude NMR signal. We argue that this setup can provide broadband detection of multiple axion masses simultaneously, and has competitive sensitivity to other axion wind experiments such as CASPEr-Wind at masses below $10^{-7}$ eV by exploiting precision frequency metrology in the readout stage., Comment: v2: typos fixed and references added. v1: 5+1 pages, 3 figures

Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article, we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high-dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.

Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.

High-harmonic generation (HHG) normally requires a careful adjustment of the driving laser intensity (typically $10^{14} - 10^{15}$ W/cm$^2$) and gas medium parameters to enable good phase matching conditions. In contrast with conventional wisdom, we present experimental results indicating phase-matched HHG in all rare gases, using a high-density medium and a driver laser intensity of around $10^{16}$ W/cm$^2$. The experimental results are corroborated by theoretical simulations, which indicate that ionization-induced self-phase modulation and plasma defocusing self-regulate the driver laser intensity to a level that is appropriate for good phase matching. A ten-fold broadening of the NIR spectrum is observed, which results in the generation of continuous spectra from $18-140$ eV in spite of using 50-fs-long driving pulses. The presented scheme represents a simple and versatile concept for the generation of XUV and soft X-ray continua, which are ideally suited for transient absorption and reflection spectroscopy., Comment: 5 pages, 5 figures

In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems., Comment: minor corrections

The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations (RDPDEs). Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas, A. Mielke: Modeling of chemical reactions systems with detailed balance using gradient structures. J. Stat. Phys. (181), 2257-2303 (2020)] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.

We give a detailed treatment of electromagnetic signals generated by gravitational waves (GWs) in resonant cavity experiments. Our investigation corrects and builds upon previous studies by carefully accounting for the gauge dependence of relevant quantities. We work in a preferred frame for the laboratory, the proper detector frame, and show how to resum short-wavelength effects to provide analytic results that are exact for GWs of arbitrary wavelength. This formalism allows us to firmly establish that, contrary to previous claims, cavity experiments designed for the detection of axion dark matter only need to reanalyze existing data to search for high-frequency GWs with strains as small as $h\sim 10^{-22}-10^{-21}$. We also argue that directional detection is possible in principle using readout of multiple cavity modes. Further improvements in sensitivity are expected with cutting-edge advances in superconducting cavity technology., Comment: 20 pages + appendix, 7 figures, matches journal version

We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples.

In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems., Comment: 25 pages, 4 figures; with an appendix by Sonja Barkhofen

In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is able to find multiple leading eigenpairs by solving a single training task. It is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide., Comment: revision with minor changes

The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules.For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators., Comment: 11 pages, 4 figures with 2 pages of Supporting info; published in the Journal of Physical Chemistry Letters

The modeling and simulation of stochastic reaction-diffusion processes is a topic of steady interest that is approached with a wide range of methods. \rev{At the level of particle-resolved descriptions, where chemical reactions are coupled to the spatial diffusion of individual particles, there exist comprehensive numerical simulation schemes, while the corresponding mathematical formalization is relatively underdeveloped. The aim of this paper is to provide a framework to systematically formulate the probabilistic evolution equation, termed chemical diffusion master equation (CDME), that governs particle-based stochastic reaction-diffusion processes. To account for the non-conserved and unbounded particle number of this type of open systems, we employ a classical analogue of the quantum mechanical Fock space that contains the symmetrized probability densities of the many-particle configurations in space. Following field-theoretical ideas of second quantization, we introduce creation and annihilation operators that act on single-particle densities and provide natural representations of symmetrized probability densities as well as of reaction and diffusion operators. These operators allow us to consistently and systematically formulate the CDME for arbitrary reaction schemes. The resulting form of the CDME further serves as the foundation to derive more coarse-grained descriptions of reaction-diffusion dynamics. In this regard, we show that a discretization of the evolution equation by projection onto a Fock subspace generated by a finite set of single-particle densities leads to a generalized form of the well-known reaction-diffusion master equation, which supports non-local reactions between grid cells and which converges properly in the continuum limit.

We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane., Comment: Revised version with new appendix on vector bundles. 36 pages, 8 figures

Multi-electron dynamics in atoms and molecules very often occur on sub- to few-femtosecond timescales. The available intensities of extreme-ultraviolet (XUV) attosecond pulses have previously only allowed the time-resolved investigation of two-photon, two-electron interactions. Here we demonstrate attosecond control over double and triple ionization of argon atoms involving the absorption of up to five XUV photons. In an XUV-pump XUV-probe measurement using a pair of attosecond pulse trains (APTs), the Ar$^{2+}$ ion yield exhibits a weak delay dependence, showing that its generation predominantly results from the sequential emission of two electrons by photoabsorption from the two APTs. In contrast, the Ar$^{3+}$ ion yield exhibits strong modulations as a function of the delay, which is a clear signature of the simultaneous absorption of at least two XUV photons. The experimental results are well reproduced by numerical calculations that provide detailed insights into the ionization dynamics. Our results open up new opportunities for the investigation and control of multi-electron dynamics and complex electron correlation mechanisms on extremely short timescales., Comment: 8 pages, 4 figures

Reaction Coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function and reduced models based on them guarantee very good approximation of the long-term dynamics of the original high-dimensional process. We show that, for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, the numerical effort required to evaluate the loss function scales only with the complexity of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.

We report on a compact and spectrally intense extreme-ultraviolet (XUV) source, which is based on high-harmonic generation (HHG) driven by 395 nm pulses. In order to minimize the XUV virtual source size and to maximize the XUV flux, HHG is performed several Rayleigh lengths away from the driving laser focal plane in a high-density gas jet. As a result, a high focused XUV intensity of $5 \times 10^{13}$ W/cm$^2$ is achieved, using a beamline with a length of only two meters and a modest driving laser pulse energy of 3 mJ. The high XUV intensity is demonstrated by performing a nonlinear ionization experiment in argon, using an XUV spectrum that is dominated by a single harmonic at 22 eV. Ion charge states up to Ar$^{3+}$ are observed, which requires the absorption of at least four XUV photons. The high XUV intensity and the narrow bandwidth are ideally suited for a variety of applications including photoelectron spectroscopy, the coherent control of resonant transitions and the imaging of nanoscale structures., Comment: 11 pages, 4 figures