arXiv subjects

Julian Schmidt

Publications and source records attributed to Julian Schmidt.

35 records · Page 2Linked to original sources

arXiv2023

SCENE: Reasoning about Traffic Scenes using Heterogeneous Graph Neural Networks

Understanding traffic scenes requires considering heterogeneous information about dynamic agents and the static infrastructure. In this work we propose SCENE, a methodology to encode diverse traffic scenes in heterogeneous graphs and to reason about these graphs using a heterogeneous Graph Neural Network encoder and task-specific decoders. The heterogeneous graphs, whose structures are defined by an ontology, consist of different nodes with type-specific node features and different relations with type-specific edge features. In order to exploit all the information given by these graphs, we propose to use cascaded layers of graph convolution. The result is an encoding of the scene. Task-specific decoders can be applied to predict desired attributes of the scene. Extensive evaluation on two diverse binary node classification tasks show the main strength of this methodology: despite being generic, it even manages to outperform task-specific baselines. The further application of our methodology to the task of node classification in various knowledge graphs shows its transferability to other domains.

cs.CV↗

arXiv2022

A Benchmark for Unsupervised Anomaly Detection in Multi-Agent Trajectories

Human intuition allows to detect abnormal driving scenarios in situations they never experienced before. Like humans detect those abnormal situations and take countermeasures to prevent collisions, self-driving cars need anomaly detection mechanisms. However, the literature lacks a standard benchmark for the comparison of anomaly detection algorithms. We fill the gap and propose the R-U-MAAD benchmark for unsupervised anomaly detection in multi-agent trajectories. The goal is to learn a representation of the normal driving from the training sequences without labels, and afterwards detect anomalies. We use the Argoverse Motion Forecasting dataset for the training and propose a test dataset of 160 sequences with human-annotated anomalies in urban environments. To this end we combine a replay of real-world trajectories and scene-dependent abnormal driving in the simulation. In our experiments we compare 11 baselines including linear models, deep auto-encoders and one-class classification models using standard anomaly detection metrics. The deep reconstruction and end-to-end one-class methods show promising results. The benchmark and the baseline models will be publicly available.

cs.RO↗

arXiv2022

Rotational spectroscopy of a single molecular ion at sub part-per-trillion resolution

We use quantum-logic spectroscopy (QLS) and interrogate rotational transitions of a single CaH+ ion with a highly coherent frequency comb, achieving a fractional statistical uncertainty for a transition line center of 4 x 10^-13. We also improve the resolution in measurement of the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, which we characterize and model. This allows us to determine the electric dipole moment of CaH+ by systematically displacing the ion to sample different known rf electric fields and measuring the resultant shifts in transition frequency.

physics.atom-ph↗

arXiv2022

MEAT: Maneuver Extraction from Agent Trajectories

Advances in learning-based trajectory prediction are enabled by large-scale datasets. However, in-depth analysis of such datasets is limited. Moreover, the evaluation of prediction models is limited to metrics averaged over all samples in the dataset. We propose an automated methodology that allows to extract maneuvers (e.g., left turn, lane change) from agent trajectories in such datasets. The methodology considers information about the agent dynamics and information about the lane segments the agent traveled along. Although it is possible to use the resulting maneuvers for training classification networks, we exemplary use them for extensive trajectory dataset analysis and maneuver-specific evaluation of multiple state-of-the-art trajectory prediction models. Additionally, an analysis of the datasets and an evaluation of the prediction models based on the agent dynamics is provided.

cs.CV↗

arXiv2022

CRAT-Pred: Vehicle Trajectory Prediction with Crystal Graph Convolutional Neural Networks and Multi-Head Self-Attention

Predicting the motion of surrounding vehicles is essential for autonomous vehicles, as it governs their own motion plan. Current state-of-the-art vehicle prediction models heavily rely on map information. In reality, however, this information is not always available. We therefore propose CRAT-Pred, a multi-modal and non-rasterization-based trajectory prediction model, specifically designed to effectively model social interactions between vehicles, without relying on map information. CRAT-Pred applies a graph convolution method originating from the field of material science to vehicle prediction, allowing to efficiently leverage edge features, and combines it with multi-head self-attention. Compared to other map-free approaches, the model achieves state-of-the-art performance with a significantly lower number of model parameters. In addition to that, we quantitatively show that the self-attention mechanism is able to learn social interactions between vehicles, with the weights representing a measurable interaction score. The source code is publicly available.

cs.CV↗

arXiv2020

Trapping, cooling, and photodissociation analysis of state-selected H$\_2^+$ ions produced by (3+1) multiphoton ionization

We report on the production of cold, state-selected H$_2^+$ molecular ions in a linear RF trap. The ions are produced by (3+1) resonance-enhanced multi-photon ionisation (REMPI) of H$_2$, and sympathetically cooled by laser-cooled Be$^+$ ions. After demonstrating and characterizing the REMPI process, we use photodissociation by a deep UV laser at 213~nm to verify the high vibrational purity of the produced H$_2^+$ ion samples. Moreover, the large difference between the photodissociation efficiencies of ions created in the $v=0$ and $v=1$ levels provides a way to detect a $v=0 \to 1$ transition. These results pave the way towards high-resolution vibrational spectroscopy of H$_2^+$ for fundamental metrology applications.

physics.atom-ph↗

arXiv2020

Mass-selective removal of ions from Paul traps using parametric excitation

We study a method for mass-selective removal of ions from a Paul trap by parametric excitation. This can be achieved by applying an oscillating electric quadrupole field at twice the secular frequency $ω_{\text{sec}}$ using pairs of opposing electrodes. While excitation near the resonance with the frequency $ω_{\text{sec}}$ only leads to a linear increase of the amplitude with excitation duration, parametric excitation near $2\, ω_{\text{sec}}$ results in an exponential increase of the amplitude. This enables efficient removal of ions from the trap with modest excitation voltages and narrow bandwidth, therefore substantially reducing the disturbance of ions with other charge-to-mass ratios. We numerically study and compare the mass selectivity of the two methods. In addition, we experimentally show that the barium isotopes with 136 and 137 nucleons can be removed from small ion crystals and ejected out of the trap while keeping $^{138}\text{Ba}^{+}$ ions Doppler cooled, corresponding to a mass selectivity of better than $Δm / m = 1/138$. This method can be widely applied to ion trapping experiments without major modifications, since it only requires modulating the potential of the ion trap.

physics.atom-ph↗

arXiv2019

Interior-Boundary Conditions for Many-Body Dirac Operators and Codimension-1 Boundaries

We are dealing with boundary conditions for Dirac-type operators, i.e., first order differential operators with matrix-valued coefficients, including in particular physical many-body Dirac operators. We characterize (what we conjecture is) the general form of reflecting boundary conditions (which includes known boundary conditions such as the one of the MIT bag model) and, as our main goal, of interior-boundary conditions (IBCs). IBCs are a new approach to defining UV-regular Hamiltonians for quantum field theories without smearing particles out or discretizing space. For obtaining such Hamiltonians, the method of IBCs provides an alternative to renormalization and has been successfully used so far in non-relativistic models, where it could be applied also in cases in which no renormalization method was known. A natural next question about IBCs is how to set them up for the Dirac equation, and here we take first steps towards the answer. For quantum field theories, the relevant boundary consists of the surfaces in $n$-particle configuration space $\mathbb{R}^{3n}$ on which two particles have the same location in $\mathbb{R}^3$. While this boundary has codimension 3, we focus here on the more basic situation in which the boundary has codimension 1 in configuration space. We describe specific examples of IBCs for the Dirac equation, we prove for some of these examples that they rigorously define self-adjoint Hamiltonians, and we develop the general form of IBCs for Dirac-type operators.

math-ph↗

arXiv2019

The Massless Nelson Hamiltonian and its Domain

In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form sense) of an unperturbed free operator. A similar situation occurs in Quantum Field Theory, where it is known as the ultraviolet problem. Recently, it was shown that some of the tools used in the context of point interactions can be adapted to solve the problem of directly defining a Hamiltonian for the Nelson model. This model provides a well studied example of a bosonic quantum field that is linearly coupled to nonrelativistic particles. The novel method employs so called abstract interior-boundary conditions to explicitly characterise the action and the domain of the Hamiltonian without the need for a renormalisation procedure. Here, for the first time, the method of interior-boundary conditions is applied to the massless Nelson model. Neither ultraviolet nor infrared cutoffs are needed.

math-ph↗

arXiv2018

On a Direct Description of Pseudorelativistic Nelson Hamiltonians

Abstract interior-boundary conditions (IBC's) allow for the direct description of the domain and the action of Hamiltonians for a certain class of ultraviolet-divergent models in Quantum Field Theory. The method was recently applied to models where nonrelativistic scalar particles are linearly coupled to a quantised field, the best known of which is the Nelson model. Since this approach avoids the use of ultraviolet-cutoffs, there is no need for a renormalisation procedure. Here, we extend the IBC method to pseudorelativistic scalar particles that interact with a real bosonic field. We construct the Hamiltonians for such models via abstract boundary conditions, describing their action explicitly. In addition, we obtain a detailed characterisation of their domain and make the connection to renormalisation techniques. As an example, we apply the method to two relativistic variants of Nelson's model, which have been renormalised for the first time by J. P. Eckmann and A. D. Sloan in 1970 and 1974, respectively.

math-ph↗

arXiv2018

Complex Charges, Time Reversal Asymmetry, and Interior-Boundary Conditions in Quantum Field Theory

While fundamental physically realistic Hamiltonians should be invariant under time reversal, time asymmetric Hamiltonians can occur as mathematical possibilities or effective Hamiltonians. Here, we study conditions under which non-relativistic Hamiltonians involving particle creation and annihilation, as come up in quantum field theory (QFT), are time asymmetric. It turns out that the time reversal operator T can be more complicated than just complex conjugation, which leads to the question which criteria determine the correct action of time reversal. We use Bohmian trajectories for this purpose and show that time reversal symmetry can be broken when charges are permitted to be complex numbers, where `charge' means the coupling constant in a QFT that governs the strength with which a fermion emits and absorbs bosons. We pay particular attention to the technique for defining Hamiltonians with particle creation based on interior-boundary conditions, and we find them to generically be time asymmetric. Specifically, we show that time asymmetry for complex charges occurs whenever not all charges have equal or opposite phase. We further show that, in this case, the corresponding ground states can have non-zero probability currents, and we determine the effective potential between fermions of complex charge.

quant-ph↗

arXiv2018

On Nelson-type Hamiltonians and abstract boundary conditions

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms of boundary conditions that relate sectors with different numbers of bosons. We treat both models in which the Hamiltonian may be defined as a form perturbation of the free operator, such as Fröhlich's polaron, and renormalisable models, such as the massive Nelson model.

math-ph↗

arXiv2017

Optical trapping of ion Coulomb crystals

The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher dimensional systems. Here, we report on the trapping of multiple Barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform which is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nano-scale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.

quant-ph↗

arXiv2017

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.

math-ph↗

arXiv2016

Long lifetimes in optical ion traps

We report on single Barium ions confined in a near-infrared optical dipole trap for up to three seconds in absence of any radio-frequency fields. Additionally, the lifetime in a visible optical dipole trap is increased by two orders of magnitude as compared to the state-of-the-art using an efficient repumping method. We characterize the state-dependent potentials and measure an upper bound for the heating rate in the near-infrared trap. These findings are beneficial for entering the regime of ultracold interaction in atom-ion ensembles exploiting bichromatic optical dipole traps. Long lifetimes and low scattering rates are essential to reach long coherence times for quantum simulations in optical lattices employing many ions, or ions and atoms.

quant-ph↗

arXiv2015

Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect

We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function and then study numerically the impact of time-correlated noise on the time evolution of a 1 + 1 dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.

cond-mat.stat-mech↗

arXiv2014

A far-off-resonance optical trap for a Ba$^+$ ion

Optical trapping and ions combine unique advantages of independently striving fields of research. Light fields can form versatile potential landscapes, such as optical lattices, for neutral and charged atoms, avoiding detrimental implications of established radiofrequency (rf) traps while mediating interaction via long range Coulomb forces, controlling and detecting motional and electronic states on the quantum level. Here we show optical trapping of $^{138}$Ba$^{+}$ ions in the absence of rf fields in a far-detuned dipole trap, suppressing photon scattering by three and the related recoil heating by four orders of magnitude. To enhance the prospects for optical as well as hybrid traps, we demonstrate a novel method for stray electric field compensation to a level below 9 mV/m. Our results will be relevant, for example, for ion-atom ensembles, to enable four to five orders of magnitude lower common temperatures, accessing the regime of ultracold interaction and chemistry, where quantum effects are predicted to dominate.

physics.atom-ph↗