arXiv subjects

Kenji Fukushima

Publications and source records attributed to Kenji Fukushima.

At least 19 recordsLinked to original sources

arXiv2026

Moment of Inertia of an Interacting Bose Gas

The response of many-body quantum systems to rotation can be characterized by the moment of inertia. For a classical gas, the moment of inertia can be expressed as the integral of the enthalpy density multiplied by the squared radial distance from the rotation axis. In quantum field theory, the finite rotation in the grand canonical ensemble demands the causality bound. This constraint imposes technical challenges in treating transverse momenta discretized with the Bessel function zeros. However, we define the moment of inertia in the limit of zero angular velocity, in which the causality constraint is irrelevant and ordinary quantum field theoretical techniques can be applied. We evaluate the moment of inertia in the $\phi^4$ theory and find that, surprisingly, the interacting effects including the ring-diagram resummation are consistent with the classical expectation and the moment of inertia density remains proportional to the enthalpy density.

hep-th↗

arXiv2026

Local Spin Polarization in Anisotropic Gubser Flow: Suppression Mechanism and Formulation Dependence

We analytically study the longitudinal spin polarization in relativistic heavy-ion collisions using a perturbed Gubser flow solution. In the large-system-size limit, we derive analytical expression of the local spin polarization along the beam direction. In our treatment, the contributions from thermal vorticity and thermal shear are of comparable magnitudes. The thermal vorticity yields the polarization with a sign opposite to that observed experimentally, while the thermal shear counteracts this effect, helping recover the desired sign. We find that the choice of the reference unit vector aligned with the fluid velocity gives the experimentally observed sign only at low transverse momenta, whereas another formulation with the unit vector fixed along the laboratory time direction yields the desired sign for a wide range of transverse momenta. Notably, a recent formulation with the unit vector normal to the freeze-out hypersurface exhibits an exact cancellation between contributions from thermal vorticity and thermal shear at leading order in the large-system-size limit. We identify a general cancellation pattern with acceleration dominance, which is manifest particularly in the latter two formulations. Thus, the total polarization originates from non-acceleration effects, which need not be substantial even when the elliptic flow is finite, as clearly demonstrated in our analytical results. For comparison, we also discuss the spin polarization in the Hubble flow with rotation.

nucl-th↗

arXiv2026

Polarized Nucleon as a Topological Dipole

We show that a polarized nucleon generically carries a dipole distribution of topological charge density. This topological dipole follows robustly from the definition of the topological form factor and the pseudoscalar nature of the topological charge density. The strength of the topological dipole is fixed, in the chiral limit, by the flavor-singlet axial charge. We demonstrate the mechanism in a two-flavor chiral soliton model with vector mesons and the $U(1)_A$ anomaly, where the rotation of the soliton induces a singlet pseudoscalar profile and realizes the predicted dipole pattern. We also discuss possible experimental probes through exclusive $\eta$, $\eta^\prime$ production and directed-flow-like pseudoscalar-meson asymmetries correlated with magnetic fields or vorticity in relativistic heavy-ion collisions.

hep-ph↗

arXiv2026

Polyakov-loop potential of accelerated gluonic matter and thermodynamic subtleties

We study the one-loop Polyakov-loop effective potential in pure gluonic matter under constant acceleration. We perform the computation in both the Euclidean Rindler spacetime and the optical spacetime, which are related via a conformal transformation. The results from the two formulations correspond to physically different observables, and we clarify their connection to specific components of the energy-momentum tensor. This identification resolves a discrepancy previously noted for fields on conical backgrounds. For the Polyakov-loop expectation value, we should minimize the effective potential computed in the optical metric formulation, which concludes that real acceleration strengthens deconfining properties. We also discuss analytic continuation from real to imaginary acceleration and find a perturbatively confined phase. We point out some suggestive similarities and differences between systems under imaginary acceleration and imaginary rotation.

hep-ph↗

arXiv2026

Energy-momentum tensor form factors and spin density distribution in the nucleon calculated in a quantized Skyrme model with vector mesons

We investigate energy-momentum tensor (EMT) form factors and the spatial spin density distribution in the nucleon within a framework of the quantized Skyrme model with vector mesons. We construct both the canonical and Belinfante improved EMTs and analyze how pseudogauge uncertainty influences local spin and momentum densities while leaving the global nucleon properties unchanged. Using the inversion formulas from nucleon matrix elements in the forward limit, we extract the form factors, $A(t)$, $D(t)$, and $J(t)$, in both pseudogauges and the additional antisymmetric form factor associated with the canonical EMT. We find that the pseudogauge choice leads to sizable differences in the local spin and momentum densities. In particular, the canonical EMT naturally encodes spin density through the antisymmetric tensor structure, while the Belinfante EMT is sensitive to the total angular momentum only. Our results illustrate explicitly how different pseudogauges correspond to different spatial interpretations of nucleon spin structure within the same underlying dynamics. These findings provide a concrete model realization of the pseudogauge ambiguity in QCD-inspired nucleon structure and offer useful intuition for interpreting spatial distributions.

hep-ph↗

arXiv2025

In-in formalism with resummmation in a constant electric field: propagators including nontrivial boundary wavefunctions

We present the derivation of an alternative representation of the real-time in-in formalism under a spatially homogeneous and time independent electric field. Because the system exhibits instability associated with pair production of particles and antiparticles, the perturbation theory should be reorganized depending on the choice of the reference vacuum. We recast the boundary wavefunctions into the quadratic self-energy-like terms in the functional integration formalism. The resulting generating functional in the modified in-in formalism leads to the propagators that resum infinite diagrams necessary to capture the vacuum-instability effects. The proper-time representations of the propagators reproduce the known expressions from the canonical operator formalism, but our derivation based on the generating functional along the closed-time path clarifies the origin of the additional proper-time contour and provides a better physical understanding. Finally, as a concrete example of the application, we compute the in-in expectation value of the vector current in a constant electric field, and find that the simple one-loop calculation captures the pair production effect.

hep-ph↗

arXiv2025

Magnetic-type Love number differentiating quark stars from neutron stars

The quark star (QS) is a hypothetical and yet undiscovered stellar object, and its existence would mark a paradigm shift in research on nuclear and quark matter. Although compactness is a well-known signature for distinguishing between two branches of QSs and neutron stars (NSs), some QSs can overlap with NSs in the radius-mass plane. To manifest their evident differences, we investigate the tidal properties of QSs and NSs. We then find that the magnetic-type Love number is a robust indicator for differentiating between QSs and NSs, whereas the electric-type one is insufficient when QSs and NSs have similar masses and radii. Finally, we show that gravitational waves from binary star mergers can, in principle, be sensitive to differences between QSs and NSs.

astro-ph.HE↗

arXiv2025

Pseudogauge ambiguity in the distributions of energy density, pressure, and shear force inside the nucleon

We study the spatial distributions of pressure, energy density, and shear forces inside the nucleon within the two-flavor Skyrme model including vector mesons. This framework has the advantage that nucleon configurations can be stabilized without the Skyrme term. In contrast to the model without vector mesons, however, we realize that the energy-momentum tensor (EMT) becomes pseudo-gauge dependent. We explicitly demonstrate that all these distributions differ between the canonical and Belinfante forms of the EMTs. We identify the pseudo-gauge ambiguity as originating from nonvanishing surface terms associated with spin currents generated by the vector-meson field strength tensors. Furthermore, we show that the pressure and shear-force distributions in the canonical EMT develop singularities at the nucleon center, whereas the corresponding Belinfante distributions remain finite. Finally, we discuss the implications of pseudo-gauge dependence for extracting the confining force and for constructing the equation of state inside the nucleon.

hep-ph↗

arXiv2025

Topological Uncertainty for Anomaly Detection in the Neural-network EoS Inference with Neutron Star Data

We study the performance of the Topological Uncertainty (TU) constructed with a trained feedforward neural network (FNN) for Anomaly Detection. Generally, meaningful information can be stored in the hidden layers of the trained FNN, and the TU implementation is one tractable recipe to extract buried information by means of the Topological Data Analysis. We explicate the concept of the TU and the numerical procedures. Then, for a concrete demonstration of the performance test, we employ the Neutron Star data used for inference of the equation of state (EoS). For the training dataset consisting of the input (Neutron Star data) and the output (EoS parameters), we can compare the inferred EoSs and the exact answers to classify the data with the label $k$. The subdataset with $k=0$ leads to the normal inference for which the inferred EoS approximates the answer well, while the subdataset with $k=1$ ends up with the unsuccessful inference. Once the TU is prepared based on the $k$-labled subdatasets, we introduce the cross-TU to quantify the uncertainty of characterizing the $k$-labeled data with the label $j$. The anomaly or unsuccessful inference is correctly detected if the cross-TU for $j=k=1$ is smaller than that for $j=0$ and $k=1$. In our numerical experiment, for various input data, we calculate the cross-TU and estimate the performance of Anomaly Detection. We find that performance depends on FNN hyperparameters, and the success rate of Anomaly Detection exceeds $90\%$ in the best case. We finally discuss further potential of the TU application to retrieve the information hidden in the trained FNN.

nucl-th↗

arXiv2025

Relativistic spin hydrodynamics with antisymmetric spin tensors and an extension of the Bargmann-Michel-Telegdi equation

We derive a formulation of relativistic spin hydrodynamics with totally antisymmetric spin tensors that satisfy the Frenkel-Mathisson-Pirani condition. In our proposed spin hydrodynamics, the second law of thermodynamics is fulfilled by the spin-induced corrections in the heat flow, the viscous tensor, and the antisymmetric part of the energy-momentum tensor. These corrections are interpreted as the inverse spin Hall effect and the anomalous Hall effect in the nonrelativistic limit. We show that our evolution equation for the spin density is interpreted as an extension of the Bargmann-Michel-Telegdi equation known in relativistic many-body systems, including the Thomas precession term, the spin-rotation term, and new coupling terms between spin and hydrodynamic variables.

nucl-th↗

arXiv2025

Imaginary Rotating Gluonic Matter at Strong Coupling

We write down an effective theory of the Polyakov loop to investigate the deconfinement phase transition of imaginary-rotating gluonic matter using the strong-coupling expansion. We find the strength of the nearest-neighbor Polyakov-loop interaction modified by the sum of contributions involving the chair-type loops along the temporal direction. Our results show that the deconfinement transition temperature increases with increasing imaginary angular velocity, which agrees with the predictions from the models and the high-temperature perturbative calculations.

hep-ph↗

arXiv2025

A New State of Matter between the Hadronic Phase and the Quark-Gluon Plasma?

Lattice-QCD simulations and theoretical arguments hint at the existence of an intermediate phase of strongly interacting matter between a confined hadron gas and a deconfined Quark-Gluon Plasma (QGP). We qualitatively and semi-quantitatively explore and differentiate the phase structures in the temperature window from the QCD pseudo-critical temperature $T_c\simeq 160\;\text{MeV}$ to the pure-gluonic deconfinement temperature $T_d\simeq 285\;\text{MeV}$. We propose a three-regime picture using a hadron resonance gas (HRG) description augmented with the glueball spectrum based on the analysis of a large number, $N_c$, of colors. We estimate the entropy density from our model to confirm that the lattice-QCD data are bracketed with three regimes, i.e., a hadron gas, a QGP, and a new phase for $T_c \lesssim T \lesssim T_d$. In this new phase that we name a Spaghetti of Quarks with Glueballs (SQGB), thermal degrees of freedom of quarks are deconfined, yet gluons remain confined in glueballs. Since the Hagedorn temperature, $T_H\sim 285\;\text{MeV}$, is universal in the meson and the glueball sectors, in the infinite $N_c$ limit, the phase diagram in the plane of the baryon chemical potential and the temperature is reduced to the one with the confined and deconfined phases and Quarkyonic Matter at high density. At large but finite $N_c$, an SQGB window may open between these phases. We point out that the SQGB has interesting similarities with Quarkyonic Matter and that this matter in the large $N_c$ limit is confined as measured by the interaction between heavy quarks, but behaves in other respects like a quasi-free gas of quarks. As a result of the extrapolation to $N_c=3$, we present a revised phase diagram with the SQGB phase bounded by thermal crossovers. Finally, we give a quantitative analysis of chiral symmetry restoration in the SQGB phase.

hep-ph↗

arXiv2025

Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics

The integration of deep learning techniques and physics-driven designs is reforming the way we address inverse problems, in which accurate physical properties are extracted from complex data sets. This is particularly relevant for quantum chromodynamics (QCD), the theory of strong interactions, with its inherent limitations in observational data and demanding computational approaches. This perspective highlights advances and potential of physics-driven learning methods, focusing on predictions of physical quantities towards QCD physics, and drawing connections to machine learning(ML). It is shown that the fusion of ML and physics can lead to more efficient and reliable problem-solving strategies. Key ideas of ML, methodology of embedding physics priors, and generative models as inverse modelling of physical probability distributions are introduced. Specific applications cover first-principle lattice calculations, and QCD physics of hadrons, neutron stars, and heavy-ion collisions. These examples provide a structured and concise overview of how incorporating prior knowledge such as symmetry, continuity and equations into deep learning designs can address diverse inverse problems across different physical sciences.

hep-lat↗

arXiv2025

QCD Phase Diagram and Astrophysical Implications

I make a brief review about the QCD phases and the equation of state inferred from the neutron star data. Along the temperature axis at low baryon density, the QCD phase transition is a smooth crossover, and it is a natural extension of our imagination to postulate a similar crossover along the density axis at low temperature. Even without phase transitions, the inferred thermodynamic properties of neutron star matter turn out to be highly nontrivial already at twice of the nuclear saturation density. I also give some discussions about the substantiation of quark matter by means of the gravitational wave signals including the multi-messenger prospect.

hep-ph↗

arXiv2024

Strongly interacting matter in extreme magnetic fields

Magnetic fields are ubiquitous across different physical systems of current interest; from the early Universe, compact astrophysical objects and heavy-ion collisions to condensed matter systems. A proper treatment of the effects produced by magnetic fields during the dynamical evolution of these systems, can help to understand observables that otherwise show a puzzling behavior. Furthermore, when these fields are comparable to or stronger than \Lambda_QCD, they serve as excellent probes to help elucidate the physics of strongly interacting matter under extreme conditions of temperature and density. In this work we provide a comprehensive review of recent developments on the description of QED and QCD systems where magnetic field driven effects are important. These include the modification of meson static properties such as masses and form factors, the chiral magnetic effect, the description of anomalous transport coefficients, superconductivity in extreme magnetic fields, the properties of neutron stars, the evolution of heavy-ion collisions, as well as effects on the QCD phase diagram. We describe recent theory and phenomenological developments using effective models as well as LQCD methods. The work represents a state-of-the-art review of the field, motivated by presentations and discussions during the "Workshop on Strongly Interacting Matter in Strong Electromagnetic Fields" that took place in the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in the city of Trento, Italy, September 25-29, 2023.

nucl-th↗

arXiv2024

Stochastic quantization and diffusion models

This is a pedagogical review of the possible connection between the stochastic quantization in physics and the diffusion models in machine learning. For machine-learning applications, the denoising diffusion model has been established as a successful technique, which is formulated in terms of the stochastic differential equation (SDE). In this review, we focus on an SDE approach used in the score-based generative modeling. Interestingly, the evolution of the probability distribution is equivalently described by a particular class of SDEs, and in a particular limit, the stochastic noises can be eliminated. Then, we turn to a similar mathematical formulation in quantum physics, that is, the stochastic quantization. We make a brief overview on the stochastic quantization using a simple toy model of the one-dimensional integration. The analogy between the diffusion model and the stochastic quantization is clearly seen in this concrete example. Finally, we discuss how the sign problem arises in the toy model with complex parameters. The origin of the difficulty is understood based on the Lefschetz thimble analysis. We point out that the SDE is not invariant under the variable change which induces a kernel and a special choice of the kernel guided by the Lefschetz thimble analysis can reduce the sign problem.

hep-lat↗

arXiv2024

Photon polarization tensor at finite temperature and density in a magnetic field

We present analytical and numerical calculations for the photon polarization tensor at finite temperature and density in a constant magnetic field. We first discuss the tensor decomposition in the presence of the magnetic field, which breaks rotational symmetry. Then, we analytically perform all the momentum integrations and numerically take the Landau level sum. We confirm that the imaginary part of the photon polarization tensor correctly reproduces the known result from the independent calculation. We utilize the Kramers-Kronig relation to estimate the real part numerically as a function of the momenta, the chemical potential, and the finite temperature. As an application, we consider the real photon limit and estimate the photon decay rate and the Stokes parameter in the hot and dense medium. We specifically quantify the difference between the X-mode and the O-mode with the polarization orthogonal and parallel to the magnetic field. As long as the magnetic field is weak, the decay rate of the X-mode photon is larger than that of the O-mode photon, while the O-mode becomes dominant due to the Landau level suppression of the X-mode at a strong magnetic field. We also find that the eigenmodes of the propagating photon change their polarization state with increasing density.

hep-ph↗

arXiv2024

Speed of sound and trace anomaly in a unified treatment of the two-color diquark superfluid, the pion-condensed high-isospin matter, and the 2SC quark matter

In a unified perturbative treatment from the high-density side, we compute the speed of sound and the trace anomaly as functions of the chemical potential $\mu$ for the two-color diquark superfluid, the pion-condensed high-isospin matter, and the 2SC quark matter. We find that the corrections induced by the gap energy $\Delta$ involve nontrivial interplay between the dimensionless magnitude $|\Delta/\mu|$ and the derivative $|\partial\Delta/\partial\mu|$. Even though the gap equation has a common structure for these phases of our interest, different numerical constants cause drastic changes in the speed of sound corrections. As long as $|\Delta/\mu|$ is dominant over the derivative, the gap effects increase the speed of sound, which is consistent with the expected behavior of exhibiting a peak at intermediate density. We then discuss the trace anomaly which is pushed down generally by the gap effects and turns out to be negative widely in the high density regime. For demonstration of non-perturbative enhancement, we take account of the instanton-induced interaction. We confirm a further increase in the speed of sound for the two-color diquark superfluid and the pion-condensed high-isospin matter, while the speed of sound for the 2SC quark matter deviates far below the conformal limit due to the derivative contribution.

hep-ph↗