Papers

We study the quantum query complexity of several basic graph problems. 1) We prove a tight $\Theta(n^{3/2})$ bound for finding a maximum-out-degree vertex in an $n$-vertex tournament, resolving a conjecture of Mande, Paraashar, and Saurabh [FSTTCS'23]. 2) Using the same proof idea, we give a direct proof that finding a maximum-degree vertex in an $n$-vertex undirected graph requires $\Theta(n^{3/2})$ quantum queries, a bound implicit in the work of Apers and Lee [CCC'21]. Both lower bounds above hold even for computing only the maximum degree or maximum out-degree. 3) We also study Maximum $(k,n-k)$-Cut, which asks for the largest cut with one side of size $k$. For every constant $k\geq 1$, we give an $O(n^{2-1/(k+1)})$-query quantum algorithm. 4) We establish a reduction to Maximum $(k,n-k)$-Cut involving $k$-Graph Collision, which asks whether the marked vertices of a known graph contain a $k$-clique. For $k\geq 3$, this yields unconditional lower bounds with exponents strictly larger than $3/2$, showing that this problem is strictly harder than computing maximum degree. Additionally, under a conjecture we propose for $k$-Graph Collision, the reduction yields a lower bound matching our upper bound above.

Fermionic Gaussian states are completely characterized by their two-point correlations, making the covariance matrix a natural reference for quantifying non-Gaussian structure. Motivated by fermionic antiflatness, we study its extremal form for pure number-conserving states and ask which states can be maximally antiflat and how they can be constructed. We show that, at fixed particle number, maximal first antiflatness is equivalent to a completely flat one-body reduced density matrix, and we obtain a complete existence classification together with explicit block and cyclic-orbit constructions of all allowed sectors. We then investigate the structure that appears beyond the covariance level. Maximally antiflat states with identical one-body data can exhibit distinct connected four-point correlations, which we characterize through the four-point Majorana Wick error and, equivalently, the connected two-body reduced density matrix cumulant. We show that this quartic structure is necessarily nonzero and formulate its extremization as a two-body reduced density matrix (2RDM) purity problem. Combining this framework with a Hilbert–Schmidt estimate of Christiansen for truncated two-body correlations, we obtain an upper bound on the connected quartic structure in terms of first antiflatness. Our results establish both a complete characterization of maximal fermionic antiflatness at fixed particle number and a constrained hierarchy linking covariance-level flatness to higher-order non-Gaussian correlations.

Machine-learning force fields (MLFFs) enable the calculation of transformation pathways in molecular crystals at a fraction of the computational cost of density functional theory (DFT). However, a good agreement in energies and structures does not necessarily imply an accurate description of vibrational properties, which are essential for characterizing transition states and determining free energies at finite temperatures. Herein, we assess the accuracy of system-specific SO3krates MLFFs trained on PBE+MBD reference data for describing vibrational properties of molecular crystal transformations. As examples, we consider a polymorph transition of 1,4-diiodobenzene and a single-crystal-to-single-crystal Diels-Alder reaction. The transition state structures obtained from solid-state nudged-elastic-band (NEB) calculations with the MLFFs exhibit a single imaginary $\Gamma$-point frequency associated with the respective transformation. Compared with PBE+MBD, the mean absolute errors of $\Gamma$-point vibrational frequencies and relative harmonic free energies at 300 K are about 3 cm$^{-1}$ and 1 kJ/mol, respectively. Furthermore, we compare for the Diels-Alder reaction a collective transformation pathway with a sequential one, in which individual diene-dienophile pairs react successively, and demonstrate that PBE0+MBD single-point corrections can significantly affect the predicted reaction energetics. These results demonstrate that system-specific MLFFs can reproduce not only the energies and forces but also the local curvature of the potential-energy surface with high accuracy, enabling reliable calculations of harmonic vibrational free energies, providing a basis for extending the studies of molecular crystal transformations to larger supercells.

We study how mixed-state correlations reorganize across island transitions in Jackiw-Teitelboim gravity coupled to a non-gravitating bath. Using the partial-dimensional-reduction realization of double holography, we compute reflected entropy for adjacent and disjoint radiation regions in the vacuum and in the thermofield-double state of an eternal black hole. Reflected entropy probes the internal partition of the entanglement wedge and therefore resolves structure that is invisible to the ordinary Page curve: its dominant saddle can change even when the entropy saddle of the union remains fixed, and it vanishes at leading order when the entanglement wedge disconnects. We show that the lower-dimensional reflected-island description agrees, to leading order in the dynamical brane fluctuation, with the higher-dimensional defect-extremal-surface picture. The finite-angle comparison further suggests a projection-covariant identification of island and brane endpoints at linear order. The resulting Page-like curves and Markov gaps provide a geometric probe of the reorganization of the purification and of non-Markovian, multipartite correlation structure during island transitions.

The $q$-deformed Weil-Petersson volumes of Do and Norbury are the top-degree parts of Okuyama's discrete volumes, which are defined by topological recursion on the spectral curve of the double-scaled SYK (DSSYK) model. We show that the same q-deformed volumes can be obtained from a double-scaled matrix model whose disk density is found by zooming in on the soft edges of the DSSYK density. Applying the same procedure to the hard edge of $\mathcal{N}=1$ DSSYK, we obtain candidate $q$-deformed $\mathcal{N}=1$ super Weil-Petersson volumes. They are polynomials of fixed degree, and they reduce to the $\mathcal{N}=1$ super Weil-Petersson volumes in a scaled $q\to1$ limit. These candidate volumes differ from the $\mathcal{N}=1$ volumes of Do and Norbury in (arXiv:2510.12431) up to what we call "irrelevant" contributions which exactly vanish in the scaled $q\to 1$ limit. Together, these results demonstrate how q-deformed volumes can be naturally associated to the spectral edges of various DSSYK models and provides an intuitive way to construct them in supersymmetric contexts.

We develop a unified description of convolution on the sphere by lifting to the rotation group. A number of definitions of spherical convolution have been proposed, differing in whether the kernel is axisymmetric or directional, whether the output is on the sphere or the rotation group, whether the signals carry spin, and in their computational cost. No unified treatment exists. Regarding the sphere as the homogeneous space $S^2 \cong \text{SO(3)}/\text{SO(2)}$, we lift a spin $s$ field to the rotation group, convolve on $\text{SO(3)}$, and project back to the sphere through the adjoint of the lift for a potentially different spin $s'$. We recover every rotation-equivariant convolution considered previously through constraints on the kernel, spin choices and inclusion or omission of the lift and projection. For maps between fields of fixed input and output spin, we prove that directional kernels, output on the sphere and equivariance cannot be achieved simultaneously. We make explicit that spin fields are sections of associated line bundles, linking the physics and bundle literatures, and express the spin rotation phase as the character of the twist of the section. We present harmonic-space algorithms for the exact and efficient computation of lifted spherical convolutions of band-limited fields by appealing to sampling theorems on the sphere and rotation group. All operators are implemented in the open-source s2conv code, and numerical experiments confirm the reductions and the equivariance of the operators to machine precision. Finally, we illustrate the operators on fields measured on the Earth and on the celestial sky.

Current AI predicts materials by speeding up energy minimisation and training on large databases. However, scaling data generation prevents manual analysis by domain experts. If novelty is evaluated by chemical compositions or traditional representations in Crystallographic Information Files, or standard structure matchers based on manually chosen thresholds, one can easily generate millions of “new” compositions or files without discovering truly novel materials. This paper uses a hierarchy of crystal invariants to continuously trace and quantify structural novelty based on the new mathematical definition of a crystal structure and asymptotic guarantees for invariant descriptors. The invariant-based analysis through cascade computations on a modest computer exposes the unexpected scale of duplication in the world's largest materials databases, shown here in the high-profile case of GNoME datasets. To prevent current “embarrassment of over-prediction”, we propose necessary conditions for next-generation AI that should be automatically enforced before claiming any new materials.

We study a continuum model of frustrated magnetism that supports particle-like field configurations with nontrivial Hopf index. The energy functional combines competing second and first order exchange interactions with a stabilizing external magnetic field and gives rise to a variational problem for maps from three-dimensional space into the two-sphere. We prove the existence of energy minimizers in infinitely many nontrivial homotopy classes. We further establish the existence of a unit-charge Hopfion in the regime of strong external fields. Finally, we analyze the corresponding large-field limit, identify the natural concentration scale, and prove strong convergence of suitably rescaled minimizers to a minimizer of a limiting variational problem.

Air pollution poses a significant threat to public health, exacerbated by the rapid industrialization and urbanization of modern society. While traditional deep learning offers predictive capabilities, recent advancements in quantum machine learning (QML) present a compelling alternative. Here, we introduce a scalable hybrid framework that integrates variational quantum circuits with quantum annealing. Leveraging a neuromorphic quantum computing platform to transcend the qubit limitations of the NISQ era, we model particulate matter (PM$_{2.5}$) dynamics using high-density urban data from the UK. We demonstrate that our Quantum Neural Networks (QNNs) exhibit an intrinsic resilience to input volatility, significantly outperforming classical baselines (MLP and LSTM) on raw, high-entropy environmental data. Furthermore, we successfully scaled the model to 172 qubits, observing a synergistic enhancement when coupled with wavelet decomposition that achieves state-of-the-art predictive fidelity. These findings establish a critical benchmark for quantum utility, proving that scalable, neuromorphic quantum machine learning can now address complex, non-linear real-world problems.

Two-block group-algebra codes are among the simplest quantum LDPC codes, and many of them are translation invariant on a twisted torus, which suits neutral-atom arrays and other platforms with movable qubits. We ask how far they go at small sizes when searched systematically across all groups. We use algebraic constraints and screens to design a search pipeline capable of enumerating broad and complete swathes of two-block codes on a laptop. With it we census about $10^8$ two-block codes with up to $320$ qubits at check weights five to nine. Several of these censuses are exhaustive, and support complete statements; for instance, the Gross code is, up to equivalence, the only abelian weight-six two-block code with $n \le 200$ to reach $kd^2/n=12$, no weight-six two-block code with $n \le 300$ beats $[[288,16,16]]$, and the known $[[64,18,8]]$ is the best two-block code by $kd^2/n$ across weights five to nine with $n \le 94$. The censuses are also large enough to give insights into where good codes live - they concentrate in a handful of groups; abelian groups give the best codes at small $n$ and non-abelian groups at large $n$, with the crossover appearing to move out as the check weight grows; and high quality codes become $100$ to $1000$ times rarer per draw from weight six to weights eight and nine. Using the group algebra and the census data to steer a statistical search finds four to fifteen times as many good codes as uniform draws in equal time. Among the codes found are $[[102,20,10]]$ and $[[120,24,10]]$ at check weight nine, which we simulate in noisy syndrome-extraction circuits, and $[[186,20,18]]$, a weight-nine code with every check in a $5\times5$ window. At check weights seven to nine, our best codes exceed the best published $kd^2/n$ with exact distance at the same check weight in most length bands up to $320$ qubits. All codes are available in a public database.

Quantum low-density parity-check (qLDPC) decoding requires reliable corrections and low latency over long syndrome histories. We extend BP-SF, an oscillation-guided belief-propagation (BP) decoder with independent syndrome-flip trials, by introducing windowed and streaming operations. Our CUDA implementation combines disordered-memory retries, sliding windows, correlation-aware graphs, and layered scheduling. Circuit-level simulations test fixed-basis memory and complete logical Pauli-frame recovery. On the [[144,12,12]] bivariate bicycle code at physical error rate p = 0.002, parallel BP-SF reduces 99.9th-percentile call latency by a factor of 13.15 relative to an eight-chain Relay-BP GPU baseline on 100,000 matched samples for which every tested method's initial BP stage fails within 80 iterations. Windowed BP-SF maintains a flat logical error rate and nearly constant per-round compute time through 512 rounds, reaching a 17.1-fold speedup over monolithic decoding. In 512-round full-frame streaming decoding with 2.97-ms syndrome arrivals, layered BP-SF on a transformed joint graph with 20 retries reduces 99.9th-percentile correction-release age from 166.29 to 36.25 ms relative to the joint graph with flooding updates and 100 retries. These results connect parallel BP post-processing to lower decoding costs and earlier correction release in streaming quantum memory.

Foundation models have recently gained significant attention in fields such as high energy physics (HEP). The tokenizers that convert detector data into discrete inputs for such models, however, are comparatively unexplored. This paper addresses this gap by learning discrete and compressed tokenized representations of HEP datasets. We demonstrate the approach on four modalities covering two different simulated detectors that vary in complexity. Treating tokenization as a rate-distortion problem, a systematic hyperparameter scan yields four design rules for tokenizing HEP data that hold across all set-based modalities studied. The cost of tokenization is evaluated on tasks including jet $p_T$ regression, particle flow reconstruction, and flavor tagging. We find that tokenization preserves much of the information needed for these tasks at compression factors of approximately 4-11$\times$ while keeping the jet $p_T$ resolution below 1%. We also present heptokens, an open-source library for tokenizing HEP data.

We construct a set of conserved charges which are deformations of quantum KdV charges. They are associated with the modular transformation of a GGE with the spin-$\sigma$ KdV charge inserted with chemical potential $\alpha_\sigma$. The charges are formal power series in the chemical potential, with coefficients given by local integrals of motion. We define local recursion relations and equivalent flow equations, prove commutativity to all orders, and establish uniqueness of the currents modulo total derivatives for a fixed generating series. We show that the eigenvalues of these deformed charges can be obtained from the thermodynamic Bethe Ansatz in two models. In the $c=1/2$ free fermion theory, the deformed charges reduce to explicit linear combinations of undeformed KdV charges, and their ground-state eigenvalues agree with the TBA expansion to all orders. In the Lee-Yang model, we find numerical agreement through cubic order in the spin-$5$ deformation for the first few charges evaluated on low-lying states.

We investigate the rate of change of equilibrium potential energy for nonlinear elastic solids undergoing evolutions that may involve changes in body geometry, material properties, applied tractions, and prescribed displacements. We represent such an evolution by a one-parameter family of variational problems and identify a class of these families for which the potential-energy release rate is well defined. Particular attention is given to the formulation of the potential energy at each evolution state: each constituent variational problem must yield the appropriate equilibrium state, while its equilibrium value must also correctly represent the physical change in potential energy between states. Within this framework, we derive a closed-form expression for the potential-energy release rate for solids with bounded domains, allowing for spatially nonuniform material evolution, sharp material interfaces, and evolving boundary geometry and prescribed boundary data. The expression is determined entirely by the equilibrium solution at the state under consideration and by the quantities prescribing the local evolution, so neighboring equilibrium problems need not be solved. Finally, we apply the result to the extension of a notch in a two-dimensional elastic body and show that the resulting potential-energy release rate reduces to the classical $J$-integral.

Extending the weak-coupling expansion of the pressure of a cold and dense ultrarelativistic electron gas to next-to-next-to-next-to-leading order (N3LO) in the gauge coupling has remained an open problem since the classic N2LO result of Freedman and McLerran, published in 1977. Here, we present the full N3LO pressure, the first thermodynamic quantity determined to this order in a physical gauge theory. The pressure exhibits good perturbative convergence and weak renormalization-scale dependence even at sizable couplings, while a Bayesian analysis of missing higher-order contributions indicates uncertainties that can exceed those inferred from scale variation alone.

Nucleosynthesis simulations of the r-process require neutron capture rates for neutron-rich nuclei, many of which lie beyond experimental reach. Predicting these rates relies on theoretical calculations of the low-energy electric dipole (E1) strength near the neutron threshold. We present the first ab initio computation of the E1 strength along the nickel isotopic chain, for $^{58}$Ni and the even-even isotopes $^{68-80}$Ni. The E1 strength is obtained with the Lorentz integral transform coupled-cluster (LIT-CC) method, extended to axially symmetric reference states to reach open-shell nuclei, using two- and three-nucleon interactions from chiral effective field theory. The approach is benchmarked against the measured photoabsorption cross section of $^{58}$Ni and the E1 strength of $^{68}$Ni. Along the chain we find low-lying E1 strength above the neutron threshold that grows with neutron number. Including it in the reaction code TALYS enhances the neutron capture rates forming $^{68-78}$Ni between 3 and 10 GK, with an effect that increases with temperature and neutron number and an uncertainty dominated by the inversion of the integral transform. For $^{80}$Ni, where strong pygmy dipole strength lies just above threshold, the enhancement sets in already around 0.5 GK. Together, these results open the way to ab initio input for neutron capture rates along isotopic chains far from stability.

Contemporary large-scale structure analyses center around the galaxy power spectrum, modeled with one-loop perturbation theory. This description naturally breaks down at large wavenumbers, prohibiting the extraction of cosmological information from small-scale clustering. In this work, we present a complete model for the redshift-space galaxy power spectrum up to two-loop order, derived in the framework of the Effective Field Theory of Large Scale Structure. This accounts for a wide variety of effects, including fifth-order galaxy bias, redshift-space distortions, small-scale non-linearities, spatial non-locality, long-wavelength bulk flows, coordinate distortions, and stochasticity, involving a total of 49 free coefficients. Our model additionally encodes all deterministic contributions to the one-loop bispectrum and trispectrum (as well as the tree-level quadspectrum and pentaspectrum), which depend on many of the same parameters. We implement the model numerically, using the vegas algorithm to precompute the loop integrals; this allows the full likelihood to be evaluated in milliseconds. The approach is validated using power spectra measured from high-resolution simulations, considering both dark matter and realistic galaxy samples. The extension to two-loop order greatly increases the range of scales over which the power spectrum can be modeled, with $k_{\rm max}$ rising from $0.2h\,\mathrm{Mpc}^{-1}$ to $0.34h\,\mathrm{Mpc}^{-1}$ for a luminous red galaxy sample at $z=0.5$. Much of the additional information is absorbed by the numerous fifth-order biases and counterterms; for this reason, constraints on $\sigma_8$ are not significantly enhanced by the inclusion of two-loop terms. Future work will assess the full implications of the two-loop model for cosmological parameter inference, both alone and in combination with higher-order statistics.

In cosmic ray propagation through turbulent magnetic fields, transport perpendicular to the mean field plays an important role in various astrophysical environments. Numerical simulations have shown that parallel and perpendicular diffusion coefficients exhibit different energy scalings, causing their ratio to increase with energy, but a comprehensive theoretical explanation remains elusive. Here, we investigate perpendicular diffusion using test particle simulations in synthetic isotropic turbulence spanning 6-7 orders of magnitude in wavenumber, together with a theoretical extension of nonlinear guiding center theory that incorporates stochastic drifts. Our approach combines field line random walk and random guiding center drifts to describe perpendicular transport. We find that parallel and perpendicular diffusion coefficients exhibit the same energy scaling only for $r_L \lesssim 10^{-2} L_c$, where $r_L$ is the particle Larmor radius and $L_c$ is the turbulence coherence length. At higher energies, perpendicular diffusion develops a stronger energy dependence, consistently across different turbulence levels. Our theoretical model suggests that this behavior arises from stochastic drifts induced by turbulent magnetic field components parallel to the mean field.

Accessing and combining the spatial information carried by light at different wavelengths is important for linking structured-light encoding with spectrally distinct detection channels. Here, we introduce a correlation-enabled linear-optical framework for cross-wavelength imaging, bidirectional replication, and spatial information mixing. Shared random holographic modulation establishes correlations between nondegenerate optical fields, allowing spatial information to be retrieved from joint intensity fluctuations. In the demonstrated replicator, a spatial pattern encoded at one wavelength is read out in the detection coordinates of another through intensity correlations. Selecting diffraction-order pairs produces correlation kernels containing either the product or the conjugate product of two input field envelopes. These operations reproduce the spatial algebra underlying sum- and difference-frequency generation, while the optical fields retain their original carrier frequencies. The theory accounts for wavelength-dependent propagation and coordinate scaling, linking the input structures to observable correlation patterns. Together, these results establish a common framework for cross-wavelength spatial information processing through engineered optical correlations and joint detection.

New physics emerges from new materials, which in turn rely on the development of new synthesis techniques. Identifying the enlargement of metastable synthesis window as enabling for realizing novel materials, we develop diffusion-activated epitaxy, a technique which combines two metastable synthesis methods of diffusion and epitaxy. We observe that within a narrow window of investigated synthesis space we can experimentally identify the stabilization of four distinct phases, three of which show X-ray diffraction and scanning transmission electron microscopy characterization data that are incompatible with the crystal structures registered in experimental and computational inorganic structure databases. These results suggest an enlarged metastable synthesis window is enabled by this synthesis approach, identifying doubly metastable synthesis as a promising method for exploration of quantum materials.

We prove that four capacities of single-mode bosonic dephasing channels coincide under an average photon-number constraint: the unassisted quantum capacity, the unassisted private capacity, the two-way classically assisted quantum capacity, and the two-way public-classically assisted private capacity. The assistance may be interactive: the parties can exchange classical messages between channel uses and choose subsequent inputs based on earlier outcomes. For every finite value of the constraint, their common value is the coherent information optimized over Fock-diagonal input states satisfying the constraint. The proof uses a relative entropy comparison with the completely dephasing channel to derive chain rules for the Rains relative entropy and the relative entropy of entanglement. These chain rules give an upper bound on the rates achievable by adaptive protocols whose mean input photon number is constrained on average over all channel uses. We also show that both chain rules are attained by canonical purifications of finite-energy Fock-diagonal states.

The introduction of two-body XX interactions has been shown to improve the performance of quantum annealing in solving certain combinatorial optimisation problems and would enable the simulation of a broader class of many-body Hamiltonians. Due to experimental constraints, such interactions are typically not natively available on analogue quantum devices. To overcome this limitation we introduce the truss gadget. This is an exact construction that generates two-body XX interactions using only one-body X and Z fields and two-body ZZ interactions which are readily accessible on, for instance, superconducting quantum annealers. We experimentally validate the construction by reproducing the dynamics of a target XX Hamiltonian on a trapped-ion quantum processor. We then apply the gadget to an illustrative set of instances of the weighted maximum-independent-set problem on a superconducting quantum annealer. We empirically determine an approximate thousand-fold improvement in the probability of finding a state close to the ground state for these instances, over implementation without an XX interaction.

Scaling trapped-ion processors by adding ions remains challenging. A complementary route exploits the multilevel internal structure of each ion to increase the computational Hilbert space per ion. We introduce a hardware-native hybrid qudit-oscillator instruction set for a general d-level internal register coupled to bosonic modes and prove that three of its native operation families suffice for universality of one qudit coupled to several modes. Adding an entangling operation between ions extends universality to a connected register of several qudits. The architecture natively supports both phase-space and sideband instruction sets and is implemented in the open-source framework HybridLane. As a representative application, we reproduce the dissipative vibronic dynamics of a three-chromophore complex previously simulated on a hybrid qubit-oscillator superconducting platform. Moving from a one-qubit-per-state register to a single qudit stores the entire electronic manifold in one ion, so every electronic coupling becomes a local intra-ion transition and the lab-frame Hamiltonian compiles directly into the ISA. Under the stated sequential timing model from a 40Ca+ qudit processor, one Trotter step is projected to run about ten times faster on the qudit, with an average RMSE of approximately 1.1 percent against the published reference.

We find a robust scenario for the emergence of the Golden Ratio (GR) dynamical universality class, characterized by the dynamical exponent $z \equiv \varphi=\frac{1}{2}(1+\sqrt{5})$. Previously, its emergence required fine-tuning of system parameters. Here, the GR universality class appears generically in a wide class of Markov processes as a consequence of a global, circulant symmetry of the flux Jacobian. This symmetry leads to GR universality in systems where the total number of conservation laws is odd and larger than three. We introduce a multilane exclusion process with Bernoulli stationary measure as a minimal, parameter-free model, which features GR universality for all conserved modes, most of which are doubly degenerate. Our predictions, based on mode-coupling theory generalized to treat degenerate conserved modes, are corroborated by large-scale Monte Carlo simulations.

Disinformation on online social media has been on the rise in the past years. While there is extensive literature modelling social cascades, online disinformation cascades show distinctive characteristics: they provoke debunking reactions, they spread over networks with heterogeneous connectivity, and they compete for the limited attention of users — which recommendation algorithms may partly offset. We propose a model including these ingredients and study it through Monte–Carlo simulations and mean–field approximations, on random graphs and an empirical Twitter network. We find that debunking reactions are double–edged: they reduce the reach of appealing items but allow unappealing ones to reach audiences they would not otherwise reach. Degree heterogeneity makes cascades trigger at a much lower content appeal but limits their final reach: heterogeneous networks are easy to ignite yet hard to saturate. Limited attention cancels the effects from degree heterogeneity, although the mediation of recommendation algorithms may restore them.

In the present work, we investigate the long-distance contributions to light hadrons and radiative decays of $\eta_c$, where the long-distance contribution is phenomenologically described by the meson loops. Our estimations indicate that the branching fractions of $\eta_c \to \mathcal{VV},\ \mathcal{V}=(\rho,\omega, \phi)$ can be roughly reproduced in the range $1.4<\alpha <1.6$. While the parameter range for $\eta_c \to \gamma \mathcal{V}$ is determined by the similarity of $\eta_c \to \gamma \mathcal{V}/\mathcal{VV}$ and $\chi_{c1} \to \gamma \mathcal{V}/\mathcal{VV}$. In this parameter range, our estimations indicate that the branching fractions for the processes $\eta_c \to \gamma \rho^0$ and $\eta_c \to \gamma \omega$ are of order $10^{-4}$, while the one for the process $\eta_c \to \gamma \phi$ is of order $10^{-5}$. The estimations in the present work are expected to be accessible by future experiments at BESIII and Belle II.

Experiments in relativistic heavy-ion collisions determine centrality from final-state quantities, usually the charged-particle multiplicity. Performing the same in hydrodynamic simulations requires millions of events, which is impractical for state-of-the-art hybrid models, and centrality is therefore commonly approximated by the initial entropy or energy. We show that neural networks trained on a few hundred hybrid events predict the event-by-event multiplicity and mean transverse momentum $[p_T]$ with relative errors of 1–2%, which makes it possible to generate millions of collisions at a small fraction of the cost of the full simulation. For Pb–Pb collisions at $2.76$~TeV and Au–Au collisions at $200$~GeV, the initial-state and final-state definitions select nearly the same events in 10%-wide classes, but up to 20% of the events change class when the classes are 1% wide. We then compute the fluctuations of $[p_T]$ and its Pearson correlations with a proxy of the elliptic flow, estimated from the initial eccentricity, and with multiplicity. The first correlation is insensitive to how centrality is defined, while the second changes substantially. The approach can be applied at every design point of Bayesian analyses at modest additional cost.

Phononic frequency combs are equidistant spectral ladders generated when a driven vibrational mode transfers energy to an autoparametrically excited subharmonic mode through anharmonic intermode coupling. In previous studies, the coupling strength governing this energy transfer has typically been treated as a free parameter, extracted from a fabricated device, or adopted from an earlier calculation for a specific mode pair. As a result, whether a given crystal can support a phononic frequency comb, and the drive strength required to generate it, has not been predictable a priori. Here we obtain the complete parameter set from density functional theory. Twisted bilayers of \MoSSe{} and \MoSMoSe{} at the commensurate angle $21.787^{\circ}$ adopt space group $P3$ in a 42-atom \rootseven{} moiré supercell. The second-order force constants provide the mode frequencies; the third-order constants provide the linewidths through the Boltzmann transport equation and hence the quality factors; and the same third-order tensor projected onto the phonon eigenvectors of a chosen mode pair provides the anharmonic couplings $\kt$ and $\kss$. Both bilayers constitute a mode pair within $0.8\%$ of the $2\!:\!1$ resonance with $\omega_1/\omega_2 = 1.9923$ in \MoSSe{} and $1.9943$ in \MoSMoSe{}. By integrating the resulting two-mode equations, both modes generate combs through a discontinuous transition: at $701\,\fth$ in \MoSSe{} the envelope variance rises from $2.1\times10^{3}$ to $1.37\times10^{4}$ and the tooth count of mode 1 from 7 to 16 within a single $5\,\fth$ increment, identifying the onset as subcritical. The spectral entropy peaks before this jump, at $341\,\fth$. The two compounds carry comparable coupling, differing by a factor of $1.2$. However, the comb excitation threshold is set by the quality-factors of signal modes: $Q_2 = 672$ for \MoSSe{} and $Q_2 = 3844$ for \MoSMoSe{}.

The Relativistic Continuous Matrix Product State (RCMPS) ansatz introduced in arXiv:2102.07741 is a translation-invariant variational ansatz intended to approximate the ground states of gapped one-dimensional relativistic Quantum Field Theories directly in the continuum limit and in infinite volume. In this work, we develop an ansatz, referred to as the Relativistic Quasiparticle (RQP) ansatz, for the low-lying one-particle excitations of the RCMPS vacuum, as well as for solitons interpolating between two distinct degenerate vacua. The corresponding energies of these states can be obtained as the eigenvalues of an effective Hamiltonian. The RQP ansatz generalizes constructions used in the Matrix Product State and Continuous Matrix Product State literature. We apply the RQP ansatz to the sine-Gordon model and find good agreement with results from integrability for both the soliton and breather masses. We also apply the RQP ansatz to the $\phi^4$ theory, in both its $\mathbb Z_2$-preserving and $\mathbb{Z}_2$-broken phases, and determine the spectrum of particles and solitons. This enables us to determine the parameter regime for which multiple stable particles exist.

Physical diagnostics recorded during simulation can organize a sharply varying response, but using them as surrogate inputs normally requires another calculation at prediction. We construct a physical-state-supervised Gaussian process surrogate that learns these diagnostics from design variables. Cross-fitted state estimates augment a retained design representation; a global Gaussian process and an optional soft mixture of response-band experts use identical inputs. On a database of 1,987 paired one-dimensional implosions, learned burn-weighted states from calculations without alpha-particle heating reduce mean squared log-response error by 60.25% and 52.98% for the global predictor on random holdout and design-space extrapolation. Random-projection and shuffled-state supervision do not reproduce these gains. For CH, matched-input comparisons show that experts help at smaller training budgets but contribute little at 1,000 designs with this representation. A thermal-feedback benchmark validates the complete learned-state procedure, while 3,000 newly calculated Be/Cocktail designs expose weaker extrapolation gains and cases where experts degrade accuracy. A conditional state-error bound separates encoding sensitivity from routing effects. An open Python implementation reproduces the archived predictions and is released with the data, per-design results, and measured costs. Physical-state supervision is thus a useful representation for finite-data surrogates, whereas expert specialization should be selected by validation.