Papers

Imaginary-time evolution (ITE) is a powerful method for ground-state preparation of a given Hamiltonian. The normalized ITE can be viewed as a gradient flow of the energy expectation value with respect to the Fubini–Study metric. In this work, we propose a generalized nonlinear imaginary-time evolution (NITE) for more general quantum state-preparation tasks. We further present a hardware-efficient variational implementation of NITE and reveal its connection to quantum natural gradient descent. NITE is applied to several subroutine tasks, including variance minimization in variational eigensolvers, probe-state preparation in variational quantum sensing, and excited-state preparation using penalty terms. We prove that NITE achieves a local exponential convergence rate under reasonable assumptions. Our results show that NITE outperforms standard gradient descent and can serve as an efficient optimization method for variational tasks beyond ground-state preparation.

Active selection of the measurement basis underpins quantum protocols including device-independent quantum key distribution, quantum teleportation with active feed-forward, and Bell tests. High-speed operation is crucial to minimize the latency between consecutive measurement choices, enabling faster protocol execution and higher achievable communication rates. Here, we demonstrate a GHz-rate all-fiber polarization state analyzer enabling active, trial-by-trial reconfiguration of the measurement basis, which we validate by performing a CHSH Bell test. The state analyzer is based on a fiber Sagnac interferometer incorporating a lithium niobate electro-optic phase modulator, built entirely using off-the-shelf fiber-optic components. Operating at a nominal repetition rate of 1 GHz, the system performs dynamic polarization measurements for the CHSH Bell test, achieving polarization visibilities up to 99% and a violation of $S = 2.6975 \pm 0.0005$, certifying entanglement at an unprecedented rate. Furthermore, the system demonstrates excellent long-term stability, preserving the Bell-inequality violation for more than 6 hours without realignment. These results establish the proposed state analyzer as a versatile, scalable platform for quantum communication protocols requiring fast, reconfigurable polarization-state measurements.

Turbulent concentric coaxial (annular) pipe flow with passive heat transfer is theoretically analyzed and numerically modeled in an extended parametric range using the stochastic one-dimensional turbulence (ODT) model. ODT provides predictive capabilities by fully resolving viscous, conductive, and turbulent advective transport processes along a representative radial coordinate within a dimensionally reduced and stochastic model formulation. Using a fixed model calibration for moderate and low Prandtl numbers, $Pr=0.71$ and $0.025$, effects of radius ratio, $\eta=R_{\rm i}/R_{\rm o}$ are investigated up to a highly turbulent flow regime. The analytical expression of the inner wall boundary layer yields a logarithmic law of the wall for the passive temperature. These results suggest that a conventional linear expression is inadequate for representing near-wall low-order statistics in the radial gap, in particular at the cylindrical inner wall. Additionally, the log-law region falls short if curvature and finite Reynolds number effects are not considered. Analytical boundary layer profiles fitting numerical predictions form the basis for heat transfer scaling relations. Heat transfer scalings are parameterized by a Nusselt correlation, which is extended to account for radius ratio effects. The findings demonstrate that the radius ratio has a significant impact on the thermal statistics over the two curved walls and should be considered even at high Reynolds numbers and low Prandtl numbers.

Pair creation from the vacuum in the presence of a U(1) gauge field in de Sitter $(\mathrm{dS})$ spacetime provides an important setting for exploring quantum field theory in curved backgrounds. In this work, we investigate massless fermion production and the associated induced current generated by a constant electric field in (1+2)-dimensional $\mathrm{dS}$ spacetime. Assuming the Bunch–Davies vacuum and employing adiabatic regularization, we derive, for the first time, a finite expression for the induced current of massless fermions in $\mathrm{dS}_{3}$. The produced fermions generate a net current opposite to the external electric field. In the strong-field regime, the induced current exhibits the expected semiclassical scaling and reproduces the standard Schwinger behavior in the flat-spacetime limit. In the weak-field regime, the current is linear in the electric-field strength. This behavior is characteristic of the fermionic nature of the particles, since the corresponding bosonic case exhibits infrared hyperconductivity, which is absent in our study. We further show that the induced current remains monotonic throughout the parameter space and, unlike in $\mathrm{dS}_4$, does not exhibit any sign change. Our results thus highlight the role of dimensionality and clarify the interplay between spin and infrared physics in $\mathrm{dS}$. This work provides a consistent basis for future investigations including backreaction effects, topologically massive fermions, and time-dependent electromagnetic backgrounds.

We introduce two non-adiabatic semiclassical methods that employ two coupled Gaussian wavepackets, each one traveling on a separate diabatic potential energy surface. The wavepackets take the form of thawed Gaussians and are driven by classical equations of motion which account for the diabatic coupling. The classical equations of motion are derived in one case by enforcing the thawed Gaussian ansatz, while in the other the time-dependent variational principles to the thawed Gaussian ansatz. After a sanity check where both approximations reproduce Rabi oscillations, the methods are applied to two non-adiabatic potential energy scenarios. The first one involves two coupled displaced harmonic oscillators, as in a typical electron transfer reaction. The second one comprises a Morse potential coupled to an upper dissociative state, modeling a photo-dissociation process. In both scenarios, the variational thawed Gaussian approach is quite accurate, while the standard thawed Gaussian one fails to fully capture the non-adiabatic effects. Ultimately, non-adiabatic molecular dynamics is reproduced by means of two classical trajectories without introducing any artificial jump or other ad-hoc non-classical effects.

The Earth's interior at depths exceeding present direct probing limit, which is just one five-hundredth of its radius, remains unknown to a significant extent due to existing ambiguities in predicting the distribution of temperature, pressure and chemical composition on the basis of seismic and geophysical observations. Scanning the Earth with neutrinos can provide independent information for refinement of existing seismological models. However, neutrinos interact with medium extremely weakly. Only tiny TeV-energy component of the atmospheric neutrino flux is noticeably absorbed while traversing the Earth, which provides limited statistical data. Flux reduction for much more common neutrinos with energies of the order of 1 GeV is vanishing. However, on their way through the planet they undergo sizable flavor oscillations that depend on the electron number density, which provides a link to seismological models. Accurate calculation of the matter effect in these oscillations is required for successful neutrino oscillation tomography of the Earth besides growing power of neutrino experiments, e. g., KM3NeT, DUNE and Hyper-Kamiokande. We obtained relevant neutrino oscillation probabilities in the second order of perturbation theory. Our results are valid for a neutrino potential that is not necessarily symmetric along the neutrino path. This allowed us to implement a multi-shell evolution scheme to better account for the density jumps between various layers of the Earth.

Let $H_a=-\Delta+a|x|^{-2}$ be the Friedrichs extension on $L^2(\mathbb{R}^d)$, where $d\ge 3$ and $-(d-2)^2/4\le a<0$ lies in the attractive Hardy range. Starting from the known positive two-sided comparison for the kernel of $H_a^{-s/2}$, we determine the complete strong non-endpoint mapping range for two power weights. If $\sigma=(d-2-\sqrt{(d-2)^2+4a})/2$ and $0<s<d-2\sigma$, then [ ||x|^{-\beta}H_a^{-s/2}f|{L^q} \lesssim ||x|^\alpha f|{L^p} ] holds for $1<p,q<\infty$ precisely under the exponent ordering, scaling, sum, and origin conditions stated in the main theorem. At either origin-critical boundary, the strong estimate and the corresponding weighted $L^p\to L^{q,\infty}$ estimate fail, whereas the Lorentz replacement $L^{p,1}\to L^{q,\infty}$ holds. We also derive weighted Sobolev consequences and treat the Hardy-critical Friedrichs case separately. No new heat-kernel, spectral multiplier, Bernstein, or Littlewood–Paley theorem is claimed.

We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.

Strongly constrained quantum systems, in which local rules forbid most configurations, play a central role in condensed matter and lattice gauge theory. Their thermalization is often thought to be delicate: extensive conservation laws and dynamically frozen states can shatter the Hilbert space into many disconnected sectors. A natural question is whether, once the frozen states are removed, the dynamics within a single sector still thermalizes. We address this in the height-conserving quantum dimer model on the square lattice, whose local plaquette flips conserve an emergent height field. Resolving the winding numbers, the four sublattice heights, and lattice momentum , we isolate the dominant connected Krylov component of each fragmented sector and analyze its spectral spectral statistics, entanglement, and connectivity. The two standard chaos diagnostics then show different behavior:across momentum sectors the level-spacing statistics range from near-Poisoon to Wigner-Dyson, yet in every sector the eigenstate entanglement entropy collapses onto a narrow, dome-shaped curve characteristic of eigenstate thermalization. Only a handful of low-entanglement outliers interrupt this thermal pattern, in selected sectors. Thus, strong kinematic constraints can lead to a situation where spectral correlations and eigenstate thermalization need not follow the same universal signatures – a manifestation of constrained quantum chaos.

This study investigates the boundary conditions for fluid-dynamic equations at the interface of a gas and its condensed phase during steady evaporation of a polyatomic gas. Evaporation curves illustrating the dependence of the temperature and pressure ratios on the Mach number are considered for a calorically perfect gas whose molecules behave like rigid rotors. At the condensed phase, complete absorption conditions are assumed. Also an extension to cases in which a part of the molecules is diffusely reflected at the condensed phase is also considered. We revisit the half-space evaporation problem for polyatomic gases based on previous results, applied to a slightly modified entropy functional. The structure of the (modified) maximal total entropy production curves is investigated, and simple functions that accurately fit the numerical results are proposed. Functions of the proposed form, with modified coefficients, also fit the evaporation curves previously obtained by different numerical methods surprisingly well. The approximation is performed for different numbers of internal degrees of freedom or ratios of specific heats. Simple functions that depend on the ratio of specific heats are found to fit the obtained evaporation curves for different ratios of specific heats very well.

We present the first calculation of the $B \to D_1(2420)$ and $B \to D'_1(2430)$ transition form factors at ${\cal O}(\alpha_s)$ using light-cone sum rules within the framework of soft-collinear effective theory (SCET). We first match the QCD transition currents onto ${\rm SCET_I}$ and then factorize the corresponding vacuum-to-$B$-meson correlation functions in ${\rm SCET_{II}}$. The resulting factorization formulae are used to construct the leading-power sum rules for the effective SCET form factors $\xi^R_{\parallel/\perp}$ and $\Xi^R_{\parallel/\perp}$ ($R=D_1,D'_1$). In particular, we calculate the additional longitudinal form factor $\xi^R_{\parallel,m_c}$ induced by the finite charm-quark mass, whose contribution depends only on the $B$-meson light-cone distribution amplitude $\phi_B^+(\omega,\mu)$. To disentangle the mixed $D_1$ and $D'_1$ states, we introduce dedicated combinations of interpolating currents, with their decay constants determined via the equations of motion. To isolate the orbitally excited states from ground-state contamination, we subtract the ground-state contribution from the total sum rules and examine the stability of the resulting sum rules. Furthermore, the $q^2$-dependence of the physical form factors is extrapolated over the full kinematic region using the Bourrely–Caprini–Lellouch parameterization. Finally, we provide phenomenological predictions for the branching fractions, differential decay widths, and lepton flavor universality ratios. Numerically, we obtain $R(D_1) = 0.070^{+0.028}_{-0.018}$ and $R(D'_1) = 0.159^{+0.032}_{-0.025}$, which can be confronted with the future measurements at Belle~II and LHCb.

We present the H-cloud formalism, a cloud-accessible and open-source finite-element framework for electromagnetic modelling of applied superconductors. The proposed method expresses the nonlinear electromagnetic response of type-II superconductors in a curl-conforming discretisation based on Nédélec finite elements, where the tangential applied-field boundary condition, nonlinear E-J power law, and fully implicit time-discrete residual are stated explicitly at the variational level, all within a scripted Python finite-element workflow. The weak form is used as the basis for forward simulation and for extension to adjoint differentiation and PDE-constrained optimisation, while keeping the governing assumptions, boundary conditions, and solver structure fully visible to the user. The implementation is realised in Firedrake with UFL and PETSc-backed nonlinear solvers, allowing the identical script to run on local machines and in browser-accessible environments such as Google Colab without reformulating the problem. The method is verified on the canonical magnetisation benchmark of a cylindrical superconductor under Bean-like penetration conditions and then benchmarked against an independently constructed COMSOL model for a practical high temperature superconducting Bi2212 wire. Across matched mesh studies, the open-source workflow reproduces the commercial-reference magnetisation loops to within approximately \(1\%\) , with relative peak errors below 1.5%, while cloud execution preserves the same numerical solution at rather modest additional runtime considering the use of (freely available) reduced hardware resources. The proposed framework provides a rigorous, reproducible, and portable route for superconducting simulation, benchmarking, and future optimisation-led modelling of applied and functional superconductors, shareable and executable into open cloud environments.

We present a hybrid halo model, which improves the description of the 2-halo term by incorporating non-linear information from simulations. A linear computation of the halo-halo power spectrum is inaccurate at the transition between the 1-halo and 2-halo regimes, whereas nonlinear approaches such as Hybrid Effective Field Theory (HEFT) are not naturally compatible with the halo model decomposition. We address this limitation by constructing a collapsed HEFT (CHEFT) framework, in which the power-spectrum templates of the HEFT operator expansion are measured from simulations where 1-halo contributions are removed by collapsing particles to their halo centres. The halo-halo power spectrum is then expressed as a sum over bias operators, with mass-dependent bias parameters deduced from simulation using the probabilistic bias approach. This provides a predictive model in which there are no free bias parameters. We validate the model for a range of weighting schemes designed to mimic the halo-mass dependence of astrophysical observables, including the Sunyaev-Zeldovich effect, the Cosmic Infrared Background, and galaxy abundances described via a halo occupation distribution. For the matter field, the model recovers the power spectrum to percent-level accuracy across the transition regime. For weighted tracers, the baseline model achieves accuracies of $\sim 5-10\%$ in power, which improves to the $\sim 3-5\%$ level when including an effective higher-derivative, Laplacian-like contribution in the bias expansion. The CHEFT model thus retains the precision and flexibility of the EFT approach, while allowing the transparent incorporation of astrophysical effects that are directly associated with haloes.

Controlling the energy scales of a quantum system is essential for defining robust qubits. In silicon spin qubits, the nearly degenerate conduction-band valleys create a leakage channel from the single-spin computational basis, posing a challenge to scaling and to shuttling-based architectures. Here, we measure the relevant energy scales of single-electron spin qubits in buried silicon quantum wells co-designed for low disorder and high valley splitting. Across a linear array of four quantum dots with an average orbital energy of 2.4(2) meV, we report an average single-electron valley splitting of 0.40(6) meV and an average two-electron singlet-triplet splitting of 0.24(7) meV. In three dots, we observe a strong correlation between valley splitting and orbital energy, with an average linear coefficient of $\approx 0.22$ (meV/meV), demonstrating that electrostatic confinement can increase the valley splitting by several hundred microelectronvolts. In contrast, the remaining dot exhibits the highest valley splitting of 0.76(2) meV and low correlation, suggesting excellent characteristics for spin-qubit operation. Our findings demonstrate that strong confinement can be exploited in buried quantum wells to effectively enhance the valley splitting, thereby establishing a viable path toward the realization of shuttling and sparse-occupation-based architectures in low-disorder heterostructures.

Every resolved image of a relativistic jet encodes its magnetic field, yet no image records which way the field points: synchrotron intensity and linear polarization probe the field only through even combinations of its components. We introduce H-MOG (Hamiltonian Magnetic Optimization of Geometry), a variational method that reconstructs the 3D field from the jet width $W(z)$ and linear polarization $p(z)$, and we determine exactly which properties of the field these observables fix. We validate H-MOG on synthetic jets and apply it to ten GRMHD simulations of magnetically arrested and standard accretion flows at five spins, testing four routes to recover the field sense: a rotation-measure term, full 3D sampling, a spin-based prior, and resolved multi-frequency polarimetry with internal Faraday rotation, including ray-traced GRMHD images. For a side-on jet, $W$ and $p$ are exactly invariant under field reversal and under reflection through the plane of the sky, which reverses the handedness of the helix. Within this four-fold degeneracy the geometry is recovered, with $\langle\cos\rangle \simeq 0.94$-$1.00$ on synthetic jets and $0.76$-$0.98$ on the GRMHD library up to the mirror image, which is inherited from the initial guess. The rotation measure fixes the sign of the toroidal field but not that of the poloidal field, at any resolution; the spin prior fails because spin does not set the poloidal sign. Internal Faraday rotation breaks all four images, but in ray-traced GRMHD images it separates them only weakly. From width and polarization alone, field sense and helical handedness are undetermined; for a side-on jet the poloidal sense requires, beyond the rotation measure, the rotation sense of the field lines, a viewing angle away from $90^\circ$, or circular polarization.

Long-chain branching profoundly modifies the nonlinear oscillatory response of entangled polymer melts by introducing arm-retraction pathways absent in linear polymers. We present a molecular tube theory that explains the characteristic maximum of the Nonlinearity Index (NLI) observed experimentally in long-chain-branched polymers. The theory extends the recently developed nonlinear tube-orientation description of linear polymers by incorporating branch-point force transmission and delayed arm retraction. The backbone initially develops nonlinear orientation as in the corresponding linear polymer, whereas long-arm retraction subsequently relaxes the stored branch-point tension and progressively erases backbone orientational memory. This competition produces a characteristic NLI maximum followed by a post-peak decay. The theory predicts two distinct nonlinear regimes corresponding to sparse and dense long-chain branching and introduces an architecture parameter governing the height and width of the nonlinear peak. The resulting framework provides a molecular interpretation of nonlinear Fourier rheology and directly links the nonlinear harmonic response to polymer architecture.

Molecular polaritons are hybrid light–matter states whose collective character is associated with a molecular excitation extended across many molecules. However, clearly resolved polariton peaks do not by themselves establish that the corresponding eigenstates retain this molecular delocalization. Here, we use a disordered Tavis–Cummings model to distinguish spectral signatures of strong coupling from eigenstate-level molecular delocalization of electronic polaritons. Static energetic disorder can strongly reduce the molecular extent of optically visible polariton states while resolved polariton peaks persist and their apparent separation can even increase. We quantify this crossover using complementary molecular localization measures applied to individual optically visible eigenstates and the photon-weighted bright sector. Finite-size scaling shows a stable large-ensemble crossover; for Gaussian disorder, retaining approximately half of the homogeneous molecular extent requires a collective coupling roughly seven times the Gaussian disorder standard deviation $\sigma$, although the numerical scale depends on the disorder distribution. Including cavity and molecular linewidths through a non Hermitian Hamiltonian reveals a contrasting spectral and eigenstate response: finite linewidths reduce spectral resolvability, while cavity–molecule linewidth imbalance shifts the localization crossover to larger static disorder by suppressing the disproportionate contribution of near-resonant molecular transitions. Spectroscopic strong coupling and eigenstate-level molecular delocalization therefore characterize distinct properties and need not evolve in parallel under disorder and dissipation.

Kuznetsov and Sahinidis (J. Glob. Optim., 2025) prove distance bounds that confine optimal Lennard-Jones clusters and shrink the search region of deterministic solvers; their diameter bound charges each unit-width layer the loosest internal energy $-\binom{n}{2}$. We replace this by a certified estimate built from their own subset inequality and the proven minima $V_5^*$, $V_6^*$, and minimize the resulting layer bound over population profiles. Centred decreasing profiles supply candidate minima; an arrangement-free relaxation, whose only classical ingredient is the rearrangement inequality for sequences, closes every certificate over all profiles; and all comparisons are re-verified in directed-rounding arithmetic. For $5 \le N \le 200$ this certifies a one-layer improvement of the published bound at 92 sizes. The improvement resolves no open global-optimization case: it is a rigorous tightening of a published a priori bound, with a precise account of the mechanism. A direct downstream test on the only tractable sizes ($N \le 6$) finds the diameter box is not the binding resource for a deterministic solver there, and no solver runs at the sizes the refinement affects ($N \ge 38$); we therefore present the result as a theoretical note. We also derive the asymptotic form of the bound, $\rho_{KS} = N - \Theta(\sqrt{N})$, resolving a point left open by Kuznetsov and Sahinidis; the gain of the refinement itself grows like $\Theta(\sqrt{N})$ layers, with an exact asymptotic constant.

Salinity gradient energy offers a sustainable route to convert ionic chemical potential differences into usable power. Capacitive mixing enables this conversion without membranes, but suffers from limited ion regulation at electrode interfaces. Here we show that by grafting electrode surfaces with titrating polymers, the performance can be substantially improved. Using Grand Canonical Monte Carlo simulations with exact image-charge Ewald summations, we demonstrate how the coupled effects of ion adsorption and charge regulation in response to an external potential can be harnessed. Grafted electrodes are shown to deliver substantially more energy relative to bare surfaces, driven by charge regulation effects that exploit the pH difference that typically exists between rivers and the ocean. While the effect is in principle maximized at high grafting densities and moderate chain lengths, the performance is fairly robust to variations of these parameters, within reasonable bounds. Complementary classical polymer Density Functional Theory calculations confirm these trends, validating the mechanistic framework. This work also establishes a practical approach to harvest electrical energy during wastewater neutralization, where acidic (or alkaline) effluents serve as complementary reservoirs, and offers a promising strategy to couple environmental remediation with renewable energy recovery.

Local time stepping (LTS) can accelerate convergence to steady states in kinetic simulations with large variations in the local time steps across the computational domain. When neighboring cells advance with unequal time steps, the time-averaged particle flux must be balanced across their common interface. For particle-based or hybrid wave-particle methods under finite volume method (FVM) framework, we rigorously establish a sufficient condition for time-averaged interfacial particle-flux balance: fixed positive local time steps together with proportional particle-mass scaling. When a particle crosses from cell $L$ to cell $R$, its mass is scaled by $\Delta t_R/\Delta t_L$. In the unified gas-kinetic wave-particle (UGKWP) implementation, the same ratio is applied to the remaining free-transport time of the crossing particle. LTS also affects the wave-particle decomposition and the time integration of the wave fluxes in UGKWP. The wave-particle decomposition in cell \(i\) is determined by the local ratio \(\Delta t_i/\tau_i\), which better reflects the local relation between the observation scale and relaxation time for multiscale cases. The equilibrium and analytic free transport wave fluxes are integrated over and normalized by the corresponding cell-side time steps to obtain the interfacial time-averaged wave fluxes. The UGKWP-LTS method is used to simulate the hypersonic flow past a cylinder at $\mathrm{Kn}=0.01$ and $0.1$, and a flat plate at $\mathrm{Kn}=0.0169$. In all three cases, the surface quantities obtained with UGKWP-LTS agree well with the reference data. Relative to global time stepping (GTS), UGKWP-LTS achieves step-count speedups of $6.6\times$, $3.8\times$, and $20\times$ for the three cases, respectively. The corresponding wall-clock speedups are $7.1\times$, $4.5\times$, and approximately $21\times$.

The study of nuclear shape evolution and coexistence provides key insight into the nuclear interaction, particularly in semi-magic systems expected to be spherical. A high-precision Coulomb-excitation measurement of $^{116}$Sn yields a comprehensive set of electromagnetic matrix elements, enabling the determination of quadrupole moments of the $2_{1,2,3}^+$ states and intrinsic deformations of the $0_{1,2,3}^+$ states. The results provide an unambiguous and direct proof of the rare phenomenon of multiple-shape coexistence, revealing a weakly deformed ground state incompatible with the spherical shape.

We study the large-charge bootstrap in three-dimensional CFTs with a global U(1) symmetry using scalar, current, and stress-tensor probes, restricting to parity-even exchanged operators. Under minimal assumptions, the bootstrap requires at least one Regge trajectory with the dispersion relation of the standard Goldstone mode of the conformal superfluid. With additional assumptions, this trajectory is unique, while all non-Goldstone trajectories contribute only to the scalar-scalar channel at this order.

We discuss two different cases of strongly correlated fermions statistics. The first of them is the non-Fermi liquid (NFL) case, $i.e.$, that of fermions with exclusion of doubly occupancy of quasimomentum states $\{\bf k\}$ with opposite spins ($\uparrow\downarrow$). The second is that of statistical spin liquid (SSL) case, in which the fermion spins hop around and mix with the holes (unoccupied) states. For both cases we calculate the system entropy and the corresponding statistical distribution function, analyzed for a two-dimensional square-lattice filling $n\in [0,1]$ and relative temperature $k_B T/|t|$, where $t<0$ is the nearest neighbor hopping integral. We are particularly interested in the situation when the system of itinerant fermions reduce to the Mott-insulator state for the half-filled band ($n\to1$). This limiting situation signals a qualitative difference between the present SSL statistics and that of uncorrelated fermions representing normal Fermi-liquid state.

In this work we consider the production of a top-antitop pair at the LHC when the mass of the pair is relatively near to the nominal threshold, that is to say to twice the top pole mass. In this regime, enhanced perturbative corrections arise that can be computed to all orders in perturbation theory. We present three generators of the NLO+PS kind (Next-to-Leading-Order that can be interfaced to parton showers) that include these threshold enhanced effects. Using these generators we address the following questions: what is the size of enhanced non-relativistic effects that are not already present in the well known NLO and NNLO perturbative results; what is the size of the contribution from these effects that can be loosely attributed to toponium production; and to what extent the finite width of the top quark affects threshold enhanced corrections. Our generators are relevant for the recent observation of enhanced $t{\bar t}$ production near threshold in the pseudoscalar channel by the ATLAS and CMS collaborations.

Processes with indefinite causal orders (ICOs), such as the quantum switch, are higher-order quantum processes that superpose the order in which quantum operations are performed. Such coherent control yields computational advantages but is not faithfully captured by existing quantum programming languages: either they are restricted to the unitary case, and thus cannot combine ICOs with measurement, or they treat coherent control nonlinearly. In both cases, they do not realize the full computational power of ICOs. We introduce a higher-order quantum functional language that supports general quantum computation, not merely the permutation of channels, and whose linear type system allows quantum control to be well-defined beyond the unitary case, on arbitrary quantum channels. We equip this language with a small-step operational semantics that synchronizes measurement outcomes across superposed branches, using device references and a memory function. We also give a denotational semantics by means of completely positive maps. With linearity as the only constraint, some well-typed terms would denote unphysical maps. We therefore impose a typing discipline that goes beyond linearity, and interpret programs in the causal category Caus[CPM], under which every well-typed program is physically meaningful, a property that can be checked statically and efficiently. We prove soundness, and study the language's expressive power: it can express every quantum channel at first order, and at second order a large subclass of the so-called quantum circuits with quantum control (QC-QCs), containing the quantum switch. Last but not least, we show that this language is well-designed enough to be extended to the nonlinear setting with recursion.

We present recent enhancements to VLTI observing capabilities from a user-oriented perspective, together with new developments in ESO's Observation Handling Tools and end-to-end operations model for VLTI. Key upgrades include GRAVITY+ Coudé guiding with laser guide stars at the UTs, improved limiting magnitudes for GRAVITY and MATISSE, and a new MATISSE narrow-field off-axis mode, all supported by a streamlined, uniform template structure. Phase 2 tools now enable finding-chart generation and the selection of Coudé guide stars and fringe-tracker targets, and will soon offer expanded preparation features and uv-coverage visualisation. We summarise usage statistics for snapshot, astrometric, imaging, and time-series observations, outline VLTI scheduling considerations, and present new video tutorials. Starting in 2026, an archive data stream of reduced GRAVITY dispersed visibilities has become available. Complementary community engagement in VLTI operations continues to grow. We close by identifying operational lessons for future interferometric facilities, including the importance of an end-to-end data-flow and user-support model, flexible scheduling, high-level observation-preparation tools, and coordinated community support to keep complex interferometric facilities usable by a broad community.

Solving quantum field theory, which is at the basis of the standard model of particle interactions, is one of the main tasks of contemporary theoretical physics. Minimal asymptotically free pseudoreal theories, containing one or two species of massless Weyl fermions in pseudoreal representations of the gauge group, flow towards a poorly understood infrared dynamics. We provide a comprehensive study of all non-supersymmetric pseudoreal theories, first identifying the ones that likely flow towards a conformal dynamics. Assuming that the remaining ones confine, we find that tumbling hints the possible formation of a non-trivial condensate dynamics, consistently with other symmetry considerations. All but one one-species theories may feature at least one massless spin-1 state. Instead, the only confining two-species theory likely features two massless spin-1 states and one Nambu-Goldstone boson. These expectations must be further tested, for instance by use of Lattice simulations, the functional renormalization group, and supersymmetric analogs.

Frequency combs, evenly spaced spectral lines locked to one fundamental frequency, are well known in optics and have also been found in phononic, magnonic, ferroelectric, and cosmological systems, but have not yet been studied in oscillating chemical reactions. In this work, we show that reaction-diffusion oscillators can also produce frequency combs. We use the Brusselator model and derive its Hopf bifurcation condition directly from the rate equations. We find that the trimolecular autocatalytic term is the only source of nonlinear harmonic content. Above the Hopf threshold, our simulations of target-wave patterns show a clear fundamental frequency followed by a long, evenly spaced ladder of harmonics, with each harmonic weaker than the one before it. We then vary the reactant concentrations and kinetic parameters one at a time and find that this comb structure holds across a wide range of values. We also test this idea experimentally using the Belousov-Zhabotinsky reaction. Intensity signals recorded at different points in a target pattern show a shared fundamental frequency with several weakening harmonics, matching the simulated pattern closely. Together, these results show that reaction-diffusion chemistry is a new platform for generating frequency combs.

Understanding the dynamical properties of coupled phase oscillator systems with heterogeneous oscillator frequencies has been a long-standing challenge of complex systems theory. While the seminal work of Ott and Antonsen dramatically improved our theoretical understanding of coupled phase oscillators for a small family of oscillator frequency distributions, we here present a mean-field reduction method for arbitrary frequency distributions. Our method leverages the drastic dimensionality reduction obtained for Lorentzian frequency distributions, and combines it with a data-driven multi-ensemble approach. As such, the method renders the Ott-Antonsen equations directly applicable to empirical distributions of phase oscillator frequencies, often achieving a drastic dimensionality reduction and allowing to study real-world physical and biological systems by means of stability, sensitivity, and bifurcation analyses.

We introduce a hybrid qubit-boson beam-splitter gate in which a microwave cavity mode couples to an exchange-dressed two-level subsystem of an interacting two-qubit system in the presence of Kerr nonlinearity. Starting from a general circuit quantum electrodynamics (cQED) model, we derive the corresponding hybrid qubit-cavity interaction, develop its open-system description including photon- and qubit-sector-bath-induced dissipation and obtain in the weak-dissipation regime an analytical expression for the average gate fidelity. We further identify carbon-nanotube circuit QED as a concrete platform for implementing and controlling the gate, provide a representative operating regime and perform noiseless and noisy numerical simulations to study the gate dynamics and benchmark the analytical results. Beyond this implementation route, the proposed hybrid primitive provides a natural building block for many-body dynamics, including quantum-cellular-automaton (QCA) and lattice-gauge-inspired architectures and, through its collision-model reformulation, also suggests connections to noisy QCA, non-Markovian extensions and reservoir-style quantum information processing.