Papers

The Breit-Wigner Enhancement mechanism provides a novel interpretation for the “enhancement factor” derived from data of the PAMELA, ATIC, and PPB-BETS experiments, and we further extends this research to the case of asymmetric Dark Matter. We investigate the impact of resonance mechanism to the asymmetric Dark Matter case and constrain the resonance model parameters to satisfy the “enhancement factor" and the asymmetric dark matter model parameters to meet the upper bound requirement imposed by the astronomical experiment.

In this study, several newly observed decay modes of the $B_c^+$ meson of the form $B_c^+\rightarrow Dh^+h^-$, where $D$ denotes a charmed meson and $h^{\pm}$ represents a charged pion or kaon, have been investigated. The decay channels $B_c^+\rightarrow D^{+}K^+\pi^{-}$, $B_c^+\rightarrow D^{*+}K^+\pi^{-}$ and $B_c^+\rightarrow D_s^+K^+K^-$ were observed for the first time. The LHCb Collaboration has measured their branching fractions relative to the reference decay $B_c^+\rightarrow B_s^0\pi^+$, and reported experimental values including $\mathcal{R}^{\exp}(B_c^+\rightarrow D^{+}K^+\pi^{-})=(1.96\pm0.23\pm0.08\pm0.10)\times 10^{-3}$ , $\mathcal{R}^{\exp}(B_c^+\rightarrow D^{*+}K^+\pi^{-})=(3.67\pm0.55\pm0.24\pm0.20)\times10^{-3}$ and $\mathcal{R}^{\exp}(B_c^+\rightarrow D_s^+K^+K^{-})=(1.61\pm0.35\pm0.13\pm0.07)\times 10^{-3}$. In this regard, by performing precise calculations using the factorization approach, we have computed similar branching ratio values, including $\mathcal{R}(B_c^+\rightarrow D^{+}K^+\pi^{-})=(1.70\pm0.08)\times 10^{-3}$, $\mathcal{R}(B_c^+\rightarrow D^{*+}K^+\pi^{-})=(3.63\pm0.45)\times 10^{-3}$ and $\mathcal{R}(B_c^+\rightarrow D_s^+K^+K^{-})=(1.09\pm0.08)\times 10^{-3}$. The obtained theoretical results show good consistency with the recent experimental measurements reported by the LHCb collaboration, confirming the effectiveness of the factorization formalism in describing these $B_c^+$ decay modes.

We develop a formal procedure of eikonal expansion for classical fields in gluodynamics. We show that in the weak field limit the expansion is straightforward and determines the eikonal components of vector potentials in terms of eikonal components of color currents via classical equations motion. We demonstrate that the recently proposed Born-Oppenheimer high energy evolution yields the ground state wave function interpretable in terms of the classical fields. The relevant classical field is indeed consistent with the eikonal expansion, and contains the leading eikonal and subeikonal components. For strong fields we find that the naive eikonal expansion is inconsistent, as nonlilearities in equations of motion lead to mixing of eikonal orders. Thus the effect of subeikonal components on the leading eikonal component is not suppressed by the eikonality parameter. We show that this problem can be rectified by classically "integrating out" high longitudional momentum components of gluon fields. This leads to a classical action for the low momentum components with small self interaction, but strongly renorlamized currents, which contain contribution due to high momentum modes.

The hydrogen molecular ion and the hydrogen molecule are treated in an approximate calculation based on classical electrodynamics which includes classical zero-point radiation. It is found within the classical theory that a molecular ion is less-well bound than a hydrogen atom plus a distant proton. The smaller binding energy is explained due to the repulsive nature of the force between the proton and the atom when considering the most natural resonant orbit of the electron. The approximate classical electromagnetic calculation gives a binding energy of $2.1eV$ and a proton separation of $0.916A^{o}$ for the hydrogen molecular ion. The hydrogen molecule is formed by adding a single additional electron to the ion. The electrostatic attraction of the electron to the ion gives a binding energy of $4.6eV$ and a inter-proton separation of $0.6A^{o}$ for the hydrogen molecule in this classical electromagnetic approximation.

This work represents an initial step towards a systematic framework for identifying hidden symmetries in algebraically general (Petrov type I) spacetimes. Motivated by this, we focus on Weyl's class, which provides a simple yet a class of algebraically general solutions of static, axisymmetric geometries. Employing the canonical forms of rank-2 Killing tensors, we systematically derive the constraints that must be satisfied for these spacetimes to admit genuine hidden symmetries. Our analysis yields an analytical characterization of the obstructions to integrability within subclasses of Weyl's class, both in vacuum and electrovacuum. In particular, we find that no two-Killing-vector member of Weyl's class, in vacuum or electrovacuum, admits an irreducible Killing tensor capable of supplying the additional integral of motion required for complete integrability. Members of Weyl's class admitting a third additional Killing-vector isometry (i.e. Levi-Civita) are already completely integrable through their manifest symmetries alone admitting only reducible Killing tensors. This result provides an analytic complement to previous analytical and numerical investigations, and establishes a systematic connection between the absence of hidden symmetries and the breakdown of complete integrability. Beyond the specific classification obtained here, these results demonstrate the potential of our approach regarding the canonical forms of Killing tensor as a systematic tool for probing hidden symmetries in Petrov type I spacetimes.

Recent experiments in van der Waals moiré materials have reported realizations of two-dimensional fractional topological insulators (FTIs). We study transport properties of FTI edges at filling factors $\nu_{\text{FTI}} = 2(1\pm 1/n)$ with integer $n \geq 2$ (even or odd), each of which supports four counter-propagating edge modes. The edge modes can undergo partial localization, leaving two of the four edge modes conducting. We identify three distinct partial-localization channels and, for each channel, determine the reduced theory describing the remaining conducting modes, from which we obtain the minimal quasiparticle charge. We further explore transport properties of each partially localized phase and in particular determine the corresponding edge conductances. We demonstrate that measurements of the conductance together with the minimal quasiparticle charge provide a fingerprint that uniquely distinguishes the three partially localized phases.

We investigate the nonequilibrium spin-phonon dynamics and energy cascades in a strongly dimerized spin-Peierls chain using a multi-tiered nonlinear phononics architecture. To bypass linear selection rules prohibiting the direct excitation of the Raman-active dimerization mode, a terahertz laser drives an infrared mode that nonlinearly couples to the Raman lattice displacement, subsequently modulating the magnetic exchange. Employing a bond-operator formalism with a second-order cumulant expansion of the Lindblad master equation, we show that maximum energy transfer into the magnetic sector is governed by a dynamical impedance-matching condition rather than the unperturbed triplon density of states. We find that the sustained energy input of continuous-wave driving builds high excitation densities that severely back-act on the lattice, overdamping the primary phonon and smearing magnetic features via power broadening. Conversely, the small time-integrated energy of a pulse keeps the response perturbative, terminating before back-action accumulates and preserving sharp Fano-like quantum interferences. These insights establish limits for controlling dynamic magnetic states without quenching the driving lattice modes.

Reliable early disruption prediction is critical for the safe operation and real-time control of tokamaks. However, machine learning based prediction frameworks have predominantly targeted medium and long pulse devices, with comparatively limited attention given to short pulse tokamaks where available warning time is inherently constrained. In this work, an interpretable machine learning framework is developed for feature engineering and early prediction of disruptions in the ADITYA using the initial plasma evolution information, prior to the activation of the negative converter of the ohmic transformer power supply. Statistical descriptors comprising the mean, variance, skewness, kurtosis and wavelet energy entropy are extracted from routinely available plasma diagnostics over different operation time windows. Decision tree based feature selection is employed to identify physically meaningful disruption precursors and to reduce feature dimensionality. These selected features are used to train a random forest classifier. The proposed framework achieves stable predictive performance across different analysis windows, with a maximum ROC-AUC of 0.87 for 0-35 ms and 0-40 ms windows. Comparable and in some cases improved, performance is obtained using the reduced feature set, demonstrating that the selected statistical descriptors retain the essential information required for disruption prediction. The proposed methodology provides an interpretable and computationally efficient framework for real time disruption prediction in short pulse tokamaks and establishes that carefully engineered statistical descriptors can effectively replace raw time series inputs for early disruption prediction, thereby offering a practical pathway toward real time plasma control in short pulse tokamaks similar to ADITYA and ADITYA-U.

The Quantum Fisher information is frequently studied in the fields of quantum sensing and quantum metrology, as it specifies the sensitivity of a sensor through the Crámer-Rao bound, and in condensed matter physics where it relates to the quantum metric. Measuring the quantum Fisher information is therefore of significant current interest. In this work, we propose a scheme for measuring the quantum Fisher information with respect to any parameter in a general two-band solid state system using angle-resolved photoemission spectroscopy with carefully tuned incidence angles and light polarization. We investigate conditions under which this can be related back to information about the ground state of the material itself changing with system parameters.

We study supersymmetric near-horizon geometries of gauged $D=5$ supergravity coupled to vector multiplets, on the branch where the canonical rotational Killing vector $\tilde V$ of the cross-section ${\cal S}$ is non-vanishing. No rotational symmetry is assumed, and nothing about the set where the frame built from the Killing spinors degenerates. On a compact connected ${\cal S}$ without boundary a second rotational Killing field, independent of $\tilde V$, always exists and is an isometry of all of ${\cal S}$. Where the moduli vary it is $$ U_i=\parallel\eta_-\parallel^2\big(\alpha Z_i-\epsilon_{ijk}Z^ju^k\big) , \qquad u_i=\Phi P_i-h_i , $$ a polynomial in the horizon data, hence smooth everywhere; where the moduli are constant the horizon is locally homogeneous. The only further hypothesis for these results is that the superpotential $\Phi=\chi V_IX^I$ is nowhere zero — weaker than the non-negativity of the scalar potential assumed in the earlier literature. The two sub-branches are separated by $K=Q_{IJ}C^IC^J$, which vanishes exactly in the minimal theory: $K\equiv0$ recovers the result of Grover, Gutowski, Papadopoulos and Sabra, while elsewhere $K>0$ and $\alpha$ is either identically zero or nowhere zero. Each of $K\equiv0$, $P\equiv0$ and $P\not\equiv0$ occurs on compact ${\cal S}$. Constant moduli return the local geometries of Kunduri and Lucietti as a conclusion, not an ansatz. Varying moduli with $\alpha\not\equiv0$ give a cohomogeneity-one $T^2$ action whose orbit space is a closed interval, so ${\cal S}$ is $S^3$, a lens space or $S^1\times S^2$; the last is excluded by two global first integrals, a new one, $\alpha\parallel\eta_-\parallel^4$, and the constant spinor norm already known. A varying-moduli supersymmetric $AdS_5$ black ring therefore cannot exist with $\alpha\not\equiv0$; the $S^1\times S^2$ window survives only at constant moduli or at $\alpha\equiv0$.

We present a computational audit of the identifiability limits for structural corrections to the Radial Acceleration Relation (RAR) using a canonical subset of the SPARC database (N = 126). Rather than proposing a new dynamical law, we establish the observational conditions under which such a law would be mathematically recoverable. We resolve three methodological controls that heavily influence RAR interpretations. First, we isolate a -0.39 dex residual offset between the eight galaxies in the lowest-quality observational tier (Q = 3, mean -0.433 dex) and the remaining 118 (mean -0.040 dex). Of five predictions that beam smearing must satisfy, four fail: the radial profile plateaus at -0.331 +/- 0.028 dex rather than decaying to zero, and the offset does not scale with the number of resolution elements across a curve. Beam smearing is disfavoured as the primary driver, though the offset remains a data-quality signature rather than a physical one – Q = 3 in SPARC flags major asymmetries and strong non-circular motions, conditions under which a rotation curve does not trace the equilibrium potential. Second, we decouple the architectural limits of the dataset into three independently measured quantities – the no-model point scatter (sigma_M0 = 0.1860 dex), the residual floor after free per-galaxy intercepts (sigma_M3 = 0.1058 dex), and the propagated analytic error floor – together with the absorbable budget sqrt(sigma_M0^2 - sigma_M3^2) = 0.1530 dex derived from the first two. Finally, we provide an 8-cell protocol grid to reconcile Leave-One-Out (LOO) Mean Squared Prediction Error (MSPE) ratios. We demonstrate that reported structural-dynamical couplings must be evaluated with strict adherence to residual definitions (median vs. mean, signed vs. absolute) and baseline denominators to avoid adopting labeling artifacts as new physics.

Complex systems are often organised into hierarchies whose internal interactions are stronger or faster than interactions across levels. When markets are treated as genuinely multilevel systems it becomes natural to represent them as systems with hierarchical causality. Here we show that reflexivity can be formulated within such a discrete hierarchical causal system; but one in which a higher-level actor state restricts the lower-level transition kernels that remain admissible. Then event dynamics can be separated from calendar embeddings: a set-valued actor-conditioned correspondence can be used to define the admissible family of event kernels, while joint state and waiting-time laws can be used to determine compatible timing to then natural demonstrate reflexivity. A selected event-state law need not determine a unique calendar embedding. Locally, uniqueness of the joint event or timing specification requires uniqueness of both the admissible event kernel and its compatible timing law. Reflexivity is thus the endogenous closure of a hierarchical constraint loop, while timing and projection can generate calendar-time memory or causal ambiguity even for Markov event dynamics.

The Boltzmann-Loschmidt dispute in 1876-1877 discussed the problem of time reversal of ther- malization from time reversible classical equations of motion. Here, 150 years later, we highlight this problem in the frame of quantum computing. A quantum protocol is proposed that allows to perform a time reversal of complex evolution in the regime of many-body quantum chaos with many qubits. The system represents an evolution of qubits on a square lattice with inter-qubit next-nearest static couplings with a driven pulsed magnetic field. The system entropy grows rapidly to maximal values but returns to initial small values after time reversal. This time reversal is shown to be stable with respect to quantum gate imperfections. However, similar to the Lorenz butterfly effect, there is the butterfly effect of qubit when inversion of only one qubit breaks time reversibility of the whole system. It is argued that this protocol is accessible to nowadays quantum computers and annealers with hundreds of qubits.

Speed of sound (SoS) is fundamental to ultrasound beamforming and a promising quantitative biomarker for tissue characterization. Although transmission- and reflector-based methods have demonstrated the diagnostic value of SoS, their need for dedicated hardware or constrained acquisition geometries limits clinical usability. Pulse-echo SoS imaging addresses these limitations by estimating SoS with conventional ultrasound probes and data acquisition paradigms. This review provides a structured overview of pulse-echo SoS estimation methods, categorized by the source of information used, the estimated SoS representation, and the reconstruction strategy. We review methods by their locality, e.g., global, layer-wise, and spatially-resolved predictions, as well as in terms of prediction strategies including gradient-free search, optimization-based solutions, analytical closed-form approximations, and deep learning-based methods. Finally, we summarize emerging diagnostic applications in the breast, liver, and muscle, while discussing challenges and possibilities with SoS imaging.

Plasma wakefield accelerators (PWFAs) offer accelerating gradients of 10-100~GV/m and relativistically propagating plasma bubbles capable of confining charged particles. We study the stationary states of a vortex electron at the bubble center by solving the corresponding quasi-relativistic Schrödinger equation. Analytical solutions are obtained with Laguerre-Gaussian transverse modes and Hermite-Gaussian longitudinal envelopes. Comparing the resulting beam parameters with experimentally accessible vortex-electron bundles, we find that the transverse beam waist supported by the plasma bubble is comparable to that achieved by current electron-optical techniques. The longitudinal confinement further provides a favorable parameter regime for stable injection. Our results indicate the feasibility of maintaining localized vortex-electron states in a plasma-bubble wakefield and provide an analytical starting point for investigating their subsequent acceleration and stability.

Low Gain Avalanche Diodes or LGADs are silicon sensors capable of achieving excellent timing resolution due to their characteristic internal gain. Detectors based on LGAD technology play a crucial role in High Energy and Nuclear Physics experiments, among other applications. However, their performance is affected by environmental factors such as temperature, humidity, and storage conditions. A systematic evaluation of the response of LGAD sensors as a function of these environmental parameters is therefore of essential importance for any application. LGAD sensors fabricated at the Brookhaven National Laboratory are characterized and stress-tested against various operating conditions, such as rapid temperature and humidity changes. Dedicated and detailed simulations are used to interpret the experimental results.

In EEG source imaging, the precision of the imaging of the brain activity depends on the accuracy of the forward head model which is, in turn, affected by the representation of tissue conductivity, including anisotropic compartments such as the skull and white matter. We introduce an EEG source imaging framework based on a hybrid volume-surface-wire integral formulation, enabling tract-aware modeling of anisotropic white matter contributions without a full volumetric head discretization. The proposed framework is assessed on a realistic MRI-derived head anatomy, showing close agreement with FEM reference solutions while avoiding full-volume meshing and providing a natural representation of white matter fiber tracts. We then integrate this model into a real-time pipeline that couples EEG processing with immersive visualization, enabling synchronized inspection of scalp potentials, cortical sources, and white matter fiber tracts-related quantities. The results support the proposed formulation as a tract-aware alternative to canonical formulations, combining robust localization performance with interactive visualization capabilities.

We study parameterized quantum circuits (PQCs) integrated as residual sidecar modules within a ResNet-50 backbone for 31-class neural population decoding—imagined handwriting classification from multi-neuron spike rasters. Under strictly controlled conditions (fixed data splits, seeds, and optimizer), we compare four model variants: baseline, quantum sidecar with frozen input projection, quantum sidecar with backbone-gradient-trained projection, and a measurement-guided variant that aligns angle encodings with circuit measurement outcomes. The backbone-gradient variant improves accuracy in 3/4 seeds (+0.19% mean, 95% CI [-1.10%, +1.48%]) and consistently reduces Linear CKA similarity to baseline features ($\Delta=-0.025$, 4/4 seeds), indicating genuine structural reorganization of representations. A nine-variant ablation identifies simple shallow architectures as the most effective and reproducible configuration. Measurement-guided training consistently improves representation geometry without reducing accuracy. All results use noiseless statevector simulation on 4 qubits, a regime chosen to reflect the practical constraints of current near-term superconducting hardware; no quantum computational advantage over classical methods is claimed.

The bilayer iridate Sr$_3$Ir$_2$O$_7$ is a $c$-axis collinear antiferromagnet, held there by a giant interlayer pseudodipolar anisotropy, whereas single-layer Sr$_2$IrO$_4$ cants in the $ab$ plane. We show from first principles that biaxial compression of a few percent ($\varepsilon_c\approx-2.4\%$) flops the easy axis of Sr$_3$Ir$_2$O$_7$ into the plane. A magnetic model Hamiltonian built from Wannier functions with no fitted parameter—reproducing the giant magnon gap of the bulk, so far known only from fits to experiment—identifies the mechanism. Compression collapses the interlayer exchange channel, whose straight Ir–O–Ir path weakens as the bent in-plane path strengthens. Hund's exchange sets the scale of the anisotropy and, beyond $J/U\approx0.15$, removes the collinear state altogether. The flop is not a rigid rotation—the ordered moments of the two states cross at $\varepsilon_c$—and it carries a stark fingerprint, in that the giant easy-axis magnon gap collapses to a gapless, Goldstone-like spectrum. Compressively strained films thus sit on a metamagnetic phase boundary ending in a zero-temperature bicritical point, a charge-neutral handle on spin–orbit-entangled order.

Block encoding embeds a matrix as a sub-block of a unitary matrix and serves as a fundamental input model for quantum algorithms based on quantum singular value transformation, enabling polynomial transformations of matrices encoded in unitary operators. Block encoding of unknown quantum states can be useful for quantum learning; however, the fundamental limits on converting between unknown quantum states and their block-encoding unitary channels remain poorly understood. In this paper, we investigate this convertibility in both directions. First, we prove that implementing an $\varepsilon$-approximate block-encoding unitary channel of an unknown quantum state requires $\Omega(1/\varepsilon)$ copies of the state, matching known upper bounds up to logarithmic factors. Second, we show that recovering a rank-$r$, $d$-dimensional quantum state $\rho$ given query access to its block-encoding unitary channel generally requires $\Omega((1/\lambda_{\max}(\rho))\sqrt{d/r})$ queries, where $\lambda_{\max}(\rho)$ is the maximum eigenvalue of $\rho$, revealing an unavoidable dependence on the dimension of the state. Our results identify inherent limitations of block encoding as a representation of unknown quantum states and reveal a separation between learning properties of a quantum state and generating the state itself. Using our techniques, we further establish lower bounds for specific state-generation tasks, including ground-state preparation and Gibbs-state preparation.

In a thermodynamic environment, thermal field theory (TFT) describes a large ensemble of interacting particles. This may appear to be the same as in classical statistical mechanics. Therefore, we study the scalar propagator and fermion propagator by considering an arbitrary parameter $\sigma$ that allows for a path integral description in real-time formalism (RTF). We constructed those propagators which allowed us to know how particles moved from one point to another point in momentum space as well as in mixed space, at finite temperature without a chemical potential.

A first-principles description of noncollinear magnets is challenging, and the practical behavior of genuinely noncollinear exchange-correlation approximations is largely untested. Spin-current density-functional theory (SCDFT) admits noncollinear approximations constrained by local U(1)$\times$SU(2) gauge invariance, an exact condition unavailable in the more restrictive framework of spin-DFT (SDFT). Using the Vienna ab initio simulation package (VASP), we compare two recently developed noncollinear SCDFT functionals, NCMSCAN and LFNCBR89-NCCS, against locally collinear SDFT extensions of four common functionals (PZ, PW92, PBE, and SCAN) for several noncollinear $d$-electron systems. The key finding is that among all tested functionals, only the SCDFT functionals recover the spin texture of the experimental ground state of NiS$_2$, and they do so at a cost comparable to standard semi-local approximations. Yet the two SCDFT functionals differ in equilibrium volumes, band gaps, and on-site magnetic moments. Overall, this survey illustrates the usefulness of SCDFT in capturing noncollinear physics with the tested approximations.

The Bandt-Pompe permutation entropy framework, alongside the complexity-entropy causality plane, has become a standard tool for characterizing the dynamical properties of time series. However, observational noise distorts ordinal pattern probability distributions in ways that can systematically misplace time series within the causality plane, compromising dynamical classification. This effect is particularly relevant for geophysical signals, which are typically poorly and irregularly sampled, and have a low signal-to-noise level. In this work, we characterize the distortions on ordinal pattern statistics using the formalism of majorization. We provide theoretical results and propose corrective strategies that restore discriminability under realistic measurement conditions. To achieve this, we introduce methodology that allows the characterization of noisy dynamical series and further allows the quantification of observational noise without the need of a fitting procedure. Finally, we illustrate our methodology by analyzing paleomagnetic records to determine if the geological evolution of the Earth dipole is better described by a stochastic or chaotic system.

We present a simple model with a n + 4-dimensional metric with compactified extra dimensions with a space dependent radius R. We show that changes in the profile of R are sourced by (visible) matter density and Newtonian potential. We can reproduce rotation curves of spiral galaxies and provide an expression for R. In order to test our hypothesis, we propose six experiments.

We investigate geometric structures defined by 4-forms, encompassing important classes of geometric structures with torsion including almost Hermitian, $\mathrm{G}_2$, $\mathrm{Spin}(7)$, and almost quaternion/hyper Hermitian. Within this unified framework, the underlying 4-form naturally determines geometric data that define a string algebroid over the manifold. In particular, it gives rise to a canonical notion of instanton, thereby linking these geometries to gauge-theoretic structures in generalized geometry and heterotic string theory. We further prove that these data induce generalized Ricci-flat metrics. Finally, we examine the main examples in the literature and construct several explicit ones.

Current particle flow filters rely on Gaussian prior assumptions that fail to capture the non-Gaussian attractor structure of chaotic systems. This study proposes a Score-based Particle Flow Filter (Score-PFF) that replaces the parametric prior gradient with a neural network-learned score function via denoising score matching. This enables flexible characterization of multimodal, skewed, and complex prior distributions in chaotic dynamics. Pure prior adjustment experiments demonstrate correct gradient directions toward the attractor (26.9%-29.0% error reduction over Gaussian priors). Under linear observations, Score-PFF significantly outperforms both Gaussian PFF and EAKF (Cohen's d = 1.03 and 1.40), preserving non-Gaussian structure that EAKF progressively Gaussianizes. Under nonlinear observation operators, Score-PFF maintains robust performance with up to 60% RMSE reduction in strongly non-Gaussian regimes. On the 1000-dimensional Lorenz-96 system, Score-PFF achieves 49.5% RMSE reduction over PFF while reducing per-assimilation cost by replacing SVD-based covariance inversion with neural network inference. Score-PFF establishes a computationally tractable, non-Gaussian data assimilation framework suitable for high-dimensional geophysical systems.

The influence of the flexoelectric coupling on the fluctuations of electric polarization and elastic strains can lead to the principal changes of the dispersion law of soft optical and acoustic phonons and ferrons in a bulk van der Waals ferrielectric. Since the size, gradient and strain effects determine phase diagrams and polarization behavior in thin films, it is reasonable to assume that the flexocoupling and mismatch strains should have a strong influence on the dispersion of phonons and ferrons in thin ferroelectric films. Using the Landau-Ginzburg-Devonshire approach, in this work we reveal that the dispersion of soft optical and acoustic phonons and ferrons is strongly dependent on the sign and magnitude of elastic strains, which originate from the lattice constants mismatch in thin strained films of van der Waals ferrielectric CuInP2S6. In particular, the frequency of acoustic phonons and ferrons approaches zero at nonzero wavevectors k>k_cr, where the critical value of the wavevector k_cr is determined by the mismatch strain, flexoelectric coupling strength and temperature. Zeroing of the acoustic phonon frequency, that appears with increase of tensile strains, indicates a possible emergence of a spatially modulated incommensurate polar phase induced by the flexo-strain effects. Analytical results, derived in this work, open the way for flexo-strain engineering of soft phonon and ferron dispersion in thin films of van der Waals ferrielectrics.

In this paper, we show how to adapt a derivation of Hartree equations due to Knowles and Pickl in the case where the one-particle hamiltonian is an Anderson-Hermite operator in dimension 1 and 2 or a formal Anderson-Hermite operator in dimension 3. By proving energy estimates for solution of the limit equation, uniform in the noise in bounded sets, we achieve a double limit. Namely, we show that we can commute the mean-field limit with a limit in noise.

For nearly two centuries, conventional self-imaging has obeyed a single rule: a periodic wave reconstructs itself at a fixed distance, independent of its bandwidth. Here we show this law is programmable. Sampling the angular spectrum in inverse powers of the mode index makes each mode rephase with its own integer period, deferring exact revival to the least common multiple of all periods: $z_{\mathrm{rev}}=z_{\mathrm{T}}\,e^{r\psi(M)}$, with $\psi$ the second Chebyshev function. We observe these revivals optically as a prime-power staircase in propagation distance, turning free-space diffraction into a readout of the multiplicative structure of the integers.

We analytically solve the evolution equation for small-$x$ gluon transverse-momentum-dependent distributions, which describes the interpolation between the Sudakov and BFKL regimes. We first derive its two limiting forms: the BFKL equation for $\xi = \alpha\sigma s{\bm z}^2/4 \ll 1$ and the Sudakov equation for $\xi \gg 1$. The analytical solutions in these limits are obtained through Mellin-space diagonalization of the BFKL kernel and direct integration of the Sudakov evolution equation, respectively. We then solve the full interpolation equation using a Mellin-space diagonalization ansatz, in which the evolution factor $F(Y,\xi)$ describes the nontrivial $\xi$-dependent modification of a Mellin eigenfunction of the BFKL kernel. This procedure reduces the original two-dimensional integral to a one-dimensional form and permits an analytical evaluation of the resulting evolution kernel. The obtained solution interpolates consistently between the BFKL and Sudakov regimes through an exponential factor $\exp[H(\xi,\gamma)]$. An analysis of the structure of $H(\xi,\gamma)$ allows a quantitative estimation of the transition region between the two dynamical regimes. Our calculation implies a potential matching point in the range of $\xi^{*}\simeq 0.04-0.15$, which is substantially smaller than the naive evaluation value.