Precontact manifolds extend contact geometry by weakening the maximal non-integrability condition of the defining $1$-form. We clarify the geometric foundations of this structure by studying general pairs of a $1$-form and a $2$-form under mild regularity conditions. We characterize them through their class, analyse the role of distinguished vector fields, such as Reeb or Liouville fields, and study other associated geometrical objects. Precontact structures are then treated as the special case of pairs formed by a nowhere-vanishing $1$-form and its exterior derivative. We also define Hamiltonian dynamics on precontact manifolds. Several examples are presented to illustrate the theory.

We introduce a propagation-based approach to thermal state simulation by adapting Pauli and Majorana propagation to imaginary-time evolution in the Schrödinger picture. Our key observation is that high-temperature states can be sparse in the Pauli or Majorana bases, approaching the identity at infinite temperature. By formulating imaginary-time evolution directly in these operator bases and evolving from the maximally mixed state, we access a continuum of temperatures where the state remains efficiently representable. We provide analytic guarantees for small-coefficient truncation and Pauli-weight (Majorana-length) truncation strategies by quantifying the error growth and the impact of backflow. Large-scale numerics on the 1D J1-J2 model (energies) and the triangular-lattice Hubbard model (static correlations) validate efficiency at high temperatures.

We investigate the hardware requirements for quantum teleportation in an intercity-scale network topology consisting of two metropolitan-scale networks connected via a long-distance backbone link. Specifically, we identify the minimal improvements required beyond the state-of-the-art to achieve an end-to-end expected teleportation fidelity of $2/3$, which represents the classical limit. To this end, we formulate the hardware requirements computation as optimisation problems, where the hardware parameters representing the underlying device capabilities serve as decision variables. Assuming a simplified noise model, we derive closed-form analytical expressions for the teleportation fidelity and rate when the network is realised using heterogeneous quantum hardware, including a quantum repeater chain with a memory cut-off. Our derivations are based on events defined by the order statistics of link generation durations in both the metropolitan networks and the backbone, and the resulting expressions are validated through simulations on the NetSquid platform. The analytical expressions facilitate efficient exploration of the optimisation parameter space without resorting to computationally intensive simulations. We then apply this framework to a representative realisation in which the metropolitan nodes are based on trapped-ion processors and the backbone is composed of ensemble-based quantum memories. Our results suggest that teleportation across metropolitan distances is already achievable with state-of-the-art hardware when the data qubit is prepared after end-to-end entanglement has already been established, whereas extending teleportation to intercity scales requires additional, though plausibly achievable, improvements in hardware performance.

Quantum mechanics provides cryptographic primitives whose security is grounded in hardness assumptions independent of those underlying classical cryptography. However, existing proposals require low-noise quantum communication and long-lived quantum memory, capabilities which remain challenging to realize in practice. In this work, we introduce a quantum digital signature scheme that operates with only classical communication, using the classical shadows of states produced by random circuits as public keys. We provide theoretical and numerical evidence supporting the conjectured hardness of learning the private key (the circuit) from the public key (the shadow). A key technical ingredient enabling our scheme is an improved state-certification primitive that achieves higher noise tolerance and lower sample complexity than prior methods. We realize this certification by designing a high-rate error-detecting code tailored to our random-circuit ensemble and experimentally generating shadows for 32-qubit states using circuits with $\geq 80$ logical ($\geq 582$ physical) two-qubit gates, attaining 0.90 $\pm$ 0.01 fidelity. With increased number of measurement samples, our hardware-demonstrated primitives realize a proof-of-principle quantum digital signature, demonstrating the near-term feasibility of our scheme.

Diagnostics for the solar chromosphere are relatively few compared to other parts of the atmosphere. Despite this, hundreds of Rydberg lines emitted by neutrals in this region have been observed at UV wavelengths. Here, we investigate their diagnostic potential by modelling the lines emitted by neutral carbon using recent atomic data. We use the radiative transfer code Lightweaver to explore how they form and how they respond to temperature, density and micro-turbulent velocity perturbations in the atmosphere. To simplify the modelling, we investigate lines emitted from levels with principal quantum number $n\geq10$, which are expected to be in Saha-Boltzmann equilibrium with the ground state of the singly-charged ion. Optical depth effects are apparent in the lines and their response to atmospheric perturbations suggest that they will be useful in reconstructions of the atmosphere using inversions. The study opens the way for using many such lines emitted by multiple elements over a range of heights, a large number of which will be observed by the forthcoming Solar-C EUV High-throughput Spectroscopic Telescope (EUVST).

Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue systems using these algebras as state spaces, which provide efficient computational algorithms for the construction of orthogonal bases in the multi-matrix case. Algebraic counting formulae in matrix and tensor systems with $U(N)$ as well as $S_N$ symmetry have led to gauged quantum mechanical models which display a negative branch of specific heat capacity in the micro-canonical ensemble followed by positive specific heat capacity at larger energies measured by a polynomial degree parameter $n$. The negative branch is associated with near-exponential or factorial growth of degeneracies for $ n \gg 1$ in a region of large $N$ stability, while the positive branch occurs when the finite $N$ reduction of degrees of freedom takes over as $n$ becomes sufficiently large compared to $N$.

The EXoplanet Climate Infrared TElescope (EXCITE) is a balloon-borne mission dedicated to measuring spectroscopic phase curves of hot Jupiter-type exoplanets. Phase curve measurements can be used to characterize an exoplanet's longitude-dependent atmospheric composition and energy circulation patterns. EXCITE carries a 0.5 m primary mirror and moderate resolution diffraction-limited spectrograph with spectral coverage from 0.8--3.5 um. EXCITE is designed to fly from a long-duration balloon (LDB). EXCITE will observe through the peak of a target's spectral energy distribution (SED) and through spectral signatures of hydrogen and carbon-containing molecules. In this paper, we present the science goals of EXCITE, detail the as-built instrument, and discuss its performance during a 2024 engineering flight from Fort Sumner, New Mexico.

We consider tunnel ionization of atomic argon in a femtosecond laser pulse of intensity $10^{21}-10^{22}{\rm W/cm}^2$ aiming to investigate the relativistic dynamics and radiation of photoelectrons released from their parent ions inside the laser focus. Radiation of such electrons accelerated along the laser field propagation direction appears to have moderate power but can be considerably enhanced by a collision with a relatively weak counter-propagating laser pulse. Using the theory of laser-induced tunneling in atoms and ions and that of nonlinear Thomson scattering, we demonstrate that angular distributions and spectra of emitted photons can serve as a probe of the peak intensity in the focus. The angular distribution of emitted radiation in the plane of polarization and propagation of the ionizing laser beam appears narrow and peaked around an intensity-dependent angle, making this ionization setup a source of collimated XUV radiation.

Mask-based lensless imagers use simple optics and computational reconstruction to design compact form factor cameras with compressive imaging ability. However, these imagers generally suffer from poor reconstruction quality. Here, we describe several advances in both hardware and software that result in improved lensless imaging quality. First, we use a precision-manufactured random multi-focal lenslet (RML) phase mask to produce improved measurements with reduced multiplexing. Next, we implement a ConvNeXt-based reconstruction architecture, which provides up to 6.68 dB improvement in peak signal-to-noise ratio over state-of-the-art attention-based architectures. Finally, we establish a parallel imaging setup that simultaneously images a scene with RML, diffuser and lens systems, with which we collect datasets with 100,000 measurements for each system, to be used for reconstruction model training and evaluation. Using this standardized system, we quantify the improved measurement quality of the RML compared to a diffuser using the modulation transfer function and mutual information. Our ConvRML system benefits from both the optical and the computational developments presented in this work, and our contributions establish resources to support continued development of high-quality, compact, and compressive lensless imagers.

We propose a computational framework for modeling opinion dynamics in electoral competitions that combines two realistic features: voter memory and exogenous shocks. The population is represented by a fully-connected network of agents, each holding a binary opinion that reflects support for one of two candidates. First, inspired by the classical voter model, we introduce a memory-dependent opinion update: each agent's probability of adopting a neighbor's stance depends on how many times they agreed with that neighbor in the agent's past $m$ states, promoting inertia and resistance to change. Second, we define an electoral shock as an abrupt external influence acting uniformly over all agents during a finite interval $[t_0, t_0+Δt]$, favoring one candidate by switching opinions with probability $p_s$, representing the impact of extraordinary events such as political scandals, impactful speeches, or sudden news. We explore how the strength and duration of the shock, in conjunction with memory length, influence the transient and stationary properties of the model, as well as the candidates' advantage. Our findings reveal a rich dynamical behavior: memory slows down convergence and enhances system resilience, whereas shocks of sufficient intensity and duration can abruptly realign collective preferences, particularly when occurring close to the election date. Conversely, for long memory lengths or large election horizons, shock effects are dampened or delayed, depending on their timing. These results offer insights into why some sudden political events reshape electoral outcomes while others fade under strong individual inertia. Finally, a qualitative comparison with real electoral shocks reported in opinion polls illustrates how the model captures the competition between voter inertia and abrupt external events observed in actual elections.

The Deep Underground Neutrino Experiment (DUNE) offers strong sensitivity to neutrinos from a Galactic core collapse supernova, providing a powerful probe of neutrino flavor conversion and the neutrino mass ordering. In this work, we study supernova neutrino oscillations at DUNE using quantum entanglement as an organizing framework. Treating the three flavor neutrino system as an effective multipartite quantum state, we quantify flavor correlations through the entanglement of formation, concurrence, and negativity, expressed directly in terms of flavor survival and transition probabilities. Benchmark scenarios defined by representative variations of the electron neutrino survival probability are constructed for each entanglement measure. Event rates and fluences are computed for a supernova at 10 kpc, and the mass ordering sensitivity is evaluated using detector-level simulations performed with the \texttt{SNOwGLoBES} framework, employing the Garching supernova flux model and including the dominant detection channels in liquid argon: $ν_e$ and $\barν_e$ charged-current interactions on argon and elastic scattering on electrons. We analyze both individual and combined detection channels and incorporate $5\%$ normalization and energy calibration systematic uncertainties. Our results show that DUNE achieves a $5σ$ determination of the neutrino mass ordering for a supernova at distances of $\sim 20$~kpc for the $ν_e$ charged current channel and $\sim 2$~kpc for the $\barν_e$ channel, with the reach depending on the entanglement scenario considered. These results demonstrate that entanglement based observables provide a complementary and robust framework for probing supernova neutrino oscillations and the neutrino mass ordering.

In a classic 1982 paper in this journal, Jean Meeus used a statistical approach for finding the mean frequency of a total and an annular eclipse of the Sun at a given place on the surface of the Earth. In this current paper we tackle the problem again, taking advantage of the much greater computing power now available. We obtain narrower estimates of once every 373 $\pm$ 7 years for a total eclipse, and once every 226 $\pm$ 4 years for an annular eclipse. In addition, we obtain a result of once every 2.59 $\pm$ 0.02 years for a partial eclipse. We provide further insights into the "latitude effect", showing that solar eclipses occur most frequently around the Arctic and Antarctic Circles. We also show how the gradual shift of aphelion and perihelion with respect to the seasons produces a $\sim$21,000-year cycle in the frequency of eclipses in the Northern and Southern Hemispheres.

Neutron-skin thicknesses provide a sensitive probe of the isovector sector of the nuclear equation of state and its density dependence, commonly characterized by the symmetry-energy slope parameter L. A wide variety of experimental and observational methods have been used to extract neutron skins, ranging from hadronic and electromagnetic probes of finite nuclei to inferences from neutron-star observations. Each approach carries distinct theoretical and systematic uncertainties, complicating global interpretations and obscuring genuine physical trends. In this work we present a hierarchical Bayesian framework for the statistically consistent synthesis of heterogeneous neutron-skin constraints. The neutron-skin thickness is modeled as a smooth latent function of isospin asymmetry and nuclear size, while method-dependent bias parameters and intrinsic nuisance widths are introduced to account for unmodeled experimental and theoretical systematics. Focusing on the tin isotopes, we infer probabilistic neutron-skin trends from 100Sn to 140Sn, finding minimal uncertainties near stability and increasing uncertainties toward the proton-rich and neutron-rich extremes. We assess the consistency of nuclear energy-density functionals and obtain conditional constraints on the symmetry-energy parameters. The resulting posterior exhibits a pronounced compression of the symmetry-energy slope parameter L, reflecting the dominant sensitivity of neutron skins to sub-saturation symmetry pressure. We demonstrate that our hierarchical Bayesian framework provides robust and transparent constraints on the sub-saturation isovector sector of the nuclear equation of state.

We demonstrate the existence of a dynamical quantum phase transition (DQPT) in a dissipative collective-spin model that exhibits the boundary time crystal (BTC) phase. We initialize the system in the ground state of the Hamiltonian in either the BTC or the non-BTC phase, and drive it across the BTC transition. The driving is done by an abrupt quench or by a finite-time linear ramp of a Hamiltonian control parameter under Markovian Lindblad dynamics. We diagnose DQPTs through zeros of the fidelity-based Loschmidt echo between the initial state and the evolving mixed state, which induce nonanalytic cusp-like features in the associated rate function. For quenches into the BTC phase, the Loschmidt echo exhibits repeated zeros due to the emergent time-periodic steady state, whereas for quenches into the non-BTC phase, the overlap vanishes and remains zero once the dynamics relaxes to a stationary state. We further show that the DQPT persists under the ramp protocol followed by unitary evolution with the final Hamiltonian. Finally, we analyze the finite-size scaling of the first critical time and find convergence to a constant in the thermodynamic limit, with distinct power-law approaches for the quench and the ramp protocols.

Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, especially for strongly correlated systems and quantum computers. However, its practical application is limited by the steep scaling of its non-terminating Baker-Campbell-Hausdorff expansion. We introduce an active space UCCSD(4)/MP2 approach that leverages a fourth-order many-body perturbation theory truncation of UCCSD within a selected active space, while treating external excitations at the MP2 level. We explore two variants: a composite method that sums separate internal and external contributions and an interacting method that couples the amplitudes for greater accuracy. We test our approach on the GW100 dataset, a metaphosphate hydrolysis reaction, and the strongly correlated torsion of ethylene. Our results suggest that the interacting method with canonical orbitals is robust for weakly and moderately correlated systems and accurately reproduces the full UCCSD(4) potential energy curves using only 15-25% of the virtual orbitals in its active space. In comparison, the composite formulation exhibits greater sensitivity to the orbital basis and active space size, leading to less systematic behavior across the benchmark set. For ethylene torsion, a system dominated by strong static correlation, both composite and interacting formulations employing canonical orbitals closely track the full UCCSD(4) reference but do not alleviate the unphysical features inherited from the underlying single-reference UCCSD(4) description. This active space framework offers a tractable approach for modeling correlated molecules and reactions on classical computers and provides a viable path for scaling UCC calculations for resource-constrained quantum hardware.

Certain integrable hierarchies appearing in random matrix theory, enumerative geometry, and conformal field theory are governed by Virasoro/$W$-algebra constraints and their $W$-representations.Motivated by the Gaussian Hermitian $β$-ensemble and recent studies of superintegrable partition function hierarchies, we build an explicit bridge from symmetric group class algebras to bosonic Fock spaces and further to geometry. On the algebraic side, we decompose the transposition class sum into cut and join channels and recover the classical cut-and-join operator on the ring of symmetric functions. On the geometric side, we use the Grojnowski-Nakajima Fock space identification to realize the ladder operator $E_1=[W_0,p_1]$ as the Hecke correspondence on $\mathrm{Hilb}_n(\mathbb C^2)$, and we interpret the cubic generator $W_0$ as a normal ordered triple incidence correspondence. We then explain how the $β$-deformed cubic generator $W_0^{(β)}$ arises from the Ward identities/Virasoro constraints of the Gaussian $β$-ensemble via a background charge parametrization, clarifying its conformal field theoretic meaning. Finally, using the Grojnowski-Nakajima Heisenberg-Fock isomorphism $Φ_{\mathrm{Hilb}}:Λ\xrightarrow{\sim}\bigoplus_{n\ge0}H_T^*(\Hilb^n(\mathbb C^2))$, we transport the resulting commutator hierarchy to Hilbert schemes, where $E_1$ is realised by the Hecke correspondence (adding one point) and the diagonal correction terms are computed by equivariant localization from the $T$-weights of the tangent bundle $T\Hilb^n(\mathbb C^2)$ and the tautological bundle $\mathcal V$. This provides a geometric realization framework that unifies $β$-deformed integrable structures and offers new tools for studying quiver gauge theory partition functions.

Predicting tensorial properties with machine learning models typically requires carefully designed tensorial descriptors. In this work, we introduce an alternative strategy for learning tensorial quantities based on scalar descriptors. We apply this approach to the Born effective charge tensor, showing that scalar (monopole) kernel models can successfully capture its tensorial nature by exploiting the definition of the Born effective charge tensor as the derivative of the polarisation with respect to atomic displacements. We compare this method with tensorial (dipole) kernel models, as established in our previous work, in which the tensorial structure of the Born effective charge is encoded directly in the kernel and obtained via its derivative. Both approaches are then used for charge partitioning, enabling the separation of monopole and dipole contributions. Finally, we demonstrate the effectiveness of the framework by computing finite-temperature infrared spectra for a range of complex materials.

Coherent elastic neutrino-nucleus scattering (CEvNS) provides a well-defined framework for studying nuclear recoil observables in low-energy neutrino interactions. In this work, we present a comparative Monte Carlo benchmark study of CEvNS-induced nuclear recoils for four target nuclei (B, Mg, Ti, and Zr) using the Geant4 simulation toolkit and the ROOT analysis framework. The study focuses on relative differences in recoil-energy spectra, nuclear form-factor effects, and angular distributions under identical simulation conditions. A deliberately simplified detector geometry is employed to ensure a controlled and transparent comparison between target materials, rather than to model a specific experimental setup. The results highlight how nuclear mass and form-factor suppression influence CEvNS recoil observables and provide a reference-level comparison that may be useful for material-selection studies in CEvNS-related simulations.

Gravitational wave standard sirens enable independent measurements of the Hubble constant $H_0$. In the absence of electromagnetic counterparts, the "dark siren" method statistically correlates GW events with potential host galaxies. We present a measurement of $H_0$ using 142 compact binary coalescences from the fourth Gravitational-Wave Transient Catalog (GWTC-4.0) combined with the Dark Energy Survey Year 6 Gold photometric galaxy catalog. Using the gwcosmo pipeline, we jointly infer cosmological and GW population parameters. We analyze the impact of galaxy catalog properties on the inference, identifying significant features in the galaxy redshift distribution which can introduce biases. By restricting the galaxy catalog to $0.05<z<0.35$ to maintain consistency with a uniform in comoving volume galaxy distribution, we obtain a result of $H_0 = 70.9^{+22.3}_{-18.6}\;\text{km}\;\text{s}^{-1}\;\text{Mpc}^{-1}$ from dark sirens and $H_0=73.1^{+11.7}_{-8.6}\;\text{km}\;\text{s}^{-1}\;\text{Mpc}^{-1}$ when combined with the bright siren GW170817. This study demonstrates the adaptation of deep galaxy catalogs for GW cosmology, highlighting key challenges and methodologies essential for maximizing the potential of next-generation galaxy surveys.

Aims. We derive a dependence of the IRX on UV slope $β$, stellar mass $M_\ast$, and redshift out to $z \simeq 5$, and establish consistent functional relations that can be used for correcting the UV/optical-selected galaxy samples for the effects of dust absorption. Methods. This work is based on a $K$-band selected sample of $\sim 10^5$ star-forming galaxies detected in the UDS and COSMOS fields. Quiescent sources and known starbursts are removed, and the IR luminosities are established through stacking in FIR {\it Herschel} and JCMT maps. UV slopes are found from SED fits and stacked IRX values are derived by taking the median of individual IRX measurements in bins of $β$, $M_\ast$ and redshift. Results. While our best-fit IRX-$β$ relation is consistent with a Calzetti-like attenuation curve at $β\gtrsim -1$, at bluer values the IRX seems to increase with redshift due to different mass-completeness limits imposed. When deriving the IRX-$β$ relation in stellar-mass bins, a systematic trend is found, where the effective slope of the attenuation law becomes progressively shallower with increasing mass. We incorporate this into the IRX-$β$ relation through the slope of the underlying reddening law, $dA_{1600}/dβ$, being a quadratic function of $\log(M_\ast/{\rm M_\odot})$. Expressing IRX as a function of the stellar mass we find a tight correlation, with IRX rising monotonically with mass but exhibiting a clear high-mass turnover at $z\lesssim 2-3$, consistent with suppressed cold-gas accretion and dust growth in massive systems.

Magnetorheological fluids consist of micrometer-sized magnetic particles in a carrier liquid. Sufficiently strong external magnetic fields lead to the formation of string-like particle aggregates. We demonstrate that hydrodynamic interactions, that is, mutual couplings via induced flows, play a substantial role during structure formation. Hydrodynamics supports the emergence of string-like aggregates, while magnetic interactions align them. This fundamental insight is substantial from an application perspective, due to the enormous technical importance and potential of magnetorheological fluids.

We study the equilibrium and nonequilibrium formation of four-particle complexes in a balanced two-species Bose-Hubbard model with repulsive intra- and attractive inter-species interactions. Using exact diagonalization, we characterize the transition from weakly- to strongly-correlated dimer and tetramer states along the one- to two-dimensional crossover in coupled-chain geometries by combining local correlation signatures with global diagnostics such as the binding energy and interspecies entanglement entropy. We show that transverse connectivity between chains qualitatively reshapes the phase diagram, substantially enlarging the tetramer region and, in particular, stabilizing weakly bound tetramers when compared to the one-dimensional chains. By tuning the interchain hopping, we identify a transition from a degenerate manifold of spatially separated dimers to a localized tetramer ground state, driven by the lifting of one-dimensional configurational degeneracies and an associated kinetic-energy gain. Finally, we demonstrate interaction and geometric quench protocols to dynamically prepare these complexes with high fidelity. Our results provide a microscopic framework for engineering and probing few-body bosonic bound states in tunable lattice geometries.

Digitized adiabatic quantum factorization is a hybrid algorithm that exploits the advantage of digitized quantum computers to implement efficient adiabatic algorithms for factorization through gate decompositions of analog evolutions. In this paper, we harness the flexibility of digitized computers to derive a digitized adiabatic algorithm able to reduce the gate-demanding costs of implementing factorization. To this end, we propose a new approach for adiabatic factorization by encoding the solution of the problem in the kernel subspace of the problem Hamiltonian, instead of using ground-state encoding considered in the standard adiabatic factorization proposed by Peng $et$ $al$. [Phys. Rev. Lett. 101, 220405 (2008)]. Our encoding enables the design of adiabatic factorization algorithms belonging to the class of Quadratic Unconstrained Binary Optimization (QUBO) methods, instead the Polinomial Unconstrained Binary Optimization (PUBO) used by standard adiabatic factorization. We illustrate the performance of our QUBO algorithm by implementing the factorization of integers $N$ up to 8 bits. The results demonstrate a substantial improvement over the PUBO formulation, both in terms of reduced circuit complexity and increased fidelity in identifying the correct solution.

We present a class of potentials $q \colon \mathbb{R}^{n} \to (0,\infty)$ that implies the weighted Schrödinger semigroup $φ^{-1}\mathrm{e}^{-tH}φ$ to map a weighted Lebesgue function space $\mathrm{L}_μ^{1}(\mathbb{R}^{n})$ into a weighted Lebesgue function space $\mathrm{L}_μ^{2}(\mathbb{R}^{n})$ continously at every time $t>0$ by Logarithmic Sobolev inequalities for $H=-Δ+ q(x)$ with it's strictly positive ground state $φ\colon \mathbb{R}^{n} \to (0,\infty)$. We use the self-adjointness of $\mathrm{e}^{-tH}$ in $\mathrm{L}^{2}(\mathbb{R}^{n})$ to infer an intrinsic ultracontractivity, i.e. $\forall t>0 \ \exists C_{t} > 0 \ : \ \left| \mathrm{e}^{-tH} u (x) \right| \ \leq \ C_{t} φ(x) \| u \|_{2}$ for every $u \in \mathrm{L}^{2}\left( \mathbb{R}^{n} \right)$ almost everywhere in $\mathbb{R}^{n}$.

The design of materials with tailored properties is crucial for technological progress. However, most deep generative models focus exclusively on perfectly ordered crystals, neglecting the important class of disordered materials. To address this gap, we introduce DMFlow, a generative framework specifically designed for disordered crystals. Our approach introduces a unified representation for ordered, Substitutionally Disordered (SD), and Positionally Disordered (PD) crystals, and employs a flow matching model to jointly generate all structural components. A key innovation is a Riemannian flow matching framework with spherical reparameterization, which ensures physically valid disorder weights on the probability simplex. The vector field is learned by a novel Graph Neural Network (GNN) that incorporates physical symmetries and a specialized message-passing scheme. Finally, a two-stage discretization procedure converts the continuous weights into multi-hot atomic assignments. To support research in this area, we release a benchmark containing SD, PD, and mixed structures curated from the Crystallography Open Database. Experiments on Crystal Structure Prediction (CSP) and De Novo Generation (DNG) tasks demonstrate that DMFlow significantly outperforms state-of-the-art baselines adapted from ordered crystal generation. We hope our work provides a foundation for the AI-driven discovery of disordered materials.

We examine the spectral structure of the two-dimensional advection-diffusion operator in flows with mixed phase space at very large Peclet number. Using Fourier discretization combined with symmetry reduction and Krylov-Arnoldi methods, we compute on the order of one hundred leading eigenpairs reliably in the asymptotic, weak-diffusion regime. While the principal eigenvalue is asymptotically diffusive and localized on the largest regular region, the broader spectrum exhibits a rich organization controlled by local Lagrangian phase-space geometry. In particular, exponential mixing in chaotic regions rapidly suppresses correlations, whereas algebraic mixing in integrable regions generates long-lived coherent structures that dominate the slow and intermediate parts of the spectrum. We identify three distinct classes of eigenmodes: advective modes associated with transport on invariant tori, diffusive modes and, within the duffusive branch, tunneling modes arising from weak coupling between dynamically separated regular regions. Drawing on a semiclassical analogy, we assign quantum-number-like labels to these families and predict the appearance, scaling, and ordering of their sub-spectra directly from the Hamiltonian phase-space structure. The coexistence of these families implies that no uniform control of the spectral gap exists across the full spectrum: although the slowest mode is diffusive, arbitrarily small gaps arise between competing families at higher mode numbers. As a result, finite-time advection-diffusion dynamics is generically governed by persistent modal competition rather than single-mode dominance, even at asymptotically large Peclet number.

High-reflective crystalline $GaAs/Al_{0.92}Ga_{0.08}As$ coatings show reduced Brownian noise compared to conventional dielectric coatings. However, several ultra stable laser systems observed additional noise sources that hinder the realization of the expected improvements in frequency stability. These additional noise sources are related to the birefringence of the coatings and its modification by intracavity light. The origin of the birefringence is not yet well understood and its modification via illumination remains unexplained. Here we present an extensive study on the steady-state and transient modification of the birefringence by intracavity light and by uniform illumination at various wavelengths using an optical cavity at room temperature. We find a unified description that suggests a primary two-photon process for photon energies below the bandgap of GaAs, or a single-photon process at higher energies. Adding external illumination allows to reduce noise induced by laser power fluctuations by balancing the photo-thermal-optic response of the mirrors and the photo-birefringent effect at a more favorable low intracavity power.

Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.

The explicit description and computation of functions defined on Riemann surfaces of various genera depends on the choice of language: while the Jacobi parametrization is widely known and used, the Schottky uniformization has been proven to provide an alternative approach, useful in particular for (but not limited to) numerical calculations. Despite capturing the geometry of the Riemann surface completely, the two languages are subject to rather different sets of auxiliary symmetries. In this article we translate and compare the symplectic transformations inherent in the Jacobi parametrization to the freedom in choosing Möbius transformations generating the Schottky group for the Schottky uniformization. Our results are aimed at transferring functional relations expressed in the Schottky language to the Jacobi language and vice versa. An immediate application would be the efficient numerical evaluation of special functions in a physics context by favorably tuning the Schottky cover leading to quicker convergence.

Resonant drag instabilities (RDIs) are a novel type of dust/fluid instability relevant to a diverse range of astrophysical environments. They are driven by a resonant interaction between streaming dust and waves in a background medium, which results in dust density fluctuations and amplification of the waves. This broad class of instabilities includes recently-proposed modes incorporating acoustic and magnetohydrodynamic waves, as well as the well-studied disk streaming instability. As the study of RDIs is at an early stage, their evolution beyond the linear regime is not well understood. In order to make inroads into the nonlinear theory of RDIs, we performed simulations of the simplest case, the acoustic RDI, in which sound waves in a gas are amplified by interaction with supersonically streaming dust. This particular instability is of interest both due its potential relevance in various poorly ionized environments, and due to its resemblance to the fast magnetosonic RDI. We find that the nonlinear growth and saturation of the instability are characterized by a balance between time scales of instability growth and turbulent eddy turnover. The simulations demonstrate a saturated state possessing an anisotropic outer forcing range in which this balance is maintained, and suggest the presence of an isotropic turbulent inertial range below this scale. By presenting a model for the nonlinear growth and saturated state of the acoustic RDI, this work provides a framework for further study of the nonlinear behavior of this and other RDIs.