arXiv subjects
Publications and source records attributed to Jingxu Wu.
This paper offers a comprehensive overview of recent technological advancements concerning the critical point of chiral phase transition, with a particular focus on Effective Field. Theories in Quantum Chromodynamics (QCD). It delves into the intricacies of these pivotal points, utilizing theoretical tools to explore associated phenomena.
The Legendre transformation is a crucial tool in theoretical physics, known for its symmetry, especially when applied to multivariate functions. In statistical mechanics, ensembles represent the central focus. Leveraging the dimensionless aspect of Legendre transformation, this paper explores the transformation process from the entropy characteristic function of microcanonical ensembles to the analogous definition of partition function transformation. Additionally, it derives characteristic functions, partition functions, and establishes their interrelations, along with deriving corresponding thermodynamic formulas for various ensembles. This streamlined approach sheds light on the fundamental principles of statistical mechanics and underscores the symmetry inherent in Legendre transformation.
This paper provides a comprehensive guide to gravitational wave data processing, with a particular focus on signal generation, noise modeling, and optimization techniques. Beginning with an introduction to gravitational waves and the detection techniques used by LIGO and Virgo, the manual covers the essentials of signal processing, including Fourier analysis, filtering, and the generation of quadratic chirp signals. The analysis of colored Gaussian noise and its impact on interferometric detectors like LIGO is explored in detail, alongside signal detection methods such as the Generalized Likelihood Ratio Test (GLRT). The paper also delves into optimization techniques like Particle Swarm Optimization (PSO), which can be applied to improve signal estimation accuracy. By providing MATLAB-based implementations, this manual serves as both a theoretical and practical resource for researchers in the field of gravitational wave astronomy.
We investigate the leading near-horizon response of Blandford-Znajek energy extraction to a compact, neutral spin-polarized source within minimally coupled Einstein-Cartan-Dirac-Maxwell theory. Eliminating the algebraic contortion yields an effective axial contact interaction, which we embed into a conserved, anisotropic phenomenological completion. Working at leading order in the torsion parameter $ε_T$, spatial anisotropy $ξ$, and slow rotation $χ=a/M$ on the fixed-ADM branch, we derive the modified energy extraction rate at optimal load. We find that the leading-order power ratio $P_{\rm BZ}^{\rm EC}/P_{\rm BZ}^{\rm K}$ receives distinct contributions from rotational dragging ($\ell=1$) and magnetostatic flux redistribution ($\ell=2$). In the isotropic limit ($ξ=0$), the power is enhanced for a co-rotating completion and suppressed for a counter-rotating one, whereas for $ξ\neq0$ the net shift depends on the polar quadrupole response. We also formulate the generalized Znajek identity and linearized Grad--Shafranov framework, demonstrating that undetermined load-factor shifts leave the leading power coefficient invariant due to stationarity at the matched load point.
We establish a sufficient one-minimum criterion for the off-shell Kerr family $Δ(r) = r^2 - 2rm(r) + a^2$ with a positive, nondecreasing mass profile $m(r)$, showing that $1 - 2m'(r) - rm''(r) > 0$ ensures strict convexity and determines root counts for $Δ$. Using a fuzzy-dark-matter-inspired benchmark satisfying this bound, we derive first-order responses for the outer horizon, extremal branch, photon sphere, and shadow functional under general deformations $m/M_{\text{ADM}} = 1 + \varepsilon h$. We demonstrate that static horizon and photon responses are profile-controlled, spin-odd shadow displacements are completion-dependent, and scale-consistent weak-field limits render local profile-gradient effects negligible ($\ll 10^{-20}$), confirming the strong-field box as a formal radial-profile benchmark rather than a self-consistent rotating scalar-field solution.
Extreme-mass-ratio inspirals (EMRIs) are sensitive probes of weak conservative perturbations in the strong-field region of massive black holes. We study a phenomenological EMRI model motivated by Einstein--Cartan gravity in which a spin-polarized dark-matter spike is described by a Weyssenhoff fluid. After torsion is eliminated algebraically, the local spin contribution contains a repulsive exterior source $U_{tt}^{\rm spin}\propto-σ_0^2/r^3$. Solving the corresponding static linearized field equation, however, does not produce a global $1/r^3$ metric perturbation; the response contains a mass renormalization, a logarithmic $r^{-1}$ tail, and an $M/r^2$ term. We therefore introduce $g_{μν}^{\rm eff}=g_{μν}^{\rm Kerr}+αh_{μν}^{\rm eff}$ only as a local near-zone matching ansatz, not as a complete rotating Einstein--Cartan black-hole solution. Within this torsion-inspired deformation we compute circular equatorial inspirals and analytic-kludge waveforms. The fiducial model can produce large phase shifts in an idealized adiabatic calculation, but the forecast is optimistic and does not include a full LISA/Taiji response, Teukolsky/self-force fluxes, eccentricity, inclination, or high-dimensional parameter degeneracies. The results should be read as constraints on an effective near-zone operator rather than as a prediction of minimally coupled Einstein--Cartan dark matter.
We study gravitational-wave dephasing induced by an effective first-order phase transition in a Kerr extreme mass-ratio inspiral (EMRI). The transition is modeled phenomenologically as a finite-width restructuring of the dissipative flux sector, and its observational consequences are quantified with standard LISA matched-filter diagnostics. For a representative system with $M=2\times10^{5}M_\odot$, $μ=1.4M_\odot$, and $\hat a=0.90$, we obtain $ρ_{\rm B}=5.064$, $ρ_{\rm T}=4.073$, $ρ_{\rm R}=1.051$, and a mismatch $\mathcal M=2.986\times10^{-3}$ after maximization over extrinsic time and phase shifts. Although the normalized mismatch remains small, the accumulated phase difference grows to $ΔΦ_{22}^{\rm SF}\sim 5\times10^{3}\,\mathrm{rad}$, indicating that a narrow transition window can generate a large coherent deformation of the inspiral clock while leaving the waveform globally close to the baseline branch in detector-weighted norm. The resulting signal therefore lies in a bias-sensitive regime, characterized by small mismatch, order-unity residual norm, and large cumulative dephasing. Our results suggest that the dominant consequence of the transition sector is not loss of detectability, but loss of faithfulness for precision inference. This motivates future LISA EMRI waveform models that incorporate parameterized transition sectors directly into the waveform manifold.
Extreme Mass Ratio Inspirals (EMRIs) constitute a prime target for future space-based gravitational-wave observatories such as LISA. In this paper, we analytically investigate the long-term phase shift (dephasing) in the gravitational wave signal induced by a first-order quantum chromodynamics (QCD) phase transition within a neutron star orbiting a supermassive Kerr black hole. By modeling the transition from a hadronic phase to a quark core phase, we quantify the sudden change in the tidal deformability ($Λ$) of the secondary object. Utilizing the Teukolsky formalism and Post-Newtonian expansions, we derive a strict analytical scaling law for the accumulated dephasing. We demonstrate that the Kerr spin parameter $a$ and the critical phase transition orbital velocity $v_c$ significantly amplify the dephasing effect. Our analytical framework provides a robust tool for probing the non-perturbative QCD equation of state at high baryon densities using gravitational wave astronomy.
We construct an explicit linear map from compact, conserved thermodynamic/effective-medium perturbations of the stress-energy tensor to the metric response in static, spherically symmetric spacetimes, and from there to geometric observables of direct relevance to horizon-scale imaging: the shadow radius and photon-sphere frequency. The response is expressed through $L^{1}$-bounded kernels written in a piecewise "local $+$ tail" form, which makes transparent the separation between near-photon-sphere sensitivity and far-zone contributions (including AdS tails). Under mild assumptions on the matter susceptibilities near a critical point, dominated convergence transfers the thermodynamic exponent to the geometric susceptibility, $γ_{\rm sh}=γ_{\rm th}$, with controlled analytic corrections. We further provide AdS far-zone bounds with explicit outside-support constants depending only on background geometric data at the photon sphere and shell geometry. A reproducible numerical pipeline with convergence diagnostics is presented and benchmarked.
We present a self-contained theoretical analysis of a dark-QCD chiral transition in which the Polyakov-loop sector retains an explicit $Z(3)$ structure and couples consistently to the chiral order parameter.Working within a coupled chiral--Polyakov effective theory, we map the homogeneous vacuum landscape and identify a metastability window bounded by spinodal loss of stability.We then construct $Z(3)$ domain-wall solutions including chiral backreaction, extracting temperature-dependent wall profiles and surface tension.Finally, we connect homogeneous metastability and wall microphysics to thermal bubble nucleation by evaluating the critical radius $R_c(T)$ and the nucleation exponent $S_3(T)/T$ in the thin-wall regime, providing a compact set of reproducible diagnostics for the decay of the metastable phase.Our results establish a coherent pipeline from vacuum structure to nonperturbative interfaces and nucleation barriers, suitable for systematic extensions to full multi-field bounce calculations and dark-sector cosmological applications.
We develop a rigorous analytical framework for metastable stochastic transitions in Landau-type gradient systems inspired by QCD phenomenology. The functional $F(σ;u)=\int_Ω[\fracκ{2}|\nablaσ|^2+V(σ;u)]\,dx$, depending smoothly on a control parameter $u\in\mathcal U$, is analyzed through the Euler-Lagrange map $\mathcal{E}(σ;u)=-κΔσ+V'(σ;u)$ and its Hessian $\mathcal{L}_{σ,u}=-κΔ+V''(σ;u)$. By combining variational methods, $Γ$- and Mosco convergence, and spectral perturbation theory, we establish the persistence and stability of local minima and index-one saddles under parameter deformations and variational discretizations. The associated mountain-pass solutions form Cerf-continuous branches away from the discriminant set $\mathcal D=\{u:\det\mathcal L_{σ,u}=0\}$, whose crossings produce only fold or cusp catastrophes in generic one- and two-parameter slices. The $Γ$-limit is taken with respect to the $L^2(Ω)$ topology, ensuring compactness, convergence of gradient flows, and spectral continuity of $\mathcal L_{σ,u}$. As a consequence, the Eyring-Kramers formula for the mean transition time between metastable wells retains quantitative validity under both parameter deformations and discretization refinement, with convergent free-energy barriers, unstable eigenvalues, and zeta-regularized determinant ratios. This construction unifies the classical intuition of Eyring, Kramers, and Langer with modern variational and spectral analysis, providing a mathematically consistent and physically transparent foundation for metastable decay and phase conversion in Landau-QCD-type systems.
This work presents a fully theoretical and self consistent framework for calculating the third-order nonlinear susceptibility of CdSe/ZnS--MOF composite quantum dots. The approach unifies finite-potential quantum confinement,the Liouville von Neumann density matrix expansion to third order, and effective-medium electrodynamics (Maxwell--Garnett and Bruggeman) within a single Hamiltonian-based model, requiring no empirical fitting. Electron hole quantized states and dipole matrix elements are obtained under the effective-mass approximation with BenDaniel--Duke boundary conditions; closed analytic forms for(including Lorentzian/Voigt broadening) follow from the response expansion. Homogenization yields macroscopic scaling laws that link microscopic descriptors (core radius, shell thickness, dielectric mismatch) to bulk coefficients and. A Kramers--Kronig consistency check confirms causality and analyticity of the computed spectra with small residuals. The formalism provides a predictive, parameter-transparent route to engineer third-order nonlinearity in hybrid quantum materials,clarifying how size and environment govern the magnitude and dispersion of.
Emergency pharmaceutical logistics during rapid-onset disasters must balance timeliness, legal compliance, and environmental uncertainty. We present a hybrid framework that co-designs quantum-inspired decision dynamics, embedded legal constraints, and blockchain-verified environmental feedback. Candidate routes are modeled as a superposed state whose collapse is governed by entropy modulation-delaying commitment under ambiguity and accelerating resolution when coherent signals emerge. Legal statutes act as real-time projection operators shaping feasible choices, while environmental decoherence cues adjust confidence and path viability. The core engine is situated within a multilevel governance and mechanism design architecture, establishing clear roles, accountability channels, and audit trails. Large-scale simulations in wildfire scenarios demonstrate substantial gains over conventional baselines in latency, compliance, and robustness, while preserving interpretability and fairness adaptation. The resulting system offers a deployable, governance-aware infrastructure where law and physical risk jointly inform emergency routing decisions.
We investigate QCD matter using the two-flavor PNJL model and find that the shear viscosity to entropy density ratio η/s reaches a minimum while the bulk viscosity ζ/s peaks near the chiral crossover line, particularly at large baryon chemical potential, indicating sensitivity to critical dynamics and offering potential signatures for the QCD critical endpoint in heavy-ion collisions.
This paper explores the ontological and epistemological foundations of Lev Landau's theoretical physics through the lens of his unpublished philosophical notes and scientific practice. We identify a unique form of geometric reductionism where physical laws emerge as inevitable consequences of symmetry breaking in progressively constrained phase spaces. Landau's dismissal of quantum interpretation debates and his famous "axiomatic minimalism" in the Course of Theoretical Physics are shown to stem from a deep epistemological commitment to dimensional aesthetics - the belief that fundamental truths must manifest through dimensional economy in mathematical representations.
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based on phase space Lie algebras. By analyzing the evolution of density matrices under phase space displacements, we derive constrained expressions for nonlinear polarization and susceptibility tensors. The implications of geometric phases, such as Berry curvature, are explored, demonstrating their role in suppressing unphysical components of the polarization. Monte Carlo simulations confirm the theoretical predictions, offering insights into nonlinear rectification and topological Hall effects. This approach opens avenues for engineering materials with tailored nonlinear properties, particularly in the realm of metamaterials and topological photonics.
We investigate the phenomenon of CP violation in the weak decay of bottom hadrons (B mesons) through comprehensive theoretical analysis and mathematical derivations. We analyze the fundamental mechanisms of B meson decay, emphasizing the interplay between CP symmetry breaking and the contributions from the quark level. By examining the role of the weak Hamiltonian, we reveal the significance of both short-range and long-range interactions in the decay process. Our theoretical framework highlights the close relationship between differential decay distributions and CP violation, providing a robust foundation for understanding CP violation phenomena in B meson decays. We discuss the implications of our findings for future research, particularly the necessity of improving the precision of CP violation measurements to validate existing theoretical models and explore potential new physics. Through a combination of mathematical derivations and theoretical insights, this study aims to contribute to a deeper understanding of the matter-antimatter asymmetry problem in particle physics.