We provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretized circle for a process in which pairs of particles occupying the same site simultaneously jump to the two neighboring sites; the reverse process involves pairs of particles at adjacent sites simultaneously jumping back to the site located between them. Depending on the rates, in the vanishing-mesh-size limit we obtain either the classical DLSS equation or a variant with nonlinear mobility of power type. Via EDP convergence, we identify the limiting gradient structure to be driven by entropy with respect to a generalization of diffusive transport with nonlinear mobility. Interestingly, the DLSS equation with power-type mobility shares qualitative similarities with the fast diffusion and porous medium equation, since we find traveling wave solutions with algebraic tails or compactly supported polynomials, respectively.

We investigate the motion of test particles in quantum-gravitational backgrounds by introducing the concept of q--desics, quantum-corrected analogs of classical geodesics. Unlike standard approaches that rely solely on the expectation value of the spacetime metric, our formulation is based on the expectation value of quantum operators, such as the the affine connection-operator. This allows us to capture richer geometric information. We derive the q--desic equation using both Lagrangian and Hamiltonian methods and apply it to spherically symmetric static backgrounds obtained from canonical quantum gravity. Exemplary results include, light-like radial motion and circular motion with quantum gravitational corrections far above the Planck scale. This framework provides a refined description of motion in quantum spacetimes and opens new directions for probing the interface between quantum gravity and classical general relativity.

Autonomous quantum machines (AQMs) execute tasks without requiring time-dependent external control. Motivations for AQMs include the restrictions imposed by classical control on quantum machines' coherence times and geometries. Most AQM work is theoretical and abstract; yet an experiment recently demonstrated AQMs' usefulness in qubit reset, crucial to quantum computing. To further reduce quantum computing's classical control, we propose realizations of (fully and partially) quantum-autonomous gates on three platforms: Rydberg atoms, trapped ions, and superconducting qubits. First, we show that a Rydberg-blockade interaction or an ultrafast transition can quantum-autonomously effect entangling gates on Rydberg atoms. One can perform $Z$ or entangling gates on trapped ions mostly quantum-autonomously, by sculpting a linear Paul trap or leveraging a ring trap. Passive lasers control these gates, as well as the Rydberg-atom gates, quantum-autonomously. Finally, circuit quantum electrodynamics can enable quantum-autonomous $Z$ and $XY$ gates on superconducting qubits. The gates can serve as building blocks for (fully or partially) quantum-autonomous circuits, which may reduce classical-control burdens.

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated hyperparameter. The method estimates the hyperparameters by marginalizing out the weights and performing (marginalized) maximum likelihood (ML) estimation. SBL returns many hyperparameter estimates to diverge to infinity, effectively setting the estimates of the corresponding weights to zero (i.e., pruning the corresponding weights from the model) and thereby yielding a sparse estimate of the weight vector. In this letter, we analyze the marginal likelihood as function of a single hyperparameter while keeping the others fixed, when the Gaussian assumptions on the noise samples and the weight distribution that underlies the derivation of SBL are weakened. We derive sufficient conditions that lead, on the one hand, to finite hyperparameter estimates and, on the other, to infinite ones. Finally, we show that in the Gaussian case, the two conditions are complementary and coincide with the pruning condition of fast SBL (F-SBL), thereby providing additional insights into this algorithm.

The Bodirsky-Kára classification of temporal constraint languages stands as one of the earliest and most seminal complexity classifications within infinite-domain Constraint Satisfaction Problems (CSPs), yet it remains one of the most mysterious in terms of algorithms and algebraic invariants for the tractable cases. We show that those temporal languages which do not pp-construct EVERYTHING (and thus by the classification are solvable in polynomial time) have, in fact, very limited expressive power as measured by the graphs and hypergraphs they can pp-interpret. This limitation yields many previously unknown algebraic consequences, while also providing new, uniform proofs for known invariance properties. In particular, we show that such temporal constraint languages admit $4$-ary pseudo-Siggers polymorphisms -- a result that sustains the possibility that the existence of such polymorphisms extends to the much broader context of the Bodirsky-Pinsker conjecture.

The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and - more generally - of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA.

In the present paper we give very simple general statements which deal with approximation of a real number by rationals and are related to isolation phenomenon. In particular we study functions f(x)>f_1(x)>0 such that existence of solutions $\frac{p}{q}$ of Diophantine inequality \left| \alpha -\frac{p}{q}\right|< \frac{f(q)}{q^2} leads to the existence of solutions of inequality \left| \alpha -\frac{p}{q}\right|< \frac{f_1(q)}{q^2} .

This is an introduction to the volume of Lecture Notes in Physics on "Strongly interacting matter in magnetic fields". The volume combines contributions written by a number of experts on different aspects of the problem. The response of QCD matter to intense magnetic fields has attracted a lot of interest recently. On the theoretical side, this interest stems from the possibility to explore the plethora of novel phenomena arising from the interplay of magnetic field with QCD dynamics. On the experimental side, the interest is motivated by the recent results on the behavior of quark-gluon plasma in a strong magnetic field created in relativistic heavy ion collisions at RHIC and LHC. The purpose of this introduction is to provide a brief overview and a guide to the individual contributions where these topics are covered in detail.

High- and medium-entropy nitride coatings from the Cr-Hf-Mo-Ta-W-N system were studied using ab initio calculations and experiments to clarify the role of entropy and individual elements in phase stability, microstructure, and high-temperature behaviour. Formation energy calculations indicated that nitrogen vacancies stabilise the cubic (fcc) phase, with hafnium and tantalum acting as strong stabilisers, while tungsten destabilises the lattice. Coatings were deposited by reactive magnetron sputtering at approx. 50C (AT) and approx. 580C (HT). All exhibited columnar fcc structures; high-temperature deposition produced denser coatings, lower nitrogen content, and larger crystallites, resulting in higher hardness and elastic modulus. Thermal stability was tested up to 1200C on Si and oxidation at 1400C on sapphire. AT coatings failed early, while most HT coatings endured. Nitrogen loss less than 10 at.% at 1000C was critical for survival. TEM revealed tungsten segregation and HfO2 formation, while fcc nitride remained dominant. Ta enrichment proved essential for superior thermal and oxidation stability.

A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon $\sigma$-term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly-represented valence-quark relative to that of the doubly-represented quark. Regarding the proton $\sigma$-term and that part of the proton mass which owes to explicit chiral symmetry breaking, with a realistic $d$-$u$ mass splitting the singly-represented $d$-quark contributes 37% more than the doubly-represented $u$-quark; and in connection with the proton's tensor charges, $\delta_T u$, $\delta_T d$, the ratio $\delta_T d/\delta_T u$ is 18% larger than anticipated from simple quark models. Of particular note, the size of $\delta_T u$ is a sensitive measure of the strength of dynamical chiral symmetry breaking; and $\delta_T d$ measures the amount of axial-vector diquark correlation within the proton, vanishing if such correlations are absent.

The NUCLEUS experiment aims to detect coherent elastic neutrino-nucleus scattering of reactor antineutrinos on CaWO$_4$ targets in the fully coherent regime, using gram-scale cryogenic calorimeters. The experimental apparatus will be installed at the Chooz nuclear power plant in France, in the vicinity of two 4.25 GW$_{\text{th}}$ reactor cores. This work presents results from the commissioning of an essential version of the experiment at the shallow Underground Laboratory of the Technical University of Munich. For the first time, two cryogenic target detectors were tested alongside active and passive shielding systems. Over a period of two months all detector subsystems were operated with stable performance. Background measurements were conducted, providing important benchmarks for the modeling of background sources at the reactor site. Finally, we present ongoing efforts to upgrade the detector systems in preparation for a technical run at Chooz in 2026, and highlight the remaining challenges to achieving neutrino detection.

We calculate the radiative corrections of order O(alpha E_e/m_N) as next-to-leading order corrections in the large nucleon mass expansion to Sirlin's radiative corrections of order O(alpha/pi) to the neutron lifetime. The calculation is carried out within a quantum field theoretic model of strong low-energy pion--nucleon interactions described by the linear sigma-model (LsM) with chiral SU(2)xSU(2) symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with SU(2)_L x U(1)_Y symmetry of the Standard Electroweak Model (SEM). Such a quantum field theoretic model is some kind a hadronized version of the Standard Model (SM). From a gauge invariant set of the Feynman diagrams with one-photon exchanges we reproduce Sirlin's radiative corrections of order O(alpha/pi), calculated to leading order in the large nucleon mass expansion, and calculate next-to-leading corrections of order O(alpha E_e/m_N). This confirms Sirlin's confidence level of the radiative corrections O(alpha E_e/m_N). The contributions of the LsM are taken in the limit of the infinite mass of the scalar isoscalar sigma-meson. In such a limit the LsM reproduces the results of the current algebra (Weinberg, Phys. Rev. Lett. {\bf 18}, 188 (1967)) in the form of effective chiral Lagrangians of pion-nucleon interactions with non--linear realization of chiral SU(2)xSU(2) symmetry. In such a limit the L$\sigma$M is also equivalent to Gasser-Leutwyler's chiral quantum field theory or chiral perturbation theory (ChPT) with chiral SU(2)xSU(2)symmetry and the exponential parametrization of a pion-field (Ecker, Prog. Part. Nucl. Phys. {\bf 35}, 1 (1995)).

We develop a method to obtain fermion spectral functions non-perturbatively in a non-Abelian gauge theory with high occupation numbers of gauge fields. After recovering the free field case, we extract the spectral function of fermions in a highly occupied non-Abelian plasma close to its non-thermal fixed point, i.e., in a self-similar regime of the non-equilibrium dynamics. We find good agreement with hard loop perturbation theory for medium-induced masses, dispersion relations and quasiparticle residues. We also extract the full momentum dependence of the damping rate of the collective excitations.

In this thesis I present numerical studies of entanglement entropy and the quantum null energy condition in strongly coupled far-from-equilibrium quantum states using holography. I give a careful introduction into the numerical methods used and provide the computer codes to compute entanglement entropy and the quantum null energy condition. These methods are then applied to systems of various degrees of complexity, including homogeneous and isotropic far- from-equilibrium quantum quenches dual to Vaidya spacetimes, to homogeneous and anisotropic finite temperature states dual to anisotropic black brane geometries, and to inhomogeneous and anisotropic states of colliding walls of energy dual to gravitational shock wave collisions in Anti-de Sitter space. For all these scenarios I compute the fully non-linear dynamics of the dual geometry, which requires to numerically solve five-dimensional Einstein equations with negative cosmological constant and asymptotic Anti-de Sitter boundary conditions. The numerical solutions for the geometries allow to extract the time evolution of the holographic energy momentum tensor and provides the background for computing two-point functions, entanglement entropy and the quantum null energy condition. From the anisotropic system one learns that the near-equilibrium dynamic of entanglement entropy has an accurate description in terms of quasinormal modes. In the shock wave system I identify characteristic features of entanglement entropy that allow to discriminate between thick and narrow shocks. All my numerical studies confirm the quantum null energy condition, also the shock wave system, which itself can violate the classical null energy condition for sufficiently narrow shocks. My results also show that the quantum null energy condition can saturate in the far-from-equilibrium regime.

The popularity of rule-based flocking models, such as Reynolds' classic flocking model, raises the question of whether more declarative flocking models are possible. This question is motivated by the observation that declarative models are generally simpler and easier to design, understand, and analyze than operational models. We introduce a very simple control law for flocking based on a cost function capturing cohesion (agents want to stay together) and separation (agents do not want to get too close). We refer to it as {\textit declarative flocking} (DF). We use model-predictive control (MPC) to define controllers for DF in centralized and distributed settings. A thorough performance comparison of our declarative flocking with Reynolds' model, and with more recent flocking models that use MPC with a cost function based on lattice structures, demonstrate that DF-MPC yields the best cohesion and least fragmentation, and maintains a surprisingly good level of geometric regularity while still producing natural flock shapes similar to those produced by Reynolds' model. We also show that DF-MPC has high resilience to sensor noise.

We analyze the correlation coefficient T(E_e), which was introduced by Ebel and Feldman (Nucl. Phys. 4, 213 (1957)). The correlation coefficient T(E_e) is induced by the correlations of the neutron spin with the antineutrino 3-momentum and the electron spin with the electron 3-momentum. Such a correlation structure is invariant under discrete P, C and T symmetries. The correlation coefficient T(E_e), calculated to leading order in the large nucleon mass m_N expansion, is equal to T(E_e) = - 2 g_A(1 + g_A)/(1 + 3 g^2_A) = - B_0, i.e. of order |T(E_e)| ~ 1, where $g_A$ is the axial coupling constant. Within the Standard Model (SM) we describe the correlation coefficient $T(E_e)$ at the level of 10^{-3} by taking into the radiative corrections of order O(\alpha/\pi) or the outer model-independent radiative corrections, where \alpha is the fine-structure constant, and the corrections of order O(E_e/m_N), caused by weak magnetism and proton recoil. We calculate also the contributions of interactions beyond the SM, including the contributions of the second class currents.

We demonstrate the polarization of electron orbital angular momentum (OAM) in neutral atoms by integrating the Zeeman effect with attosecond transient absorption spectroscopy (ATAS). Using density matrix simulations, we show that in a helium atom, the absorption probability asymmetry between mj=-1 and mj = 1 in the 1s2p state can be precisely controlled by adjusting the time delay between infrared (IR) and extreme ultraviolet (XUV) fields, the strength of an applied static magnetic field, as well as the angle between laser polarization and magnetic field direction. This approach has significant implications across various fields, including quantum computing, quantum communication, and spintronics. Moreover, it paves the way for advancements in applications such as manipulating chemical reactions control, tailoring the magnetic properties of matter, and enabling novel laser emissions.

Fast neutron-induced nuclear reactions are crucial for advancing our understanding of fundamental nuclear processes, stellar nucleosynthesis, and applications, including reactor safety, medical isotope production, and materials research. With many research reactors being phased out, compact accelerator-based neutron sources are becoming increasingly important. Laser-driven neutron sources (LDNSs) offer unique advantages -- ultrashort neutron pulsees for superior energy resolution, high per-pulse flux, and a drastically reduced footprint. However, their use in single-event fast neutron spectroscopy remains unproven, requiring stable multi-shot operation and detectors capable of functioning in the extreme environment of petawatt-class laser-plasma interactions. Here, we present a proof-of-concept experiment at the DRACO~PW laser in a pitcher-catcher configuration, stably producing 6-7e7 neutrons/shot with energies above 1 MeV, over more than 200 shots delivered at a shot-per-minute rate. Neutron time-of-flight measurements were performed using a single-crystal diamond detector, which is located only 1.5 m away from the source and capable of resolving individual neutron-induced reactions. Observed reaction rates are consistent with Monte Carlo simulations inferred by real-time diagnostics of accompanying gamma, ion, and electron fluxes. With the recent advances in repetition rate, targetry, and ion acceleration efficiency, this work establishes LDNSs as a promising, scalable platform for future fast neutron-induced reaction studies, particularly for measurements involving short-lived isotopes or requiring high instantaneous neutron flux.

We present the Neural Simplex Architecture (NSA), a new approach to runtime assurance that provides safety guarantees for neural controllers (obtained e.g. using reinforcement learning) of autonomous and other complex systems without unduly sacrificing performance. NSA is inspired by the Simplex control architecture of Sha et al., but with some significant differences. In the traditional approach, the advanced controller (AC) is treated as a black box; when the decision module switches control to the baseline controller (BC), the BC remains in control forever. There is relatively little work on switching control back to the AC, and there are no techniques for correcting the AC's behavior after it generates a potentially unsafe control input that causes a failover to the BC. Our NSA addresses both of these limitations. NSA not only provides safety assurances in the presence of a possibly unsafe neural controller, but can also improve the safety of such a controller in an online setting via retraining, without overly degrading its performance. To demonstrate NSA's benefits, we have conducted several significant case studies in the continuous control domain. These include a target-seeking ground rover navigating an obstacle field, and a neural controller for an artificial pancreas system.

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin-Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows to identify the topological charge in the sine-Gordon model with the fermion number.