AI for Science

In a previous work, the topology of inversion-symmetric one-dimensional periodic media was characterized through the pole-zero pattern of an impedance-like function associated with Bloch waves. This construction reproduces the Berry--Zak invariant and provides a criterion for topological interface states. In the present work, we give a geometric interpretation of this formalism. We show that poles and zeros arise naturally from the action of inversion symmetry on the projectivized space of Cauchy data. The corresponding Dirichlet and Neumann states are identified with the two fixed points of the induced $\mathbb Z_2$ action on the Riemann sphere. The key observation is that Bloch eigenvectors are naturally constructed on the universal covering of the Brillouin circle. The topology of the associated Real eigenline bundle is encoded in the action of the deck transformation group on lifted eigenvectors. This action is described by a monodromy sign $ρ\in\{\pm1\}$, determined by the inversion representations carried by the band at the fixed points of the Brillouin zone. We show that this monodromy defines a natural rank-one local system over the Brillouin circle. The corresponding Real line bundle is classified by its first Stiefel--Whitney class, which coincides with the associated $\mathbb Z_2$ pole-zero invariant. This establishes a geometric connection between the pole-zero formalism, Berry--Zak phases, Real bundles and local coefficient systems.

We develop an operator-algebraic framework for boundary conditions and bulk-boundary correspondence in one-dimensional gapped phases with categorical symmetry. Working directly in the thermodynamic limit, we construct half-infinite fusion spin chains and commuting-projector boundary Hamiltonians from a unitary fusion category $\mathcal{C}$, an indecomposable semisimple right $\mathcal{C}$-module category $\mathcal{M}$, a Q-system $Q\in\mathcal{C}$ specifying the bulk phase, and a right $Q$-module $K\in\mathcal{M}_{Q}$, regarded as an object of $\mathcal{M}_{Q}^{\mathrm{op}}$, specifying the boundary. We prove that these Hamiltonians have unique ground states and that the resulting realization functor $\mathcal{M}_{Q}^{\mathrm{op}}\to\mathrm{BCond}$ is an equivalence, so simple boundary conditions are classified by simple objects of $\mathcal{M}_{Q}$ and general boundary conditions by their finite direct sums. We also give a microscopic formulation of the boundary symmetry topological field theory using DHR bimodules of the boundary quasi-local algebra. For a half-infinite fusion spin chain, the boundary DHR category is monoidally equivalent to $(\mathcal{C}_{\mathcal{M}}^{\vee})^{\mathrm{rev}}$, and the canonical action of the bulk DHR category on it agrees with the categorical action of $Z_1(\mathcal{C}^{\mathrm{rev}})$. Finally, we identify the action of the boundary DHR category on boundary conditions with the categorical action of $(\mathcal{C}_{\mathcal{M}}^{\vee})^{\mathrm{rev}}$ on $\mathcal{M}_{Q}^{\mathrm{op}}$. This yields a one-dimensional bulk-boundary correspondence: the enriched monoidal category describing the bulk is the enriched center of the enriched category describing the boundary.

We present a detailed numerical study of a protocol for momentum-selective transport of a Bose-Einstein condensate (BEC) in a one-dimensional optical lattice, achieving narrow momentum distributions through controlled non-adiabatic dynamics. The protocol consists of non-adiabatic loading into the lattice, coherent acceleration using a symmetric trapezoidal acceleration profile, and non-adiabatic release into free space. Using the time-dependent Gross-Pitaevskii equation, we simulate the full sequence and analyze the role of non-adiabatic excitations on the final momentum distribution. We identify the intra-site breathing dynamics as the dominant mechanism governing spectral purity under fast loading conditions. By tracking the condensate's spatial width during the evolution, we demonstrate a direct correlation with the final momentum spread. A variational model based on a Gaussian ansatz quantitatively reproduces the observed dynamics and provides physical insight into the breathing mechanism. Our results reveal the existence of "magic" times, i.e., specific loading or acceleration durations synchronized with the breathing oscillation period, where quasi-monochromatic momentum distributions can be achieved even with loading times as short as 100 microseconds. In the tight-binding regime, this approach offers speedup factors of 3 to 6 compared to adiabatic protocols while maintaining high transfer fidelities, providing a practical route to coherent transport for quantum sensors operating under stringent timing constraints.

Out-of-time-ordered correlators (OTOCs) have emerged as a diagnostic of information scrambling and quantum chaos in many-body systems. We investigate the imprints of chaos in the dynamics of OTOCs in the Heisenberg spin-$1/2$ chain with random fields. The system is parameterized to exhibit a crossover from integrable to chaotic dynamics. We demonstrate numerically that the approach to saturation of the OTOC can distinguish between integrable and chaotic regimes, with a power-law $(1/t)$ relaxation for integrable systems and a higher-degree power-law decay $(1/t^α; α\ge 1)$ followed by an exponential relaxation for the chaotic regime. We further show that long-range spectral statistics, such as the number variance, are more effective in characterizing quantum chaos in the regime near saturation of OTOC. We also demonstrate that the relaxation and initial scrambling regimes exhibit distinct and universal features, with the former being sensitive and the latter being robust against different realizations of random-fields. The long-time saturation of OTOC also fluctuates with different realizations, and its exact expression is derived through the Eigenstate Thermalization Hypothesis.

The path integral of the Dirac fermion with vector and axial gauge backgrounds is analyzed near the infrared limit in the presence of residual irrelevant current-current interaction. After integrating out fermions, a semiclassical low-energy effective action is obtained, written in terms of currents. Its expression is found to correspond to the hydrodynamic action previously proposed for perfect barotropic fluids with anomalies at zero temperature. This approach also leads to two further hydrodynamic actions to be associated, respectively, with the Weyl fermion, and the Dirac fermion having independent vector and axial currents. These actions feature four- and five-dimensional bulk-boundary terms, owing to anomaly inflow, which are identified as being the so-called transgression forms. These are generalizations of Chern--Simons forms that involve two gauge fields: the dynamical field and the background field. The path-integral argument provides a ``microscopic'' explanation for several ingredients of the action formulation of hydrodynamics that are necessary to incorporate anomalies. It also clarifies the infrared reduction required to pass from the effective field theory to a local hydrodynamic description. This reduction is implemented by considering restricted variations of the action, familiar from hydrodynamics, which at the same time lead to four-dimensional equations of motion from the five-dimensional transgression terms.

We present a holographic dual of a two dimensional conformal field theory with non-hermitian but Parity-Time (PT) symmetric boundary conditions, by applying the AdS/BCFT duality and by introducing an imaginary valued scalar field localized on an end-of-the-world brane. We find that as we increase the strength of the non-hermitian PT symmetric interactions, the system experiences a spontaneous PT symmetry breaking. We also consider its Wick rotated setup as a new quantum quenched state and show that its growth of entanglement entropy can be larger than the standard results obtained from standard Cardy states.

The macroscopic instability of soft materials undergoing extreme deformations is traditionally viewed as a pure structural or mechanical failure. Driven by the quest to uncover universal principles across disparate physical systems, we bridge two vibrant yet seemingly disconnected research frontiers: macroscopic finite-strain solid mechanics and quantum-like topological physics. Here, we demonstrate that the classical elastic surface instability of a deformed hyperelastic manifold is not merely a mechanical bifurcation, but fundamentally a topological phase transition. By incorporating Lie group metric evolution into a generalized Stroh formalism, we map the highly nonlinear geometric frustration onto an algebraic surface impedance matrix $\mathbf{H}$. For a semi-infinite hyperelastic half-space under finite compression, we analytically map the system to a one-dimensional Dirac Hamiltonian, where the macroscopic mechanical stretch acts as a tunable knob for the Dirac mass. We reveal that the onset of surface wrinkles marks a topological transition from a trivial to a non-trivial phase characterized by a quantized step in the winding number, naturally giving rise to a robust, macroscopically localized zero-energy edge state. This fundamental linkage unifies macroscopic symmetry breaking with the topological paradigm, opening a new theoretical pathway for programmable smart soft matter.

We consider the problem of identifying a topological order based on bulk entanglement of the ground-state wavefunction. Previous work showed that some universal information can be extracted from multi-entropy measures, a class of multipartite entanglement measures obtained by applying permutation operators exchanging the degrees of freedom between different replicas of the wavefunction. It remains an open question to what extent such entanglement measures can be used to extract any universal information from the ground state. Here we show that the topological partition function $Z(M)$ of a manifold $M$ can be extracted provided that $M$ satisfies a topological condition which we term ``local achirality". We show that locally-achiral manifolds can be used to extract universal properties of 2+1d topological phases that go beyond the $S$ and $T$ matrices. As a first step towards classifying locally-achiral manifolds, we show that, in four dimensions, such manifolds have vanishing Pontryagin number. We relate this property to the existence of beyond-cohomology time-reversal symmetry protected topological order (T-SPT) in four dimensions. Finally, we present an entanglement measure that detects this nontrivial T-SPT.

We study signatures of quantum chaos in finite-loop truncations of the planar dilatation operator in the $\mathfrak{su}(2)$ sector of $\mathcal N=4$ super Yang-Mills and its $β$-deformation. These truncations define holographically motivated long-range deformations of the nearest-neighbour XXX spin chain. At one-loop the model is integrable, while the all-loop planar theory is expected to again be integrable. Finite-loop truncations therefore provide a natural setting for investigating how chaotic behaviour emerges between these two integrable limits. We analyse this question using spectral statistics, eigenvector diagnostics and spread complexity. We find that the two- and four-loop truncations develop GOE-like level statistics at sufficiently large coupling but with features characteristic of weak integrability breaking. The integrability breaking at four-loops is weaker than at two-loops and the critical coupling at which chaos occurs is larger, at least for long spin chains. The three-loop truncation does not show the same onset of chaos in the range studied. Eigenvector diagnostics show that the corresponding eigenstates remain less random than GOE vectors, indicating weak ergodicity and multifractality. Finally, we can identify signatures of the eigenvalue and eigenvector chaos in the Krylov-space data. Namely, we demonstrate a correlation of the level spacing statistics with the peak of spread complexity and disorder on the Krylov chain. The delocalisation of the initial state in the Hamiltonian eigenbasis is shown to strongly affect the saturation of complexity. Our results suggest that finite-loop dilatation operators are not generic long-range spin chain Hamiltonians, but already display patterns consistent with the restoration of integrability in the all-loop planar theory.

In equilibrium physics, topological defect insertions in quantum and classical partition functions provide non-perturbative probes of phase transitions beyond local observables. In non-equilibrium physics, the spectral form factor provides a minimal probe of universal quantum dynamics, and admits a representation as a product of two partition functions at imaginary inverse temperature. We define the topological spectral form factor (TopSFF) by inserting topological defects acting non-trivially on the doubled partition functions, producing mismatched spacetime world-sheet topologies. For the minimal $\mathbb{Z}_2$ spatially extended defect, implemented by the global swap operator, we derive an exact mapping of the TopSFF of a generic 1D many-body chaotic system to an emergent $(3+1)$D non-Hermitian single-particle problem describing a temporal domain wall (tDW). We show analytically that the effective tDW dynamics undergoes a $\mathcal{PT}$ symmetry breaking transition at a finite interaction strength $ε_{\mathrm{EP}}$: below $ε_{\mathrm{EP}}$, the leading modes are polarized into Gaussian or non-Gaussian tDW sectors and the TopSFF varies monotonically and exponentially with system size; above $ε_{\mathrm{EP}}$, the tDW sectors hybridize and the TopSFF oscillates with system size; at the exceptional point $ε_{\mathrm{EP}}$, Jordan non-diagonality produces a linear-in-system-size enhancement. For temporally extended topological defects, we derive exact universal scaling forms for the TopSFF free energy in systems with time reversal or time translation symmetry, and verify them numerically in independent models.

The gravitational potential of a galaxy encodes its mass distribution, formation history, and dark matter halo structure. Accurate potential models are therefore critical for interpreting stellar kinematics, orbital dynamics, and the influence of satellite systems like the Large Magellanic Cloud. Analytic potential models offer interpretability and efficiency but struggle to capture complex, non-axisymmetric structure and time-dependent perturbations. Neural network-based methods can capture this complexity but offer little interpretability. We introduce a physics-informed neural network (PINN) framework that combines data-driven learning with embedded physical constraints, available as the open-source package GalactoPINNS. Trained on acceleration measurements, the framework captures complex, small-scale features while preserving global physical consistency. We test on systems of increasing complexity, from controlled analytic halos to cosmological simulations of Milky Way-like galaxies, achieving sub-percent acceleration errors with orbit reconstruction that consistently outperforms analytic baselines. Additionally, we implement a Bayesian neural network to provide spatially calibrated uncertainty estimates, and a time-dependent extension to capture smooth temporal evolution. By treating an analytic model as a structured prior and learning corrections on top of it, the method retains physical interpretability while gaining the flexibility to represent realistic galactic potentials, making it well suited for Milky Way modeling and dynamical inference in the era of current and upcoming large-scale surveys.

Strong light-matter coupling between molecules and optical or plasmonic cavity modes has emerged as a promising platform for advancing photonics, materials science, and chemistry. However, optical cavities and plasmonic resonators in particular are inherently lossy systems characterized by finite photon lifetimes. Accurate theoretical descriptions of molecular dynamics under strong coupling therefore require a proper treatment of cavity losses. In this work, we compare three theoretical approaches for modeling dissipative molecule-cavity dynamics within a realistic parameter regime: the Lindblad master equation, the stochastic Schrödinger equation, and the non-Hermitian Schrödinger equation. As an example, we consider the two lowest energy state of Na2 molecule coupled to a cavity mode and analyze the time evolution of the excited-state population and the mean photon number. Our results demonstrate that the stochastic Schrödinger equation provides an accurate and computationally efficient alternative to the Lindblad master equation, while the non-Hermitian Schrödinger approach is found to be applicable only within a limited range of conditions. Furthermore, we show that inclusion of molecular rotation leads to rotational-vibrational-photonic coupling and gives rise to pronounced nonadiabatic dynamics through light-induced conical intersections. These findings highlight the importance of both dissipation and rotational degrees of freedom for a realistic description of molecular dynamics in strongly coupled molecule-cavity systems.

Measuring the mechanical response of liquid interfaces without direct contact remains a major experimental challenge, particularly in liquid-liquid systems where no solid reference exists. Here, we develop a frequency-modulation atomic force microscopy (FM-AFM) method that probes liquid interfaces through the hydrodynamic confinement of a viscous liquid film between an oscillating probe and the interface. This approach provides simultaneous access to the in-phase and dissipative components of the effective mechanical response under confinement. The method is first validated on a liquid-solid interface, where the measured confinement thickness and the evolution of the mechanical impedance are consistent with elastohydrodynamic theory over nearly one decade in elastic modulus. It is then applied to a liquid-liquid interface, which exhibits a predominantly viscous response with a finite in-phase contribution and a confinement thickness in the micrometric range. These results show that hydrodynamic confinement provides a sensitive, non-contact approach to compare the mechanical response of soft and liquid interfaces, and opens new perspectives for investigating complex and highly deformable systems such as polymer films, biological membranes, and rafts of nanoparticles.

We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into subsets called "centroids", and, as a new ingredient, approximates the homogenized coefficients using sensitivity analysis of micro-configurations with respect to the macroscopic deformation. The novel "model-order reduction" approach significantly reduces the number of microscopic problems that must be solved in nonlinear simulations, thereby accelerating the overall computational process. The degree of reduction can be controlled by a user-defined error tolerance parameter. The algorithm is implemented in the finite element framework SfePy, and its performance effectiveness is demonstrated using two-dimensional test examples, when compared with solutions obtained by the proper orthogonal decomposition method, and by the full "FE-square" simulations. Extensions beyond the present implementations and the scope of tractable problems are discussed.

In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop order in the expansion parameter $\varepsilon = 4-d$. We show that a large group of the necessary three-loop Feynman diagrams can be mapped onto already existing three-loop results, and develop a technique for the calculation of the remaining -- truly novel -- ones. The described semi-analytic procedure is further used to verify existing two-loop results. The main aim of this study is to provide an update on this ongoing work, as full three-loop calculations utilizing the described procedure are in progress.

For a gas-solid interfacial system where chemical species undergo reversible adsorption, we develop a mesoscopic stochastic modeling method that simulates both gas-phase hydrodynamics and surface coverage dynamics by coupling the Langmuir adsorption model with compressible fluctuating hydrodynamics. To this end, we derive a thermodynamically consistent mass-energy update scheme that accounts for how the mass and energy variables in the gas and surface subsystems should be updated according to the changes in the number of molecules of each species in each subsystem due to adsorption and desorption events. By performing a stochastic analysis for the ideal Langmuir model and the full hydrodynamic system, we analytically confirm that our mass-energy update scheme captures thermodynamic equilibrium predicted by equilibrium statistical mechanics. We find that an internal energy correction term is needed, which is attributed to the difference in the mean kinetic energy of gas molecules colliding with the surface from that computed from the Maxwell-Boltzmann distribution. By performing an equilibrium simulation study for an ideal gas mixture of CO and Ar with CO undergoing reversible adsorption, we validate our overall simulation method and implementation.

It is essential that mesoscopic simulations of reactive systems reproduce the correct statistical distributions at thermodynamic equilibrium. By considering a compressible fluctuating hydrodynamics (FHD) simulation method of ideal gas mixtures undergoing reversible reactions described by the chemical Langevin equations, we show that thermodynamic consistency in reaction rates and the use of instantaneous temperatures for the evaluation of reaction rates is required for fluctuations for the overall system to be correct. We then formulate the required properties of a thermodynamically-consistent reaction (TCR) model. As noted in the literature, while reactions are often discussed in terms of forward and reverse rates, these rates should not be modeled independently because they must be compatible with thermodynamic equilibrium for the system. Using a simple TCR model where each chemical species has constant heat capacity, we derive the explicit condition that the forward and reverse reaction rate constants must satisfy in order for the system to be thermodynamically consistent. We perform equilibrium and non-equilibrium simulations of ideal gas mixtures undergoing a reversible dimerization reaction to measure the fluctuational behavior of the system numerically. We confirm that FHD simulations with the TCR model give the correct static structure factor of equilibrium fluctuations. For the statistically steady simulation of a gas mixture between two isothermal walls with different temperatures, we show using the TCR model that the temperature variance agrees with the corresponding thermodynamic-equilibrium temperature variance in the interior of the system, whereas noticeable deviations are present in regions near walls, where chemistry is far from equilibrium.

Violation of local realism via Bell inequality - a profound and counterintuitive manifestation of quantum theory that conflicts with the prediction of local realism - is viewed to be intimately linked with quantum entanglement. Experimental demonstrations of such a phenomenon using quantum entangled states are among the landmark experiments of modern physics and paved the way for quantum technology. Here we report the violation of the Bell inequality that cannot be described by quantum entanglement in the system but arises from quantum indistinguishability by path identity, shown by the multi-photon frustrated interference. By analyzing the measurement of four-photon frustrated interference within the standard Bell-test formalism, we find a violation of Bell inequality by more than four standard deviations. Our work establishes a connection between quantum correlation and quantum indistinguishability, providing insights into the fundamental origin of the counterintuitive characteristics observed in quantum physics.

Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying space is transformed with the same group element, as opposed to a local ``gauge'' symmetry, where each point is transformed with a different group element, exponentially enlarging the size of the symmetry group. Gauge equivariant networks have so far mainly been applied to problems in quantum chromodynamics. Here, we introduce a novel application domain for gauge-equivariant networks in the theory of topological condensed matter physics. We use gauge equivariant networks to predict topological invariants (Chern numbers) of multiband topological insulators. The gauge symmetry of the network guarantees that the predicted quantity is a topological invariant. We introduce a novel gauge equivariant normalization layer to stabilize the training and prove a universal approximation theorem for our setup. We train on samples with trivial Chern number only but show that our models generalize to samples with non-trivial Chern number. We provide various ablations of our setup. Our code is available at https://github.com/sitronsea/GENet/tree/main.

Uncovering the true informational architecture of real-world complex systems requires disentangling how their components uniquely store, redundantly share, and synergistically integrate information over time. Integrated Information Decomposition ($Φ$ID) is a framework for decomposing the information dynamics of multivariate systems into sixteen non-overlapping atoms that characterize redundant, unique, and synergistic modes of information storage, transfer, and integration. Existing methods to compute $Φ$ID are restricted to Gaussian or discrete systems, preventing its application to continuous non-Gaussian dynamical systems. We address this limitation by proposing DIPHINE (Diffusion-based $Φ$-ID Neural Estimator), the first neural estimator that leverages score-based diffusion models to jointly estimate all the mutual information terms required by $Φ$ID from a single amortized network, recovering the sixteen atoms through Möbius inversion. We provide a theoretical analysis of error propagation through the inversion, showing that the Jacobian of the mapping from mutual informations to atoms is integer-valued and that the synergy-to-synergy atom is provably the hardest to estimate. We demonstrate accurate recovery of ground-truth atoms on synthetic benchmarks, superior performance compared to established mutual information estimators, and the ability to extract physiologically interpretable information-dynamic structure on an application involving real data without any distributional assumptions.

Time-dependent partial differential equations (PDEs) arise in many engineering systems, including thermo-fluid applications. Classical numerical simulations of such systems can become computationally expensive for long-time dynamics because they typically require sequential time integration with time steps constrained by stability, accuracy, or nonlinear solvers. Although scientific machine learning provides an alternative for approximating PDE solutions, standard neural network approximations often degrade when extrapolated beyond the training time interval. In this work, we propose a steady-state-informed neural network representation for dissipative PDE systems whose solutions relax toward a stationary equilibrium. The proposed ansatz decomposes the solution into a steady-state component and a transient correction modulated by a time-dependent decay profile. When the decay profile vanishes at long time and the transient correction remains bounded, the representation embeds convergence to the prescribed steady state directly into the architecture, rather than enforcing it through an additional penalty term. This allows the network to learn the transient dynamics while preserving the correct asymptotic behavior. We implement the approach within a physics-informed neural network (PINN) framework and train the resulting model using the SOAP optimizer. The method is evaluated on a sequence of problems of increasing physical and geometric complexity, ranging from the one-dimensional heat equation to incompressible Navier-Stokes flow in a lid-driven cavity, natural convection in a square cavity, and a full three-dimensional conjugate heat transfer problem. The numerical results show that the steady-state-informed architecture substantially improves temporal extrapolation beyond the training interval compared with architectures that do not explicitly enforce the asymptotic condition.

Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing. By mapping infinite-dimensional function spaces, this approach provides an efficient surrogate modeling framework for high-dimensional partial differential equations (PDEs). Compared to traditional numerical solvers, it achieves a superior trade-off between computational complexity and approximation accuracy, demonstrating significant advantages in many-query tasks such as real-time prediction and parameter sweeps. Given the stringent accuracy requirements of both forward simulation and inverse inference, as well as the precision bottlenecks of existing operator learning methods in handling complex boundaries or long-term evolution, we propose the Starter-Iterator Neural Operator (SINO). Our framework reinterprets the initialization strategies and iterative formats of traditional iterative methods through neural networks, establishing an efficient approach for spectral-spatiotemporal collaborative modeling. Specifically, the frequency-domain initialization module captures globally stable low-frequency features, while the time-domain learning module focuses on optimizing local solution residuals, thereby effectively overcoming the inherent limitations of conventional single-domain modeling approaches. Extensive experiments on typical dynamical systems such as the Navier-Stokes equations and acoustic wave equations, as well as practical applications including super-resolution imaging and weather forecasting, demonstrate that SINO achieves outstanding performance in numerical accuracy, generalization capability, and robustness.

Photonic quantum machine learning offers a route to trainable physical representations built from phase, interference and measurement. However, its role in scientific machine learning remains largely unexplored. Physics-informed neural fields provide a natural setting, because differential equations require trial spaces that preserve phase, frequency and derivative structure. Here we introduce a photonic quantum neural field in which coordinates become trainable optical phases, are mixed by multi-photon Fock-space interference and are decoded from photon-number measurements. The photonic circuit is optimized as the neural-field representation itself, not as a fixed feature map or hardware accelerator. Photonic measurement is therefore a trainable representation on which the physics-informed residual is minimized. Across seven elliptic, wave, nonlinear dispersive and inverse PDE benchmarks, we observe a phase-complexity transition: classical coordinate and Fourier-feature networks suffice in smooth regimes, whereas the photonic field is most accurate when residual derivatives amplify phase mismatch. In the hardest regimes it gives the lowest errors, with margins reaching an order of magnitude and about one quarter of the trainable parameters of classical baselines. Frozen and shuffled controls, together with noise stress tests, attribute this gain to learned interference and stable Fock-probability readout under compound perturbations. These results identify photonic quantum measurement as a representation-learning principle for scientific machine learning.

We review beam-quality physics in laser-driven (LWFA) and beam-driven (PWFA) plasma wakefield accelerators through the symmetry group of the idealised blowout wake -- axisymmetry $\mathrm{SO}(2)_ϕ$, adiabatic longitudinal translation, and propagation-direction parity. Transverse perturbations of the wake are classified by an integer azimuthal multipole order $m$ labelling the irreducible representations of $\mathrm{SO}(2)_ϕ$, with the lowest beam-quality observables coupling at a specific multipole: the bunch centroid at $m=1$, cross-plane emittance coupling at $m=2$. A symplectic analogy relates transverse matching to longitudinal beam loading. Several phenomena common to LWFA and PWFA -- hose instabilities, pulse-front-tilt jitter, spot-asymmetry emittance growth, polarisation-dependent centroid motion, resonant cross-plane mixing -- populate the two lowest non-trivial $m$-channels and admit a unified discussion. The positron-witness problem reorganises in the same language: each known mitigation abandons one specific feature of the uniform-density blowout, drawn from a finite set. The classification also raises the possibility of an $m=3$ response channel whose magnitude remains open. We note the connection to symmetry-equivariant Bayesian optimisation of plasma accelerators.

We investigate the driving mechanism of low-frequency unsteadiness in bow shock-turbulent boundary layer interactions due to protuberances. Wind tunnel experiments are conducted at a freestream Mach number of 2.87 with protuberances of different shapes and sizes. From time-resolved surface pressure measurements and schlieren imaging, the unsteadiness is characterized by low-frequency shock oscillations, with a Strouhal number of $St_δ\sim 0.01$ based on the boundary layer thickness ($δ$), while the separated region exhibits predominantly mid-frequency pressure oscillations, with $St_δ \sim 0.1$. Mid-span separation length, $L_{sep}$, is identified as a key parameter in determining time and length scales of shock oscillations. Further details of the interaction are examined through compressible adaptive detached eddy simulations for one particular case, viz.,the cubical protuberance of side 15 mm. A detailed modal analysis using proper orthogonal decomposition (POD) is performed with the 3-D data from computations. Flapping of shock-foot about mid-span was apparent, over and above the coherent to-and-fro oscillations, with the dominance of anti-symmetric mode in the POD of wall pressure fluctuations. The motion of the shock foot is initiated near mid-span, while the shock foot at other spanwise locations lags behind. The flap and asymmetries are related to the spanwise extent of reverse flow. From the reconstructed 3-D flow field using low-frequency modes, along with corroborating observations from the two-point correlations, it is inferred that the imbalance and time lag between the mass injected into the separated region at reattachment and the mass leaving spanwise at the horseshoe vortex core govern the observed shock motion.

Free-surface liquid metal flows are a leading candidate for the plasma-facing components of future fusion reactors. Existing transient, three-dimensional, free-surface MHD solvers rely on the inductionless approximation in which the induced magnetic field is neglected. This paper extends the open-source solver FreeMHD [B. Wynne et al., Phys. Plasmas 32, 013907 (2025)] beyond the inductionless approximation to resolve the induced magnetic field self-consistently using a vector-potential formulation that enforces $\nabla\cdot\boldsymbol{B}=0$ by construction while preserving the original multi-region, two-phase framework. The solver is verified against analytical Shercliff and Hunt duct-flow solutions across a range of Hartmann numbers and validated against free-surface height measurements from the LMX-U experiment. To the best of our knowledge, FreeMHD2 is the first open-source, experimentally validated free-surface liquid metal solver to resolve the evolution of the induced magnetic field without invoking the inductionless approximation. By removing this approximation rather than relaxing it, the formulation provides the basis for future modeling of the finite magnetic Reynolds number conditions expected in large-scale, transient fusion events.

The dynamic response of a zero-pressure gradient turbulent boundary layer (TBL) to a large-scale perturbation in the outer region was investigated experimentally. The baseline TBL had a moderate Reynolds number such that there was no naturally occurring energetic large-scale structure (LSS) present. An active plasma-based actuator was then placed in the outer region of the TBL to introduce a periodic, spanwise-uniform, synthetic LSS. This novel actuation scheme provides a new tool by which to experimentally examine the `top-down' view of TBL dynamics/interactions. The TBL response to this synthetic structure was investigated using a combination of planar particle imaging velocimetry and spanwise offset hot-wires, over a large streamwise extent downstream of the actuator device. Phase-locked analysis was implemented to isolate and measure the streamwise development of large-scale motions and changes in turbulence amplitude induced by this synthetic LSS. A strong correlation was observed between large-scale motions near the wall, linearly superimposed from the synthetic LSS, and a periodic modulation of turbulence amplitudes. This periodic modulation was found to be linked to phase-dependent changes in both the production and transport of turbulence driven by the induced large-scale motions. The phase speed of these induced large-scale motions, coupled with intermittent changes to spanwise coherence near the wall, revealed an additional, but transient, effect of the synthetic LSS on near-wall cycle dynamics. Overall, these results characterize the influences, and limitations, of top-down interactions on global TBL dynamics.

This study presents a comparative investigation of Physics-Informed Neural Networks (PINNs) and data-driven Deep Operator Networks (DeepONets) for predicting the evolution of plane Newtonian Couette flow with dynamic wall slip. While traditional numerical methods, such as the Crank-Nicolson scheme, offer high accuracy, their computational demand poses challenges in real-time applications. To address this, we first implement a PINN framework to solve the governing equations for specific physical parameters. Subsequently, we develop a data-driven DeepONet, trained on high-fidelity numerical data, to learn the continuous solution operator across a broad range of slip boundary conditions and upper wall velocities. Our results indicate that while the PINN achieved superior point-wise precision with a relative L_2 error of 0.083%, it remains constrained by the requirement for instance-specific retraining. In contrast, the DeepONet demonstrates robust generalization on unseen and out-of-distribution signals with a mean relative error of 0.36% and 0.88%, respectively. Most notably, it provides near-instantaneous inference, achieving a speedup factor of approximately 540X over the numerical solver and 30.5% over the PINN. This work demonstrates the synergy between physics-based and data-driven architectures and establishes DeepONet as a highly efficient surrogate model for rapid parametric exploration and real-time fluid dynamics forecasting.

Quantum systems governed by unitary and reversible microscopic dynamics may nevertheless exhibit equilibration, in the sense that some effective description becomes time-independent. Standard equilibration results usually consider two separate situations: system-environment structures, in which the composite system evolves unitarily while the system of interest equilibrates, and restricted measurements, such as coarse-grained POVMs and observables, in which the measurement statistics equilibrate. Here, we bring these descriptions into a common state-level framework using the concept of generalized subsystems, where the accessible effective state appears as the output of a quantum channel acting on the microscopic state. We derive bounds showing that generalized subsystems equilibrate when their dimension is small compared with the effective dimension of the discarded microscopic information. We further show that this condition is met for typical initial states in large subspaces and that the resulting equilibrium description is largely insensitive to microscopic initial details. The framework recovers the usual equilibration bounds for ordinary subsystems and finite families of POVMs. As an example, we also introduce a finite-resolution energy channel that maps unresolved microscopic energy levels into effective energy levels, thereby making residual effective coherences explicit and showing how spectral multiplicities constrain those coherences while strengthening equilibration. Our results provide a unified state-level formulation of quantum equilibration under general forms of limited accessible information.

Spectral kissing, recently realized in a Kerr parametric oscillator (KPO), refers to the merging of pairs of energy levels and arises as a manifestation of an excited-state quantum phase transition (ESQPT). Here, we show that this phenomenon has a dissipative counterpart encoded in the spectrum of the steady-state density matrix. Using a dissipative KPO as a representative example, we demonstrate that, in the weak-dissipation regime, the eigenvalues of the steady-state density matrix organize into quasi-degenerate pairs that mirror the spectral kissing of the corresponding closed system. As the dissipation strength increases, this pairing gradually disappears. By analyzing the classical limit of the system, we derive analytical expressions for the critical lines governing both the onset of steady-state spectral kissing and its disappearance at a dissipative phase transition.