The extraction of the nuclear surface diffuseness from relativistic heavy ion collisions is limited by the intertwined responses of geometry-driven observables to surface diffuseness and intrinsic nuclear deformation. We investigate this limitation using event-by-event Monte Carlo Glauber simulations, focusing on the sensitivity of multiparticle correlations to the Woods–Saxon surface diffuseness a_0 in intrinsically deformed nuclei. We systematically examine the local correlations between a_0 and quadrupole and octupole deformation parameters, β_2 and β_3, and determine how these correlations affect the ability of different observables to constrain a_0. We find that observables dominated by elliptic geometry exhibit a strong response to quadrupole deformation, leading to a local a_0–β_2 degeneracy that substantially limits their sensitivity to the nuclear surface diffuseness. Triangular correlations provide a more independent response to the nuclear surface and therefore retain additional information on a_0, although their sensitivity can also be modified by intrinsic deformation. Extending the analysis to simultaneous quadrupole and octupole deformation shows that the local degeneracy and least-constrained directions depend on the nuclear configuration, demonstrating that the limitation on extracting a_0 is not described by a single global parameter correlation. We quantify these effects using multidimensional response maps, local sensitivity and information-geometric measures, and a Bayesian analysis of the resulting parameter constraints. The results clarify the fundamental limitations imposed by intrinsic multipole deformation on the determination of nuclear surface diffuseness from relativistic heavy ion collisions and identify multiparticle correlations that provide more independent information on a_0.

Determining the role of intrinsic hexadecapole deformation (β_4) in nuclear structure remains a long-standing challenge. Relativistic heavy-ion collisions provide a unique opportunity to address this problem by converting the initial nuclear geometry into the collective motion of the quark–gluon plasma (QGP). Using event-by-event viscous hydrodynamic simulations of ultra-central ^238U+^238U collisions at √(s_NN)=193 GeV, we investigate whether higher-order collective flow can isolate the contribution of β_4 and test the β_2-β_4 correlation. We demonstrate that information carried by the sign of β_4 survives the QGP evolution and is enhanced through nonlinear hydrodynamic response: the fourth-order flow harmonic acquires its topology dependence predominantly from the linear response, whereas the sensitivity of the sixth-order harmonic originates almost entirely from nonlinear mode coupling. As a consequence, the nonlinear response coefficient ξ_6,222 cleanly separates the (β_2,β_4) intrinsic nuclear topologies. These results establish the sign of β_4 as an experimentally accessible signature of deviations from the quadrupole–hexadecapole correlation, demonstrating that higher-order collective flow provides a direct probe of nuclear multipole structure while revealing how nonlinear QGP dynamics encode subtle higher-order geometric information into final-state observables.

We investigate hydrodynamic contributions to short-range two-particle correlations in relativistic heavy-ion collisions using the Boltzmann-Langevin equation. We derive and solve the transport equation for equal-time two-point correlations, obtaining both local and non-local contributions that scale with transport coefficients. The non-local correlations emerging from 2-to-2 scattering dynamics provide a hydrodynamic signature in short-range correlation measurements.

Heavy-ion collision physics has entered the high precision era, demanding theoretical models capable of generating huge statistics to compare with experimental data. However, traditional hybrid models, which combine hydrodynamics and hadronic transport, are computationally intensive, creating a significant bottleneck. In this work, we introduce DiffHIC, an end-to-end generative diffusion model, to emulate ultra-relativistic heavy-ion collisions. The model takes initial entropy density profiles and transport coefficients as input and directly generates two-dimensional final-state particle spectra. Our results demonstrate that DiffHIC achieves a computational speedup of approximately 10^5 against traditional simulations, while accurately reproducing a wide range of physical observables, including integrated and differential anisotropic flow, multi-particle correlations, and momentum fluctuations. This framework provides a powerful and efficient tool for phenomenological studies in the high-precision era of heavy-ion physics.

The thermalization of quark-gluon plasma created in heavy-ion collisions is crucial for understanding its behavior as a relativistic fluid and the thermodynamic properties of the Quantum Chromodynamics (QCD). This study investigates the role of fluctuations in the relationship between transverse momentum and particle multiplicity, with a particular focus on their impact on extracting the QCD speed of sound. In a thermalized quark-gluon plasma, these fluctuations mostly originate from quantum fluctuations in the colliding nuclei, and exhibit a Gaussian distribution as a consequence of their independence from thermodynamic response. In contrast, non-thermalized systems display non-Gaussian fluctuations, reflecting the breakdown of thermalization. By leveraging the Gaussianity condition of quantum-initiated fluctuations, the physical value of the speed of sound can be extracted statistically, even in the presence of significant event-by-event fluctuations. This framework provides a robust diagnostic tool for probing thermalization and extracting thermodynamic properties in both large and small collision systems.

We have investigated the late-time asymptotic solutions, attractor, and focusing behavior of minimal causal spin hydrodynamics in Bjorken expansion. Using the method of dominant balance, we derive the late-time asymptotic solutions of the evolution equation for spin density and identify the specific conditions necessary for the spin density to exhibit a power-law decay. We then analyze both the late-time and early time attractors for the decay rate of spin density. Additionally, we report the focusing behavior in spin hydrodynamics, which has not been found in conventional relativistic hydrodynamics in Bjorken expansion. Our findings suggest that spin density can be treated as a conventional hydrodynamic variable at late times under certain conditions.

The determination of the speed of sound in quark-gluon plasma is a crucial aspect of understanding the properties of strongly interacting matter created in relativistic heavy-ion collisions. In this study, we investigate the impact of initial-state fluctuations on the extraction of the speed of sound in a quark-gluon plasma in the ultra-central collisions. By employing the TRENTo model for simulating initial conditions, we demonstrate that these fluctuations lead to sizable volume effect, which in turn corrects the measured values of the speed of sound. Once the volume corrections are systematically taken into account, the extracted speed of sound approach the physical value, while dependence on model parameters is substantially suppressed.

We propose the weak magnetic effect, which emerges as the dissipative correction to the quark phase space distribution function in quark-gluon plasma close to local thermal equilibrium, as a novel contribution to the observed Lambda hyperon local spin polarization. A finite field strength that is consistent with previous estimates of the magnetic field in heavy-ion collisions can be used to xplain the experimentally observed Lambda local spin polarization through all centrality classes. Moreover, the weak magnetic effect plays an unambiguous role in the ordering between the second-order and third-order modulations of experimental Lambda local spin polarization.

The thermalization of quark gluon plasma created in relativistic heavy-ion collisions is a crucial theoretical question in understanding the onset of hydrodynamics, and in a broad sense, a key step to the exploration of thermalization in isolated quantum systems. Addressing this problem theoretically, in a first principle manner, requires a real-time, non-perturbative method. To this end, we carry out a fully quantum simulation on a classical hardware, of a massive Schwinger model, which well mimics QCD as it shares the important properties such as confinement and chiral symmetry breaking. We focus on the real-time evolution of the Wigner function, namely, the two-point correlation function, which approximates quark momentum distribution. In the context of the eigenstate thermalization hypothesis and the evolution of entropy, our solution reveals the emergence of quantum thermalization in quark-gluon plasma with a strong coupling constant, while thermalization fails progressively as a consequence of the gradually increased significance of quantum many-body scar states in a more weakly coupled system. More importantly, we observe the non-trivial role of the topological vacuum in thermalization, as the thermalization properties differ dramatically in the parity-even and parity-odd components of the Wigner function.

The momentum distribution of particle production in heavy-ion collisions encodes information about thermalization processes in the early-stage quark-gluon plasma. We use kinetic theory to study the far-from-equilibrium evolution of an expanding plasma with an anisotropic momentum-space distribution. We identify slow and fast degrees of freedom in the far-from-equilibrium plasma from the evolution of moments of this distribution. At late times, the slow modes correspond to hydrodynamic degrees of freedom and are naturally gapped from the fast modes by the inverse of the relaxation time, τR−1. At early times, however, there are an infinite number of slow modes with a gap inversely proportional to time, τ−1. From the evolution of the slow modes we generalize the paradigm of the far-from-equilibrium attractor to vector and tensor components of the energy-momentum tensor, and even to higher moments of the distribution function that are not part of the hydrodynamic evolution. We predict that initial-state momentum anisotropy decays slowly in the far-from-equilibrium phase and may persist until the relaxation time. Published by the American Physical Society 2024

We propose a novel effect that accounts for the photon emission from a quark-gluon plasma in the presence of a weak external magnetic field. Although the weak magnetic photon emission from quark-gluon plasma only leads to a small correction to the photon production rate, the induced photon spectrum can be highly azimuthally anisotropic, as a consequence of the coupled effect of the magnetic field and the longitudinal dynamics in the background medium. With respect to a realistic medium evolution containing a tilted fireball configuration, the direct photon elliptic flow from experiments is reproduced. In comparison to the experimental data of direct photon elliptic flow, the strength of the magnetic field during the evolution of quark-gluon plasma can be extracted. For the top energy of RHIC collisions, |eB| is found no larger than a few percent of the pion mass square.

There must be electromagnetic fields created during high-energy heavy-ion collisions. As the quark-gluon plasma (QGP) starts to evolve hydrodynamically, although these fields may become weak comparing to the energy scales of the strong interaction, they are potentially important to some electromagnetic probes. In this work, we focus on the dissipative corrections in QGP due to the presence of a weak external magnetic field, and calculate accordingly the induced photon radiation in the framework of viscous hydrodynamics. By event-by-event hydrodynamical simulations, the experimentally measured direct photon elliptic flow can be well reproduced. Correspondingly, the direct photon elliptic flow implies a magnetic field strength around 0.1$m_\pi^2 \sim 10^{16}$ G. This is indeed a weak field in heavy-ion physics that is compatible to the theoretical predictions, however, it is still an ultra-strong magnetic field in nature.

We present an alternative approach to deriving second-order non-conformal hydrodynamics from the relativistic Boltzmann equation. We demonstrate how constitutive relations for shear and bulk stresses can be transformed into dynamical evolution equations, resulting in Israel-Stewart-like (ISL) hydrodynamics. To understand the far-from-equilibrium applicability of such ISL theories, we investigate the one-dimensional boost-invariant Boltzmann equation using special moments of the distribution function for a system with finite particle mass. Our analysis reveals that the mathematical structure of the ISL equations is akin to that of moment equations, enabling them to approximately replicate even the collisionless dynamics. We conclude that this particular feature is important in extending the applicability of ISL theories beyond the hydrodynamic regime.

We provide a generalized formulation of fluctuating hydrodynamics for the far-from-equilibrium noisy medium. As an example, we consider a noisy plasma experiencing Bjorken expansion, for which the leading order evolution is captured by the hydrodynamic attractor of classical hydrodynamics, while the quadratic couplings of fluctuations are solved effectively via a generalized version of the hydrodynamic kinetic equation. In the far-from-equilibrium plasma, backreaction of hydrodynamic fluctuations results in renormalization of transport properties, as well as long-time tails, of high orders. In particular, corresponding to a renormalized hydrodynamic attractor, evolution in a noisy plasma towards equilibrium becomes nonmonotonic.

Using and comparing kinetic theory and second-order Chapman-Enskog hydrodynamics, we study the non-conformal dynamics of a system undergoing Bjorken expansion. We use the concept of ‘free-streaming fixed lines’ for scaled shear and bulk stresses in non-conformal kinetic theory and hydrodynamics, and show that these ‘fixed lines’ behave as early-time attractors and repellors of the evolution. In the conformal limit, the free-streaming fixed lines reduce to the well-known fixed points of conformal Bjorken dynamics. A new fixed point in the free streaming regime is identified which lies at the intersection of these fixed lines. Contrary to the conformal scenario, both kinetic theory and hydrodynamics predict the absence of attractor behavior in the normalised shear stress channel. In kinetic theory a far-off-equilibrium attractor is found for the normalised effective longitudinal pressure, driven by rapid longitudinal expansion. Second-order viscous hydrodynamics fails to accurately describe this attractor. From a thorough analysis of the free-streaming dynamics in Chapman-Enskog hydrodynamics we conclude that this failure results from an inaccurate approximation of the fixed lines and a related incorrect description of the nature of the fixed point. A modified anisotropic hydrodynamic description is presented that provides excellent agreement with kinetic theory results and reproduces the far-from-equilibrium attractor for the scaled longitudinal pressure.

We study the one-dimensional boost-invariant Boltzmann equation in the relaxation-time approximation using special moments of the distribution function for a system with a finite particle mass. The infinite hierarchy of moments can be truncated by keeping only the three lowest moments that correspond to the three independent components of the energy-momentum tensor. We show that such a three-moment truncation reproduces accurately the exact solution of the kinetic equation after a simple renormalization that takes into account the effects of the neglected higher moments. We derive second-order Israel-Stewart hydrodynamic equations from the three-moment equations, and show that, for most physically relevant initial conditions, these equations yield results comparable to those of the three-moment truncation, albeit less accurate. We attribute this feature to the fact that the structure of Israel-Stewart equations is similar to that of the three-moment truncation. In particular, the presence of the relaxation term in the Israel-Stewart equations, yields an early-time regime that mimics approximately the collisionless regime. A detailed comparison of the three-moment truncation with second-order nonconformal hydrodynamics reveals ambiguities in the definition of second-order transport coefficients. These ambiguities affect the ability of Israel-Stewart hydrodynamics to reproduce results of kinetic theory.

Photons produced in the pre-hydrodynamics stage of the quark-gluon plasma created in relativistic heavy-ion collisions were computed using momentum distribution functions of partons obtained from solutions of the Boltzmann equation. The effect of the initial gluon momentum anisotropy ξ and the dependence on the saturation momentum Qs was investigated; we report on results obtained by varying the latter in this work. We see that small Qs results in a photon yield enhancement, whereas a larger Qs results in a pre-equilibrium photon suppression, owing to the strict constraint of matching to experimental energy density used in this work.

In this article we prove the existence of Kähler-Ricci solitons on smoothable, K-stable Q-Fano varieties. We also investigate the behavior of twisted Kähler-Ricci solitons in the Gromov-Hausdorff topology under this smoothing family.

Existing traditional and ConvNet-based methods for light field depth estimation mainly work on the narrow-baseline scenario. This paper explores the feasibility and capability of ConvNets to estimate depth in another promising scenario: wide-baseline light fields. Due to the deficiency of training samples, a large-scale and diverse synthetic wide-baseline dataset with labelled data is introduced for depth prediction tasks. Considering the practical goal for real-world applications, we design an end-to-end trained lightweight convolutional network to infer depths from light fields, called LLF-Net. The proposed LLF-Net is built by incorporating a cost volume which allows variable angular light field inputs and an attention module that enables to recover details at occlusion areas. Evaluations are made on the synthetic and real-world wide-baseline light fields, and experimental results show that the proposed network achieves the best performance when compared to recent state-of-the-art methods. We also evaluate our LLF-Net on narrow-baseline datasets, and it consequently improves the performance of previous methods.

Different orientations of $$\alpha $$ -clustered carbon nuclei colliding with heavy ions can result in a large variation in the value of anisotropic flow. Thus, photon flow observables from clustered $${\mathrm{^{12}C}}$$ and $${\mathrm{^{197}Au}}$$ collisions could be a potential probe to study the ‘direct photon puzzle’. We calculate the transverse momentum spectra and anisotropic flow coefficients ( $$v_n$$ ) of thermal photons from collisions of triangular $$\alpha $$ -clustered carbon and gold at $$\sqrt{s_{\mathrm{NN}}}=200$$ GeV at RHIC using a hydrodynamic model framework and compare the results with those obtained from unclustered carbon and gold collisions. The slope of the thermal photon spectra is found to vary moderately for different orientations of collisions. However, we find that the elliptic ( $$v_2$$ ) and triangular flow ( $$v_3$$ ) coefficients of direct photons for specific configurations are significantly larger and predominantly formed by the QGP radiation. A strong anti-correlation between initial spatial ellipticity and triangularity is observed in an event-by-event framework of $$\alpha $$ -clustered $${\mathrm{C+Au}}$$ collisions. These special features provide us an opportunity to detect the exotic nature of cluster structure inside carbon nucleus using the photon probe in the future experiments.