Papers

This paper presents a study of dispersion for the two-dimensional Friedlander model with Neumann and Robin boundary conditions, thereby extending previous works treating only Dirichlet boundary conditions. By considering an Airy-type special function, we obtain a parametrix construction similar to the Dirichlet case but with additional terms requiring careful control. By studying the dispersion of this parametrix, we obtain the same dispersive estimates as in previous results for the Dirichlet case, and therefore the same Strichartz estimates.

Probabilistic downscaling must represent kilometer-scale structure left unresolved by a deterministic regional prediction. We introduce an analog-initialized latent transport method that uses historical regional residuals as a meteorologically informed empirical source. A frozen graph neural network predicts the deterministic state from the Integrated Forecasting System (IFS). For each input, residuals from 20 training dates with similar IFS conditions initialize the ensemble. A conditional flow-matching model transports these fields in a carefully designed 65-factor, 100,000-node latent space, and a grid decoder reconstructs 81 atmospheric channels including precipitation at 2.5km spacing. On a season- and cycle-balanced 2025 test, ensemble CRPS improves over deterministic mean absolute error for all 81 variables. Matched analogs improve point and spatial errors over Gaussian initialization and reduce spectral error compared with covariance matching. Comparisons with released CorrDiff, a local CorrDiff-mini model and full grid EDM provide context on the 2023 validation sample. Total training of the downscaling model takes approximately 12h on one NVIDIA H200, and inference takes about 12s per 81-field member. The frozen networks also generate fields over France when supplied with local static data and a high-resolution IFS-derived analog bank. The method combines empirical initialization with whole-domain latent transport for computationally practical regional ensembles.

The free-energy principle (FEP) and active inference describe adaptive systems through probabilistic generative models and free-energy functionals, whereas integrated information theory (IIT) characterizes intrinsic cause-effect organization. We separate two questions: whether revised IIT quantities admit local free-energy-like representations and whether scalar expected free energy can determine system integrated information. We show that the 2026 IIT intrinsic-differentiation and specification terms admit exact surprisal representations, and hence variational-free-energy representations under exact inference. We then construct noisy binary permutation networks whose causal topology varies while local transition reliability is fixed. In a homogeneous state, all permutations yield the same one-step predictive distribution and state-risk expected free energy under common preferences and observation models, yet revised IIT distinguishes them: multicycle permutations have zero whole-system integration, whereas a single noisy cycle has positive integration at intermediate reliability. For an n-unit noisy single cycle, we derive a closed-form expression for revised system integrated information, prove that the minimum-information partition cuts exactly two causal edges, and show that as n grows the optimal reliability approaches unity, the joint specified-state probability approaches one half, and the maximum integration approaches one ibit. Numerical IIT calculations for n = 2-5 and exhaustive partition enumeration through n = 8 reproduce the analytical results. Thus, local surprisal/free-energy correspondence coexists with global non-equivalence: equal expected free energy does not imply equal revised IIT system integrated information. Any synthesis of IIT with FEP/active inference must retain counterfactual causal information beyond a scalar free-energy value.

We clarify the relation between the time-optimal quantum evolution of Carlini et al. and the coherent two-boundary optimal-control formulation recently proposed for quantum algorithm design.

Multi-objective optimization (MOO) problems are common in logistics, where routing decisions must balance conflicting objectives such as travel distance, delivery time, and operational risk. A recently proposed Quantum Approximate Optimization Algorithm (QAOA) parameter-transfer strategy solves multi-objective MAX-CUT problems by reusing parameters trained on smaller instances, avoiding costly reoptimization for each scalarized problem. However, its effectiveness has only been demonstrated on proof-of-concept instances tailored to quantum hardware connectivity. In this work, we evaluate the applicability of this strategy to realistic routing problems. We formulate the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) as Quadratic Unconstrained Binary Optimization (QUBO) models, reduce them to MAX-CUT, and assess the parameter-transfer framework under conditions matching the original study. Validation is performed through classical simulations and experiments on IBM quantum hardware. The resulting Pareto fronts are compared with those obtained using an adapted classical {\epsilon}-constraint method, using hypervolume as the primary quality metric. Results indicate that parameter transfer remains effective, frequently achieving higher hypervolume and often finding competitive solutions earlier. However, performance depends on problem structure. The approach is consistently effective for TSP instances but less stable for the more constrained VRP, suggesting that QAOA parameter transferability decreases as the optimization landscape becomes more complex. These results provide the first comprehensive evaluation of QAOA parameter transfer on realistic multi-objective routing problems and demonstrate its potential beyond proof-of-concept MAX-CUT benchmarks.

Establishing a lasting human settlement beyond Earth requires a habitable destination at arrival and sustained renewal of its population/infrastructure. We compare Earth delivery, robotic predeployment, local resource processing, localized manufacture under coupled protection, power, recovery, health requirements. In a 1,000-resident case, specific retention times and 1% annual growth require ~1.8 tonnes of equipment replacement/expansion per resident-year. Local manufacture raises mean site electricity from 11.8 to 19.5 MW; the declared retention range gives 17-26 MW at fixed processing intensity. A separate 100-ton/year pilot reduces 10-year deliveries from 1,000 to 419 tonnes after a 3-year commissioning ramp, while retaining imported inputs. Local production thus reduces freight by adding maintained capacity at the destination. Receiving capacity is bounded by replacement-adjusted supply, not passenger throughput. Published Martian transport gives ~63,000 tonnes of planar cover per hectare for the selected 10-mSv/year GCR allocation; Earth-like acceleration at 2~rpm requires a 224-m rotation radius. These scales favor local shielding and modular rotating habitats. Repeated 10-day wastewater outages every 35 days require capacity at least 1.4 times inflow; storage cannot correct a persistent deficit. Existing evidence leaves lifelong partial-gravity, mixed-field radiation responses, gestation, development and subsequent fertility unresolved. With sustained investment, recoverable habitats, resource pilots, controlled-gravity investigations are credible 10-20-year objectives; broad industrial renewal requires multidecade development. Earth-supported habitation is a credible development path. Independent population continuity requires demonstrated health, recovery, demographic resilience, essential-product renewal within one exposure/resource history; its completion cannot yet be dated.

The core-diagonal closure of Bothe and Druet identifies multicomponent Darken diffusion as a thermodynamically consistent Maxwell-Stefan model in which the constitutive data are species tracer diffusivities. Building on the Stieltjes-coordinate and De Giorgi regularity framework introduced in our recent preprint for additive Maxwell-Stefan frictions, we prove global maximal-$L^p$ strong well-posedness, without smallness assumptions, for the affine Darken class with composition-dependent scalar coefficients and uniformly positive tracer diffusivities. We show that this is exactly the maximal Darken class preserving the fixed Stieltjes eigenframe underlying the global argument. For general smooth, uniformly positive Darken tracer diffusivities we also derive the direct constrained flux form, exact mixing-entropy symmetrization, Fisher dissipation, composition-uniform normal ellipticity, and local strong well-posedness. Solutions in the affine class remain uniformly separated from the simplex boundary, become classical for positive times, and converge exponentially to equilibrium. Constant multiplicative frictions, including repeated factors, are covered by grouping species with equal factors.

Young's law on a rigid solid and the Neumann balance at a three-fluid junction describe different admissible motions. We connect them through an ordered continuum construction. An affine viscoelastic third phase first acquires permanent deformation memory in the no-relaxation limit at fixed modulus. Independently specified material-surface laws distinguish surface free energy from mechanical surface stress. On the deformable support, displacement of solid material and migration of the wet-dry partition give separate equilibrium conditions. Stiffening an anchored support suppresses displacement at a fixed macroscopic observation distance but leaves reversible migration possible. The surviving variation gives Young's law; the constrained mechanics remains as a reaction carrying normal and, in general, tangential capillary loads. Two complementary results substantiate this reduction. A clamped finite-strain model with circular liquid interfaces yields uniform convergence of reduced energies and recovery of the spatial Young angle for global almost minimisers. A separate quadratic half-space model gives convergence of stationary migration derivatives and a nonzero limiting traction distribution. The results explain how a local Neumann-like ridge can coexist with a Young angle measured against the distant wall, while distinguishing geometric convergence from the control of migration and reaction forces.

Power magnetic materials are characterized on the sinusoidal and triangular waveforms that excitation hardware conveniently produces, whereas deployed converters expose cores to trapezoidal, PWM-shaped flux trajectories, so loss models must predict exactly where their training data are thinnest. The final test of the MagNet Challenge embeds a deliberately extreme instance of this characterization-deployment mismatch: for material D, trapezoids form 16.4% of the test set but only 1.4% of the training set. The 95th-percentile relative error, hereafter p95, of the best submission, built on sequential transfer learning, stalled at 15.9%, the worst among the five materials. This paper shows that the obstacle is missing information under covariate shift rather than class imbalance, and that the missing support can be borrowed from sibling materials instead of being extrapolated. Controlled experiments first refute the imbalance reading: four standard remedies fail, and raising the trapezoidal share to the test-set level degrades accuracy further. The proposed material-identity support transfer, MIST, then trains one 2784-parameter predictor jointly on all five challenge materials. Material identity enters through feature-wise linear modulation, or FiLM, the scarce material's true-label loss is reweighted, and material D receives no fine-tuning, so that the bias of its trapezoid-free training set is never re-installed. MIST lowers the five-seed material-D p95 from 20.39+/-2.03% to 12.38+/-0.92% and the trapezoidal-class p95 from 37.4+/-8.8% to 15.16+/-1.69%, surpassing the best submission with one-sixth of its parameters and no fine-tuning stage; removing material identity at matched capacity inflates the error by an order of magnitude. These results argue that scarce materials should be characterized jointly with their siblings.

For the neutral periodic one-dimensional Riesz gas with pair potential locally $-|x|^a$, $0<a<1$, we prove a particle-displacement variance bound of order $\beta^{-1}$, uniformly in the number of particles. Log-concavity also gives exponential displacement tails. Every stationary periodic thermodynamic limit is simple, has intensity one, and admits a stationary ordered matching to the unit lattice with the same bounds. Each limit satisfies the canonical Gibbs equations for the full-line interaction, with an ordinary symmetric spatial principal value for the exterior potential. The matching implies uniformly bounded interval number variance and a positive limiting second moment of the reciprocal-lattice Fourier average at sufficiently low temperature. The main estimate compares the inverse random Hessian, through deterministic electrical flows, to a transient long-range network.

For the hard-sphere Boltzmann equation, we derive an exact nonlinear generating vertex for collisional stress and heat-flux production. The complete two-input Hermite hierarchy for stress resums to a universal traceless tensor times one scalar radial law, while the heat-flux vertex follows from the same law by an exact contraction. Taylor differentiation yields universal bilinear collision tensors with exact stress and heat-flux gradings, without a finite moment closure. DSMC tests, including wall-driven flows and a bimodal Mach-5 shock, recover independently sampled Boltzmann productions and the predicted convergence, while the converged production is independent of the thermal Gaussian foot used for its Hermite representation.

Classical electrodynamics is one of the most well-tested and understood theories in physics. After more than a century of history, it may be surprising that such an established theory still makes new predictions that have not yet been experimentally verified. A noteworthy example is the memory effect—a prediction that an electromagnetic wave can leave a lasting influence long after it has passed. This influence is manifested in a velocity “kick” on a test charge. This simple remark lies at the heart of modern investigations of the low-energy behavior of gravity, electrodynamics, and gauge theories and awaits confirmation (or refutation) through experiments. From a pedagogical perspective, this current research topic beautifully epitomizes how standard concepts from undergraduate electrodynamics can still lead to new physics. In this work, we use the Liénard–Wiechert solutions for the electromagnetic fields of moving charges to understand what the memory effect is, where it comes from, and how it could be experimentally probed in the near future. We also discuss the connections between the memory effect and other important topics in fundamental physics, as well as the search for memory in modern gravitational wave observatories.

Transfer and multi-nucleon transfer reactions are essential tools for probing nuclear structure and reaction dynamics, requiring precise determination of the identity, energy, and emission angles of reaction products. The increasing granularity of modern silicon telescope arrays enhances experimental capabilities but challenges detector calibration, as conventional channel-by-channel approaches become inefficient and difficult to scale. In this work, we present a fully automated, physics-informed calibration framework based on neural networks, specifically designed for highly segmented silicon detector arrays. The method formulates calibration as a global optimization problem, in which detector gains and geometrical corrections are determined simultaneously by minimizing the width of the reconstructed excitation energy under two-body kinematics constraints. The approach relies exclusively on experimental data and well-established physical principles, without requiring explicit modeling of detector response. A distinctive feature is the use of multiple neural network sub-models sharing a common loss function with embedded physics constraints, enabling coherent and self-consistent calibration across all detector channels. This strategy ensures scalability, robustness, and reproducibility, making it particularly suitable for next-generation detector systems with increasing complexity. The performance of the method is demonstrated using experimental data from the Particle-Identification Silicon-Telescope Array (PISTA) in high-resolution fission studies in inverse kinematics. The results show excellent agreement with theoretical kinematics, high-quality particle identification, and a significant improvement in calibration efficiency. The proposed framework provides a general and adaptable solution for the calibration of complex detector systems in modern nuclear physics experiments.

Physics has traditionally advanced through two interrelated activities: inferring the laws of nature from observations and testing theoretical predictions. This Perspective proposes a new research paradigm – adversarial physics – that subjects physical limits regarded as insurmountable to active stress testing. We introduce the heuristic concept of a "cosmic bug" to denote an exploitable physical anomaly: a reproducibly realizable physical configuration that grants an observer new capabilities previously considered outside the set of achievable physical operations. The proposed paradigm currently encompasses at least three levels: (1) actively constructing complex systems under established physical laws to seek and exploit unforeseen loopholes in specific configurations and combinations of operations; (2) actively seeking, testing, and exploiting anomalous mechanisms beyond the explanatory scope of currently known theories, prompting revisions to our understanding of physical laws or the discovery of new physics; and (3) exploring how loopholes might be exploited to control or modify local physical rules. We further argue that traditional searches centered on the energy, intensity, and precision frontiers may have comparatively neglected another dimension – the configuration frontier: the vast space of physical configurations comprising complex temporal sequences, phase correlations, coherent and entangled states, feedback protocols, topological structures, multiscale organization, and engineered spacetime or vacuum conditions. Artificial intelligence provides an important tool for exploring this high-dimensional configuration space. The ultimate aim is not merely to map nature's capability boundaries, but to discover and exploit possible loopholes in the laws governing it – including physically realizable routes to controlling or modifying local physical rules.

For a ferromagnetic Ising model on a graph of maximum degree $\Delta\ge3$, we prove a bound of order $\sqrt n$ on every row of the influence matrix at the tree uniqueness threshold. The estimate is uniform in the degree, the external fields, and all pinnings. More generally, if the couplings are bounded by $\beta$ and $\varepsilon=((\Delta-1)\tanh\beta-1)_+$, the bound is $C(\sqrt n+n\varepsilon)$. The proof combines a pointwise cavity bound with a positive-series magnetization tilt and the field comparison theorem of Ding, Song and Sun. The critical estimate removes the logarithm in recent general graphical bounds for the ferromagnetic case. As a consequence, zero-field single-site Glauber dynamics mixes in polynomial time throughout the supercritical window $\varepsilon=O(\sqrt{\log n/n})$, with the polynomial degree depending on the window size.

We present a covariant modified gravity theory which reproduces all the galactic phenomenology usually attributed to dark matter in the low acceleration regime, including the flat rotation curves of massive tracers, and the deflection angles of photons as inferred through gravitational lensing. We first derive a fully covariant description of galactic space-times under a spherically symmetric and static approximation. This description accounts for flat rotation curves, observed gravitational lensing phenomenology and the Tully-Fisher mass scalings of the above. The resulting covariant description is then used to constrain the parameters of a minimally coupled gravitational action using power laws for both the Ricci scalar and the matter Lagrangian. The action presented hence leads to field equations whose trace, under the approximations taken, has as solutions metric coefficients which exactly reproduce flat rotation curves, gravitational lensing observations and observationally determined Tully-Fisher galactic mass scalings of any required index. This last allowing for an accurate fitting of observational dynamics up to galaxy cluster scales.

The answer is "Yes". As it has been shown in the Ref.[1] (22 Sep.2017, see also the comments), useing a new definite mathematical axiomatic-algebraic matrix approach, all the fundamental laws of nature could be derived uniquely (where the axiom of "no zero divisors" of the ring of integers has been generilzed and written in a new definite formulation, then basically assuming that all the physical quantities could only and only take the rational values). Based on this new mathematical approach along with the C, P and T symmetries of the derived field equations, it is concluded that the universe could be realized solely with the (2+1) and (3+1)-dimensional space-times. Moreover it is shown that the (3+1) dimensional cases of the directly determinated general covariant field equations (including two definite classes: a two indexes and a four indexes tensor fields), respectively, represent two new massive forms of the bispinor fields of spin-1and spin-2 particles; and the (2+1)-dimensional cases of the drived equations (including: a two indexes and a four indexes tensor fields), represent (asymptotically) two new massive forms of the bispinor fields of spin-3/2 and spin-1/2 particles, respectively. As a particular result, based on the formulation of the derived Electromagnetic Maxwell equations (representing by the bispinor fields of spin-1 particles, including new field equations - corresponding to the YangMills equations - compatible with two specified forms of the gauge symmetry groups), it has been concluded that magnetic monopoles could not exist in the nature to any extend. Furthermore, as the only elementary particles that could be existed in nature, along with the all discovered particles, eight new particles, including four charge-less right-handed spin-1/2 fermions (two leptons and two quarks), and a spin-3/2 fermion, and also three spin-1 massive bosons are also solely predicted.

Liquid droplets deform from spherical shape due to aerodynamic variation of pressure along the surface as the droplet moves through a gas. The deformation is predicted for axisymmetric droplets translating through a gas with low Weber numbers, We < 1, and Reynolds number Re = O(10). That deformation analysis is based on the relations between local pressure jump and the two radii of curvature. A thin boundary layer on both sides of the gas-liquid interface is considered with a surface-velocity jump due to pressure-gradient-driven flow with a large density jump and a pressure jump due to surface tension. A near-ellipsoidal shape is predicted using $We$ as a perturbation parameter. Then, the quasi-steady internal liquid-phase stream function and velocity field are predicted, describing internal circulation and a vortex ring structure with vorticity distributed through an inviscid liquid. The gas-phase flow over the oblate droplet is described using a ring doublet as an image within the droplet. The ring-doublet radius is related to We. Gas potential flow results are presented and compared using both the exact analytical solution and a perturbation analysis based on the square root of We. The perturbation analysis provides a lower computational cost. Three analyses for local curvature, liquid circulation, and gas potential flow are matched to yield the velocity and pressure fields. The appropriate radius for the image ring doublet is matched to the square root of We. Liquid-phase stream function, two velocity components in each fluid, and gas potential field are predicted. S Some comments on droplet drag are presented.

The exploration of non-hexagonal two-dimensional topologies has opened new possibilities for tailoring the properties of group III-V monolayers beyond those accessible through conventional honeycomb phases. In this context, we have investigated the structural, mechanical, electronic, and optical properties of T-GaN, a two-dimensional tetragonal gallium nitride monolayer composed of alternating four- and eight-membered rings featuring coexisting homoelemental (Ga-Ga, N-N) and heteropolar (Ga-N) bonds, using density functional theory (DFT) within the generalized gradient approximation (GGA/PBE) and the hybrid HSE06 functional. The dynamical stability of T-GaN was confirmed by phonon dispersion calculations, which revealed the absence of imaginary frequencies throughout the Brillouin zone, and was further supported by ab initio molecular dynamics (AIMD) simulations. The mechanical characterization reveals a pronounced in-plane anisotropy, with critical strains of approximately 16.5% and 7.0% along the $x$- and $y$-directions, respectively. The electronic band structure analysis indicates that T-GaN is a nonmagnetic semiconductor with an indirect band gap of 0.35~eV (PBE) and 1.15~eV (HSE06), with the valence band maximum dominated by nitrogen 2p orbitals and the conduction band minimum governed by gallium 4s and 4p states. The optical response was evaluated along three crystallographic directions, exhibiting considerable anisotropy in the absorption coefficient, refractive index, and reflectivity. These findings provide new insights into the physical properties of tetragonal group III-V monolayers and suggest that T-GaN may serve as a promising candidate for anisotropic nanoelectronic and optoelectronic applications.

Atomic vacancies and vacancy aggregates control the thermodynamic stability and the functional response of graphene, yet the configurational space spanned by many vacancies at variable concentration and separation is too large to be mapped exhaustively by first-principles methods. Here, we map and rationalize this stability landscape by combining semiempirical atomistic thermodynamics, interpretable machine learning, and symbolic regression. Several hundred defective supercells, built from a 72-atom cell by varying the vacancy concentration and the inter-vacancy distance up to the fourth neighbor, were relaxed with the PM7 Hamiltonian in MOPAC, and the heat of formation was adopted as the stability metric. Each structure was encoded with the Dynamic Collision Fingerprint, a translationally and rotationally invariant descriptor that maps the local topology onto transport-like statistics of virtual probe particles. A gradient boosted decision tree model, optimized by Bayesian hyperparameter search, reproduces the heat of formation of an independent test set with a root mean squared error of approximately 23.5~kcal/mol and no evidence of overfitting, and a SHAP analysis identifies the defect concentration and the inter-vacancy distance as the two variables that dominate the stability. Symbolic regression then condenses the learned mapping into a compact closed-form expression that reproduces the heat of formation with a coefficient of determination of $R^{2} = 0.9966$, a mean absolute error of 15.51~kcal/mol, and a root mean squared error of 24.18~kcal/mol. The workflow turns a high-dimensional structure–stability problem into an interpretable analytical law, providing a transferable route to rational defect engineering in two-dimensional materials.

Background and Objectives: Spatial mapping retains the spatial distribution of radiomic features, but computational cost and fragmented software limit its use. We developed Flash-Radiomics with scalar extraction and spatial mapping, a central processing unit (CPU) backend, a hybrid Compute Unified Device Architecture (CUDA) backend, consistent feature names, and Hierarchical Data Format version 5 (HDF5) storage. Methods: We evaluated Image Biomarker Standardisation Initiative (IBSI) compliance, CPU-CUDA concordance, and end-to-end processing time. Compliance testing included 825 chapter 1 (IBSI-1) tests covering 165 high-consensus features and 323 chapter 2 (IBSI-2) tests with numerical references. Concordance testing included 1,148 scalar pairs and 93 spatial-map pairs. End-to-end processing time was measured five times per input volume of interest (VOI) size. Comparisons included the Medical Image Radiomics Processor (MIRP) and PyRadiomics for 102 shared scalar features and PyRadiomics for 93 shared spatial maps. Results: Both backends passed all 1,148 IBSI tests, and all paired results were concordant. At the largest scalar input, CPU required 76.343 s and hybrid CUDA 81.915 s; CPU was 4.7 times faster than MIRP and 190.7 times faster than PyRadiomics. At the largest spatial input completed by both backends, hybrid CUDA reduced processing time by 68.6% relative to CPU (79.280 versus 252.791 s). At PyRadiomics' largest completed spatial input, hybrid CUDA was 84.9 times faster. Conclusions: Flash-Radiomics unified standardized scalar extraction, spatial mapping, concordant CPU-CUDA results, and HDF5 storage. CPU processing time was similar or shorter for scalar extraction, whereas hybrid CUDA was faster for spatial mapping under the tested conditions.

We study the effects of conductivity variation on the Ponomarenko dynamo. Taking monotonically increasing/decreasing and sinusoidally varying radial profiles, we study the kinematic dynamo problem. The threshold of the dynamo, given by the critical magnetic Reynolds number Rm$_c$, is found to strongly depend on the form of conductivity variation near the discontinuity of the velocity field where the shear is dominant. For monotonically varying profiles in the limit of sharp variation, this threshold maps to the problem of the dynamo with a jump in conductivity, while for the sinusoidal profile with large variations/wavenumbers, the threshold increases due to effective diffusivity arising from the rapid changes in conductivity. Far from the threshold, it is found that the growth rate depends only on the local gradient of the conductivity near the discontinuity, with the opposite sign of shear and conductivity gradient leading to a larger growth rate, thereby aiding the dynamo instability in regenerating B$_{\phi}$ from B$_r$. We calculate the expression for the growth rate in the limit of large Rm$(\gg 1)$ and find that the conductivity variation leads to a modification proportional to the local gradient of conductivity times Rm$^{-1/2}$. This correction is found to depend only on the local gradient of the conductivity at the discontinuity. Similar dependencies are found for realistic, smooth velocity profiles and for different magnetic boundary conditions.

(Suzuki-)Trotter decompositions, splitting methods, (Lie) product formulae... The most common numerical methods for the time evolution of quantum systems come with many names. And they are used practically everywhere with applications ranging from the solution of classical equations of motion and various Monte Carlo simulations to the real and imaginary time evolution on classical as well as quantum computers. Here we review the state of the art of said methods, focussing especially on the progress made over the last few years. We highlight recently discovered efficient time evolution algorithms and explain how best to use them in practice. A central part of this work is the estimation of error bounds that has improved greatly within the past decade. The relevance of time evolution methods for quantum computing is discussed with a focus on noisy hardware. Finally, a comprehensive overview of generalisations, related methods and alternatives to Trotterization is provided. This includes time-dependent Hamiltonian dynamics, processed methods, multi-product formulae, symplectic integrators, TDVP for tensor networks, quantum signal processing, Crouch-Grossman methods and more. The overall perspective in this work is that of a theoretical physicist. All mathematical proofs as well as some technical details are omitted for easier readability. Instead, this review serves as a hands-on guide and, of course, as a starting point for references that provide further details.

Whether human or large language model (LLM), an agent in a discussion reads only a few of the others' contributions, bounded by cognition, context, or cost. LLM collectives can settle on a wrong consensus even when a majority starts out correct; we ask how far that reading bound alone decides the outcome. We model the bound with one number, the message capacity, which sets how many of the others' messages an agent reads, and generate the communication network from it. Over 31,824 randomized queries, we found that an 8-billion-parameter model's judgment of a claim effectively reduces to a logistic function of a weighted sum of its inbox, the update rule of a stochastic binary neuron with divisively normalized weights. From these weights and the network's degree statistics alone, the wrong consensus should become unreachable from any start once agents read, on average, fewer than 6.4 of their 31 sources. In 1,414 episodes with assigned starts the prediction failed: the correct side won in fewer than 50% of episodes from every start, and in only 28-45% when 75% of agents started correct. The failure traces to the field, the threshold that a claim's wording sets for the agent's answer before any message is read: the experimental claims' fields lay below the calibration mean, and with each claim's own field the same weights reproduce the outcomes. Reversing the wording showed that the threshold follows what a claim asserts, not whether it is true. On a second 8B model the pipeline predicts claim-dependent bistability; transition points appeared where computed, and an eight-claim calibration matched in 15 of 16 conditions. At 70B the assertion bias is not detected. Thus a collective's fate is largely set by two single-agent measurements: the threshold a claim's wording sets, and the message capacity that sets the transition point.

We study single-particle Penrose extraction from a rotating black hole whose mass decreases in time, described by the ingoing Kerr-Vaidya metric, imposing exact four-momentum conservation at the decay. We prove that the local efficiency is bounded by the instantaneous Kerr value, through a covariant bound that reduces to the Bardeen-Press-Teukolsky limit at the horizon, and we derive an exact transport law, dE/dtau = -dm/dt (r/Sigma) p_r^2 for fixed spin parameter, by which every timelike geodesic gains energy while the hole loses mass. The net energy gain therefore splits into a local Penrose term and two transport terms, which we compute numerically as functions of spin and mass-loss rate for two mass-loss laws. With fixed spin parameter, extraction is possible only below a critical rate alpha_crit(a) = (M-a)/Delta v, set by the approach of the hole to extremality; with fixed a/m no such boundary exists. The transport law extends to the Kerr-Newman-Vaidya family, and the regime where the dynamics matter is shown to lie far outside astrophysical mass-loss rates.

The classic theory of Landau damping requires the velocity distribution function (VDF) to be analytically continued into the complex plane, implicitly requiring analyticity, which imposes constraints far more severe than infinite smoothness. Yet physical plasmas—encountered in discrete simulations, noisy spacecraft measurements, or truncated fusion distributions—are inherently non-analytic. This discrepancy poses a foundational “smoothness paradox”: why does Landau damping robustly persist in systems where the mathematical prerequisite of analyticity is profoundly violated? Here we resolve this paradox by demonstrating that wave-particle interaction is governed by a time-dependent resonance width $\Delta v_\mathrm{res}\sim 1/kt$. Using a dispersion-free Lagrangian time-domain solver, we show that this finite width kinematically coarse-grains microscopic VDF defects at early times, acting as a natural low-pass filter that validates smooth analytical proxies—explaining the observed robustness. However, as $t\to\infty$ the resonance width narrows, inevitably forcing the wave to resolve exact topological non-smoothness. This late-time resolution triggers three distinct breakdowns: VDF truncation arrests the resonant phase transition to yield undamped discrete Van Kampen modes; observational noise induces transient algebraic spikes via linear phase-space aliasing; and step-like gradients drive anomalously violent reactive instability growth. We establish the breakdown timescale $t_b\sim 1/k\delta v$, where $\delta v$ is the characteristic scale of the non-smooth defect, providing a quantitative criterion that redefines the validity boundaries of analytic continuation in kinetic theory.

In this work, benefiting from the increased sample of neutron stars with measured masses and radii as well as the incorporation of the chiral effective field theory and perturbative QCD constraints, the tidal parameter $\kappa_2^T$ is constrained to be $78^{+17}_{-11}$ (68.3% credible interval, mainly adopted in this work unless mentioned specifically) for the binary neutron stars involved in GW170817. Such a $\kappa_2^T$ is in favor of strong gravitational wave radiation in the post-merger phase and the corresponding energy is estimated to be $E_{\rm GW,p} \simeq 0.051^{+0.022}_{-0.017}\,M_\odot c^2$. Assuming the remnant from binary neutron star merger is a supramassive neutron star, as suggested by the modeling of the electromagnetic counterparts of GW170817, we examine the maximum mass of nonrotating neutron stars ($M_{\rm TOV}$) while accounting for the uncertainty in the remnant's lifetime ($t_{\rm c}$). Our results show that $M_{\rm TOV}$ varies from $2.09^{+0.11}_{-0.09}\,M_\odot$ for $t_{\rm c}=0.1$ s to $2.18^{+0.10}_{-0.09}\,M_\odot$ for $t_{\rm c}=1$ s. This result is consistent with that independently inferred from the re-construction of the equation of state of neutron star matter, i.e., $M_{\rm TOV,exc}=2.16^{+0.10}_{-0.07}M_\odot$, particularly if the very massive neutron stars with masses measured indirectly have been removed in constructing the prior distribution of $M_{\rm TOV}$. The consistency of the maximum mass of nonrotating neutron stars found in different approaches suggests a reasonable understanding of this key parameter for dense-matter physics.

The LUX-ZEPLIN experiment reported a candidate nuclear recoil at $248\,\mathrm{keV}$. This work proposes that endothermic self-scattering $\chi_1+\chi_1\to\chi_2+\chi_2$ in the Galaxy can produce an excited dark matter population, whose exothermic scattering $\chi_2+\mathrm{Xe}\to\chi_1+\mathrm{Xe}$ in xenon can account for the LZ candidate event. In a benchmark with a light scalar mediator, the conversion cross section is large enough for high-velocity Galactic dark matter particles to generate an excited fraction at the percent level. For dark matter masses near the TeV scale and mass splittings $\delta\gtrsim 500\,\mathrm{keV}$, the xenon recoil spectrum covers the candidate region and can yield an $\mathcal O(1)$ event count. The $\chi_2$ population produced in the Galaxy is colder than a relic population from the early Universe and yields a different nuclear recoil spectrum.

Primordial black hole dark matter is formed from the collapse of enhanced primordial density fluctuations. The formation of primordial black holes is accompanied by scalar induced gravitational waves whose infrared scaling only depends on the equation of state, $w$, of the background at leading order. Establishing whether this characteristic scaling remains robust under corrections of arbitrary perturbative order, including in the presence of non-Gaussianities, requires a physical understanding of the infrared scaling. In this work, we provide such a physical interpretation. We find that the stress of sound waves with nearly equal frequencies produces a slow beat. Although the incoming waves oscillate rapidly, this slow beat continues to source the long wavelength tensor perturbation before its horizon entry, thus generating an infrared scaling that only depends on the expanding background. We show that higher order interactions generate freely propagating waves that finally lead to the same slow beat deep inside the horizon. Since non-Gaussianities would not change the speed of the freely propagating waves, they do not modify the infrared scaling. As the source with a slow beat has enough time to accumulate before the horizon entry of the infrared tensor mode, it records the background expansion and thus the infrared scaling could provide a robust probe of the cosmological equation of state.

Posture control in slender bodies such as snakes and eels arises from the interplay between passive deformation, active internal actuation, and task-level constraints. We formulate a general framework for the selection of stable postures in active elastic filaments subject to distributed forcing from gravity and fluid drag, by combining the constraints of mechanical equilibrium with optimal control theory. Our theory leads to a minimal description in terms of parameters governing the competition between hydrodynamic and gravitational loading, elasticity, and activity. We show that posture selection reflects a trade-off between control cost, function and dynamical stability, leading to the coexistence of distinct solution branches and abrupt transitions between them. Applying the theory to sessile eels in flow, we recover the experimentally observed transition from upright to reclining postures and predict scaling laws for body shape and exposed length. More generally, our results provide a unified perspective on how active filaments can regulate geometry to maintain function in external fields, with implications for biological and artificial systems.