Initial Fluctuations Research Articles

Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench

Dynamical quantum phase transitions are at the forefront of current efforts to understand quantum matter out of equilibrium. Except for a few exactly solvable models, predictions of these critical phenomena typically rely on advanced numerical methods. However, those approaches are mostly restricted to one dimension, making investigations of two-dimensional systems highly challenging. Here, we present evidence of dynamical quantum phase transitions in strongly correlated spin lattices in two dimensions. To this end, we apply our recently developed cumulant method [Phys. Rev. X 11, 041018 (2021)] to determine the zeros of the Loschmidt amplitude in the complex plane of time, and we predict the crossing points of the thermodynamic lines of zeros with the real-time axis, where dynamical quantum phase transitions occur. We find the critical times of a two-dimensional quantum Ising lattice and the XYZ model with ferromagnetic or antiferromagnetic couplings. We also show how dynamical quantum phase transitions can be predicted by measuring the initial energy fluctuations, for example in quantum simulators or other engineered quantum systems.

Maximal L1 regularity for solutions to inhomogeneous incompressible Navier-Stokes equations

This paper is devoted to the maximal L1 regularity and asymptotic behavior for solutions to the inhomogeneous incompressible Navier-Stokes equations under a scaling-invariant smallness assumption on the initial velocity. We obtain a new global L1-in-time estimate for the Lipschitz seminorm of the velocity field without any smallness assumption on the initial density fluctuation. In the derivation of this estimate, we study the maximal L1 regularity for a linear Stokes system with variable coefficients. The analysis tools are a use of the semigroup generated by a generalized Stokes operator to characterize some Besov norms and a new gradient estimate for a class of second-order elliptic equations of divergence form. Our method can be used to study some other issues arising from incompressible or compressible viscous fluids.

The Feedback Loop Between the Demand for Voluntary Private Insurance and the Burden of Healthcare System: An Explanatory System Dynamics Model of Hong Kong.

Many countries with universal healthcare have a parallel private healthcare sector due to the waiting time in the public sector. People purchase individual health insurance to pay for private services. Past studies on the relationship between the public sector's waiting time and the demand for health insurance have two limitations: not considering the capacity of the private sector, and subsequently, the omission of a feedback loop. These limitations are also present in the health insurance policy discussion in Hong Kong, where the public sector is overstretched. A lack of understanding of market dynamics might lead to unrealistic expectations of public policy. This study highlights these limitations, and tries to answer the research question: whether the historical dynamics between the intersectoral imbalance of burden and the demand for health insurance in Hong Kong could be quantitatively explained. A system dynamics model was created based on a negative feedback loop. The model's initial input was the percentage of population with health insurance in 2009, and to simulate the percentage continuously until 2019. Results from 2015 to 2019 were compared with actual figures to examine the model's explanatory power. Multivariable sensitivity analysis was performed. With initial fluctuation, the simulated result stabilized and was within the acceptable error range from 2015 to 2019. The mean absolute percentage error (MAPE) was 0.94%. At the end of 2019, the simulated percentage of population with health insurance is 36.6% versus the "real value" of 36.7%. Simulated patient admissions and occupancy rates also approximate the reality. Sensitivity analysis demonstrates the robustness of the model. We can quantitatively explain the feedback loop between health system burden and demand for health insurance. With local parameterization, this model should be transferable to other universal health systems for a better understanding of the system dynamics and more informed policy-making.

New physics from the polarized light of the cosmic microwave background

Cosmology requires new physics beyond the Standard Model of elementary particles and fields. What is the fundamental physics behind dark matter and dark energy? What generated the initial fluctuations in the early Universe? Polarised light of the cosmic microwave background (CMB) may hold the key to answers. In this article, we discuss two new developments in this research area. First, if the physics behind dark matter and dark energy violates parity symmetry, their coupling to photons rotates the plane of linear polarisation as the CMB photons travel more than 13 billion years. This effect is known as `cosmic birefringence': space filled with dark matter and dark energy behaves as if it were a birefringent material, like a crystal. A tantalising hint for such a signal has been found with the statistical significance of $3\sigma$. Next, the period of accelerated expansion in the very early Universe, called `cosmic inflation', produced a stochastic background of primordial gravitational waves (GW). What generated GW? The leading idea is vacuum fluctuations in spacetime, but matter fields could also produce a significant amplitude of primordial GW. Finding its origin using CMB polarisation opens a new window into the physics behind inflation. These new scientific targets may influence how data from future CMB experiments are collected, calibrated, and analysed.

Multi-tube energy-absorbing structures with different matching patterns of heights and diaphragm spacings

There are defects including peak stacking and large load fluctuations in existing multi-tube combined structures. To overcome these defects, a differentiated combination design based on the idea of peak load dislocation superposition is undertaken for the height configuration and diaphragm spacing configuration of each tube. The influence of time to peak load is revealed by combining experiment, theory, and simulation. The results show that the height difference only induces a difference in the time to initial peak loads of tubes, while the subsequent peak loads remain stacked, which cannot reduce the load fluctuations. The variations of the diaphragm spacing can prolong or shorten the duration of deformation of folds in a designated area, thus changing the formation timings of subsequent peak loads, which is a feasible method for controlling the time to formation of the peaks. By optimally setting heights and distributing diaphragm spacings of tubes, peak loads of multi-tube structures can be fully separated, thus reducing the initial peak and load fluctuations. The initial peak load and the fluctuations of the 6-4GT-ΔJ-ΔH 2-Adj combined tube constructed based on the configuration differentiated design idea are reduced by 45.33% and 76.62% respectively, while maintaining the high energy absorption of the system.

Effects of hydrodynamic and initial longitudinal fluctuations on rapidity decorrelation of collective flow

We investigate the interplay between hydrodynamic fluctuations and initial longitudinal fluctuations for their effects on the rapidity decorrelation of collective flow in high-energy nuclear collisions. We use a (3+1)-dimensional integrated dynamical model in which we combine initial conditions with longitudinal fluctuations, fluctuating hydrodynamics and hadronic cascades. We analyse the factorisation ratio in the longitudinal direction to study the effect of these fluctuations on the rapidity decorrelation. We find an essential difference between the effects of the hydrodynamic fluctuations and the initial longitudinal fluctuations in the centrality dependence of the factorisation ratios. A combination of the hydrodynamic fluctuations and the initial longitudinal fluctuations leads to reproduction of the centrality dependence of the second-order factorisation ratio, r2(ηpa,ηpb), measured by the CMS Collaboration. Our model also qualitatively describes the centrality dependence of the third-order factorisation ratio, r3(ηpa,ηpb). These results demonstrate the importance of the hydrodynamic fluctuations, as well as the initial longitudinal fluctuations, in understanding the longitudinal dynamics of high-energy nuclear collision reactions.

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5′,10′,20′,40′,80′,160′,320′, and 640′, and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80′. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320′, but at a low dimensionless threshold ν = −2.5. Under a Gaussian assumption, this would amount to a deviation of ∼4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320′. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640′, both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

The large-scale structure from non-Gaussian primordial perturbations

ABSTRACT The late-time effect of primordial non-Gaussianity offers a window into the physics of inflation and the very early Universe. In this work, we study the consequences of a particular class of primordial non-Gaussianity that is fully characterized by initial density fluctuations drawn from a non-Gaussian probability density function, rather than by construction of a particular form for the primordial bispectrum. We numerically generate multiple realizations of cosmological structure and use the late-time matter power spectrum, bispectrum, and trispectrum to determine the effect of these modified initial conditions. We show that the initial non-Gaussianity has only a small imprint on the first three polyspectra, when compared to a standard Gaussian cosmology. Furthermore, some of our models present an interesting scale-dependent deviation from the Gaussian case in the bispectrum and trispectrum, although the signal is at most at the per cent level. The majority of our models are consistent with cosmic microwave background constraints on the trispectrum, while the others are only marginally excluded. Finally, we discuss further possible extensions of our study.

Single-particle fluctuations dominate the long-time dynamic susceptibility in glass-forming liquids.

Liquids near the glass transition exhibit dynamical heterogeneity, i.e., correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by measurements of a dynamic susceptibility χ_{4}(t), which is sometimes interpreted in terms of the size of those relaxing regions and the intensity of the fluctuations. We show that the results of those measurements can be affected not only by the collective fluctuations in the relaxation rate, but also by density fluctuations in the initial state and by single-particle fluctuations. We also show that at very long times the average overlap C(t) probing the similarity between an initial and a final state separated by a time interval t decays as a power law C(t)∼t^{-d/2}. This is much slower than the stretched exponential behavior C(t)∼e^{-(t/τ)^{β}} previously observed at times within one or two orders of magnitude of the α-relaxation time τ_{α}. We find that for times longer than 10-100τ_{α}, the dynamic susceptibility χ_{4}(t) is dominated by single-particle fluctuations, and that χ_{4}(t)≈C(t)∼t^{-d/2}. Finally, we introduce a method to extract the collective relaxation contribution to the dynamic susceptibility χ_{4}(t) by subtracting the effects of single-particle fluctuations and initial state density fluctuations. We apply this method to numerical simulations of two glass-forming models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system. This allows us to extend the analysis of numerical data to timescales much longer than previously possible, and opens the door for further future progress in the study of dynamic heterogeneities, including the determination of the exchange time.

Three-dimensional Hybrid Simulation Results of a Variable Magnetic Helicity Signature at Proton Kinetic Scales

Abstract Three-dimensional hybrid kinetic simulations are conducted with particle protons and warm fluid electrons. Alfvénic fluctuations initialized at large scales and with wavevectors that are highly oblique with respect to the background magnetic field evolve into a turbulent energy cascade that dissipates at proton kinetic scales. Accompanying the proton scales is a spectral magnetic helicity signature with a peak in magnitude. A series of simulation runs are made with different large-scale cross helicity and different initial fluctuation phases and wavevector configurations. From the simulations a so-called total magnetic helicity peak is evaluated by summing contributions at a wavenumber perpendicular to the background magnetic field. The total is then compared with the reduced magnetic helicity calculated along spacecraft-like trajectories through the simulation box. The reduced combines the helicity from different perpendicular wavenumbers and depends on the sampling direction. The total is then the better physical quantity to characterize the turbulence. On average the ratio of reduced to total is 0.45. The total magnetic helicity and the reduced magnetic helicity show intrinsic variability based on initial fluctuation conditions. This variability can contribute to the scatter found in the observed distribution of solar wind reduced magnetic helicity as a function of cross helicity.

Tuneable phase behaviour and glass transition via polymerization-induced phase separation in crosslinked step-growth polymers.

Once limited to chain-growth polymerizations, fine control over polymerization-induced phase separation (PIPS) has recently been demonstrated in rubber-toughened thermoset materials formed through step-growth polymerizations. The domain length scales of these thermoset materials can be elegantly tuned by utilizing a binary mixture of curing agents (CAs) that individually yield disparate morphologies. Importantly, varying the composition of the binary mixture affects characteristics of the materials such as glass transition temperature and tensile behavior. Here, we establish a full phase diagram of PIPS in a rubber-toughened epoxy system tuned by a binary CA mixture to provide a robust framework of phase behaviour. X-Ray scattering in situ and post-PIPS is employed to elucidate the PIPS mechanism whereby an initial polymerization-induced compositional fluctuation causes nanoscale phase separation of rubber and epoxy components prior to local chain crosslinking and potential macrophase separation. We further demonstrate the universality of this approach by alternatively employing binary epoxy or binary rubber mixtures to achieve broad variations in morphology and glass transitions.

Quantifying the Effect of Initial Fluctuations on Isospin-Sensitive Observables from Heavy-Ion Collisions at Intermediate Energies

Initial fluctuation is one of the ingredients that washes fingerprints of the nuclear symmetry energy on observables in heavy-ion collisions. By artificially using the same initial nuclei in all collision events, the effect of the initial fluctuation on isospin-sensitive observables, e.g., the yield ratio of free neutrons with respect to protons Nn/Np, 3H/3He yield ratio, the yield ratio between charged pions π−/π+, and the elliptic flow ratio or difference between free neutrons and protons v2n/v2p (v2n-v2p), are studied within the ultrarelativistic quantum molecular dynamics (UrQMD) model. In practice, Au + Au collisions with impact parameter b = 5 fm and beam energy Elab = 400 MeV/nucleon are calculated. It is found that the effect of the initialization on the yields of free protons and neutrons is small, while for the yield of pions, the directed and elliptic flows are found to be apparently influenced by the choice of initialization because of the strong memory effects. Regarding the isospin-sensitive observables, the effect of the initialization on Nn/Np and 3H/3He is negligible, while π−/π+ and v2n/v2p (v2n-v2p) display a distinct difference among different initializations. The fingerprints of symmetry energy on π−/π+ and v2n/v2p can be either enhanced or reduced when different initializations are utilized.

Lifting weak lensing degeneracies with a field-based likelihood

ABSTRACT We present a field-based approach to the analysis of cosmic shear data to infer jointly cosmological parameters and the dark matter distribution. This forward modelling approach samples the cosmological parameters and the initial matter fluctuations, using a physical gravity model to link the primordial fluctuations to the non-linear matter distribution. Cosmological parameters are sampled and updated consistently through the forward model, varying (1) the initial matter power spectrum, (2) the geometry through the distance-redshift relationship, and (3) the growth of structure and light-cone effects. Our approach extracts more information from the data than methods based on two-point statistics. We find that this field-based approach lifts the strong degeneracy between the cosmological matter density, Ωm, and the fluctuation amplitude, σ8, providing tight constraints on these parameters from weak lensing data alone. In the simulated four-bin tomographic experiment we consider, the field-based likelihood yields marginal uncertainties on σ8 and Ωm that are, respectively, a factor of 3 and 5 smaller than those from a two-point power spectrum analysis applied to the same underlying data.

Void Replenishment: How Voids Accrete Matter Over Cosmic History

Abstract Cosmic voids are underdense regions filling up most of the volume in the universe. They are expected to emerge in regions comprising negative initial density fluctuations, and subsequently expand as the matter around them collapses and forms walls, filaments, and clusters. We report results from the analysis of a cosmological simulation specially designed to accurately describe low-density regions, such as cosmic voids. Contrary to the common expectation, we find that voids also experience significant mass inflows over cosmic history. On average, 10% of the mass of voids in the sample at z ∼ 0 is accreted from overdense regions, reaching values beyond 35% for a significant fraction of voids. More than half of the mass entering the voids lingers on periods of time ∼10 Gyr well inside them, reaching inner radii. This would imply that part of the gas lying inside voids at a given time proceeds from overdense regions (e.g., clusters or filaments), where it could have been preprocessed, thus challenging the scenario of galaxy formation in voids, and dissenting from the idea of them being pristine environments.

Hyperuniformity of expected equilibrium density distributions of Brownian particles via designer external potentials

Disordered hyperuniformity (DHU) is a recently discovered novel state of many-body systems that is characterized by vanishing normalized infinite-wavelength density fluctuations similar to a perfect crystal, yet possesses an amorphous structure like a liquid or glass. Due to their unique structural characteristics, DHU materials are typically endowed with unusual physical properties, such as large isotropic photonic band gaps, optimal transport properties and superior mechanical properties, enabling a wide spectrum of novel applications. Here we investigate hyperuniformity of expected equilibrium distributions of Brownian particles induced by external potentials. In particular, we analytically derive sufficient conditions on the external potentials in order to achieve distinct classes of DHU density distributions of Brownian particles in thermal equilibrium, based on the stationary-state solutions of the corresponding Smoluchowski equation. We show for a wide spectrum of tight-binding potentials, the desirable DHU distributions of Brownian particles can be controlled and achieved by imposing proper hyperuniformity conditions on the potentials. We also analyze the evolution dynamics of an initial density distribution (hyperuniform or non-hyperuniform) to the desirable equilibrium DHU distribution determined by the prescribed external potentials, which is shown to be coupled with the full spectra of the force fields associated with the imposed potentials. We find that although the transient density distribution can rapidly develop local patterns reminiscent of those in the equilibrium distribution, which is governed by the fast dynamics induced by the external potential, the overall distribution is still modulated by the initial density fluctuations which are relaxed through slow diffusive dynamics. Our study has implications for the fabrication of designer DHU materials.

Cluster assembly times as a cosmological test

ABSTRACT The abundance of galaxy clusters in the low-redshift Universe provides an important cosmological test, constraining a product of the initial amplitude of fluctuations and the amount by which they have grown since early times. The degeneracy of the test with respect to these two factors remains a limitation of abundance studies. Clusters will have different mean assembly times, however, depending on the relative importance of initial fluctuation amplitude and subsequent growth. Thus, structural probes of cluster age such as concentration, shape, or substructure may provide a new cosmological test that breaks the main degeneracy in number counts. We review analytical predictions for how mean assembly time should depend on cosmological parameters, and test these predictions using cosmological simulations. Given the overall sensitivity expected, we estimate the cosmological parameter constraints that could be derived from the cluster catalogues of forthcoming surveys such as Euclid, the Nancy Grace Roman Space Telescope, eROSITA, or CMB-S4. We show that by considering the structural properties of their cluster samples, such surveys could easily achieve errors of Δσ8 = 0.01 or better.

Fe and Cr phase separation in super and hyper duplex stainless steel plates and welds after very short aging times

Fe and Cr phase separation in ferrite, causing 475 °C-embrittlement, was studied after very short aging times in super duplex stainless steel (SDSS) and hyper duplex stainless steel (HDSS) plates and welds. Atom probe tomography showed that hot-rolled SDSS, experiencing significant metal working, had faster kinetics of phase separations compared to the SDSS and HDSS welds after 5 min aging at 475 °C. The surface of the 33-mm SDSS plate had faster Fe and Cr phase separation and larger toughness drop. A higher density of dislocations next to the austenite phase boundary in ferrite, detected by electron channeling contrast, can promote the phase separation at the surface of the plate with lower austenite spacing. The toughness dropped in HDSS welds after aging, but SDSS welds maintained their toughness. An inverse simulation method considering an initial sinusoidal nanometric Cr and Fe fluctuation showed that Ni increases the interdiffusion of Cr in the system, resulting a higher degree of phase separation in SDSS welds than the HDSS weld. Within the composition range of the studied SDSS and HDSS materials, the processing influences the Fe and Cr phase separation more than the variation in composition during short aging or typical fabrication times.

Variation Law of Infrared Radiation Temperature of Unloading Fracture of Composite Coal-Rock

For composite mining coal-rock dynamic disaster, combining the theory of thermodynamics, damage mechanics, and other disciplines, the thermodynamic coupling mathematical model of composite coal-rock under an unloading condition is deduced, and the simulation model of composite coal-rock is established for numerical simulation. And the variation law of thermal infrared radiation under triaxial loading and unloading of composite coal-rock is analyzed and verified by experiments. The results show the following findings: (1) The distribution of thermal infrared radiation temperature of composite coal-rock is different in different stages of stress. The overall temperature of the temperature field is lower than the initial temperature field in the three-dimensional stress loading stage and the stage of stress-keeping pressure, but the internal temperature of the coal body is the highest. In the first stage of “loading and unloading,” the temperature of a coal seam increases slightly, and the temperature of other parts of the rock layer increases except for the circular low-temperature zone. In the second stage of “loading and unloading,” an alternating zone of high and low temperatures appears in the rock mass, and the temperature field is enhanced, among which the temperature field reaches the strongest after unloading the confining pressure. After jumping over the maximum stress, the temperature field decreases as a whole at the instability and rupture stage. (2) The variation of surface average thermal infrared radiation temperature ( T ave ) of composite coal-rock can be divided into the initial fluctuation stage, the linear heating stage, the local decline stage, the temperature sudden increase stage, and the fracture decline stage. At three different unloading rates of 0.003 MPa/s, 0.03 MPa/s, and 0.05 MPa/s, the T ave of coal body, floor rock, and roof rock reach the maximum before composite coal-rock instability and fracture, and the temperature change of the coal body is the most obvious. (3) Under different confining pressure unloading rates, the T ave of roof rock, coal body, and floor rock shows a strong linear relationship with stress after linear fitting. And the correlation between simulation and experimental results after fitting is above 0.89. The larger the confining pressure unloading rate is, the shorter the peak time of T ave arrives, and the larger the peak value. The comparison between the experimental results and the simulation analysis shows that the two results are consistent, and the research results can provide a theoretical basis for the prevention and control of dynamic disasters in coal and rock mining.

Jasmonic Acid Plays a Pivotal Role in Pollen Development and Fertility Regulation in Different Types of P(T)GMS Rice Lines.

Two-line hybrid rice systems represent a new technical approach to utilizing the advantages of rice hybrids. However, the mechanism underlying the male sterile-line fertility transition in rice remains unclear. Peiai 64S (PA64S) is a photoperiod- and thermo-sensitive genic male sterile (PTGMS) line in which male sterility manifests at an average temperature above 23.5 °C under long-day (LD) conditions. Nongken 58S (NK58S) is a LD-sensitive genic male sterile (PGMS) rice that is sterile under LD conditions (above 13.75 h-day). In contrast, D52S is a short-day (SD)-PGMS line that manifests male sterility under SD conditions (below 13.5 h-day). In this study, we obtained fertile and sterile plants from all three lines and performed transcriptome analyses on the anthers of the plants. Gene ontology (GO) analysis suggested that the differentially expressed genes identified were significantly enriched in common terms involved in the response to jasmonic acid (JA) and in JA biosynthesis. On the basis of the biochemical and molecular validation of dynamic, tissue-specific changes in JA, indole-3-acetic acid (IAA) levels, gibberellin (GA) levels, and JA biosynthetic enzyme activities and expression, we proposed that JA could play a pivotal role in viable pollen production through its initial upregulation, constant fluctuation and leaf-spikelet signaling under certain fertility-inducing conditions. Furthermore, we also sprayed methyl jasmonate (MEJA) and salicylhydroxamic acid (SHAM) on the plants, thereby achieving fertility reversal in the PGMS lines NK58S and D52S, with 12.91–63.53% pollen fertility changes. Through qPCR and enzyme activity analyses, we identified two key enzymes—allene oxide synthase (AOS) and allene oxide cyclase (AOC)—that were produced and upregulated by 20–500-fold in PGMS in response to spraying; the activities of these enzymes reversed pollen fertility by influencing the JA biosynthetic pathway. These results provide a new understanding of hormone interactions and networks in male-sterile rice based on the role of JA that will help us to better understand the potential regulatory mechanisms of fertility development in rice in the future.

Evolution of initial stage fluctuations in the glasma

We perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using the glasma graph approximation, but our approach for the time dependence can be applied to a general four-point function of the initial color fields. Our results provide analytical insight into the preequilibrium phase of heavy ion collisions without requiring a numerical solution to the Yang-Mills equations.