Neutrino oscillations confirm the presence of mode entanglement, as each flavor eigenstate is composed of a coherent superposition of distinct mass eigenstates. In this work, we investigate the dynamics of quantum resources in neutrino oscillation systems by analyzing quantum steering, logarithmic negativity, and quantum coherence within a two-flavor framework. Treating neutrino oscillations as an effective two-level quantum system, we study the influence of environmental decoherence on these nonclassical features by modeling the system as an open quantum system. Three representative noise channels are considered, namely amplitude damping (AD), phase flip (PF), and phase damping (PD), allowing us to capture both dissipative and dephasing mechanisms. We examine the evolution of quantum resources in both Markovian and non-Markovian regimes, highlighting the role of memory effects in the system-environment interaction. The results reveal a clear hierarchy in the robustness of quantum resources under decoherence. Quantum steering is the most sensitive correlation in the hierarchy under decoherence effects, while logarithmic negativity exhibits intermediate robustness. Quantum coherence displays the highest resilience by persisting over a wider parameter range. Within the PF and PD channels, both logarithmic negativity and coherence display identical dynamical behaviors, a feature that reflects their shared dependence on phase-related noise. In contrast, the non-Markovian regime delays decoherence and induces partial revivals of entanglement and coherence due to information backflow, whereas quantum steering remains strongly suppressed. These findings provide a detailed comparison of different quantum resources in neutrino oscillation systems and offer new insights into the interplay between decoherence mechanisms and quantum correlations.

Morocco

Omar Bachain

Elhabib Jaloum

Mohamed Amazioug

Saudi Arabia

Nazek Alessa

Wedad R. Alharbi

Rachid Ahl Laamara

Abdel-Haleem Abdel-Aty

Dephasing effects on the dynamical evolution of quantum correlations and coherence in neutrino oscillations

We introduce a two-level residual construction for elliptic XYZ-type regular-derivative chains. The first level places a full two-spin Pauli <italic>W</italic>-envelope into the ordinary Yang&#8211;Baxter residual and closes the bulk sector, inside a nonsingular finite-coefficient leakage chart and a selected equal-orientation component, onto Baxter&#8217;s elliptic eight-vertex branch. The second level places a full operator-valued boundary <italic>V</italic>-envelope into the reflection residual and records a boundary residual-reduction ledger which isolates an explicit boundary-extension candidate carrying an antisymmetric impurity-algebra coupling outside the displayed factorized dressing span. We then insert the closed bulk object and the ledger-retained boundary object into a double-row trace functional and compute its normalized regular derivative, obtaining an algebra-valued XYZ-type regular-derivative operator with a boundary-extension impurity. In physical terms, this object gives a residual-level route from elliptic eight-vertex bulk weights to an open XYZ spin-1/2 chain with an algebra-valued boundary impurity. The construction does not claim a complete reflection-equation certificate for the displayed boundary object; rather, it separates the proven bulk closure, the boundary residual-reduction diagnostic, and the resulting regular-derivative algebraic operator.

China

Ze Tao

Minghui Sun

Fujun Liu

Bulk residual closure and boundary residual reduction for elliptic XYZ-type regular-derivative chains

We show that elliptic curves with complex multiplication (CM) naturally emerge in the spectral geometry of Hermitian one-matrix models in the two-cut phase. Focusing on a symmetric quartic potential, we derive the corresponding genus-one spectral curve and compute its modular <italic>j</italic>-invariant in closed form as a function of the quartic coupling <italic>g</italic>. We identify specific values of <italic>g</italic> for which the elliptic curve exhibits <italic>CM</italic>, i.e., its endomorphism ring is larger than <math altimg='si29.svg'><mi mathvariant='double-struck'>Z</mi></math>. This establishes a direct connection between number-theoretic structures and the spectral data of random matrix ensembles.

Egypt

Ali Nassar

Spectral curves with complex multiplication in Hermitian matrix models

We investigate the emergence of a time-crystalline phase in a single-band holographic superconductor, extending the Anti-de Sitter/Conformal Field Theory (AdS/CFT) framework. By incorporating a nonlinear gauge-scalar coupling and external driving, we derive coupled equations of motion for the plasma and Higgs modes, analogous to those in high- <italic>T<inf>c</inf></italic> superconductors. Multi-scale analysis reveals a sum resonance with subharmonic growth indicating broken time-translation symmetry. We perform numerical computation of quasinormal mode and demonstrate the transition to the time-crystalline phase. The holographic model may serve as a robust tool for studying strongly coupled time crystals.

Taiwan

Chi-Hsien Tai

Wen-Yu Wen

Time-crystalline phase in a single-band holographic superconductor

Our recent result on the construction of perfect fluid equations with <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math> Schr&#246;dinger supersymmetry [Mod. Phys. Lett. A 41 (2026) 2550214] is extended to accommodate nonrelativistic conformal supersymmetries of other types. Two cases are considered in detail, which include the <math altimg='si2.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> conformal Newton-Hooke superalgebra and <math altimg='si3.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> &#8467;-conformal Galilei superalgebra with arbitrary half-integer parameter &#8467;. Supersymmetric fluid models are built within the Hamiltonian framework by introducing real (for <math altimg='si3.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>) or complex (for <math altimg='si2.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math>) anticommuting field variables as superpartners for the density and velocity. For both the cases the full set of conserved charges associated with the superalgebras is constructed and the Lagrangian description is given. Subtleties with the construction of perfect fluid equations with <math altimg='si2.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> &#8467;-conformal Galilei supersymmetry are discussed as well.

Russia

Timofei Snegirev

Perfect fluid equations with nonrelativistic conformal supersymmetries

We explore the Kazakov-Solodukhin quantum deformed black hole spacetime, characterized by a single deformation parameter <italic>&#951;</italic> that encodes quantum corrections to the classical Schwarzschild solution. The model preserves the correct general-relativistic limit as <italic>&#951;</italic>&#8239;&#8594;&#8239;0, while introducing significant and physically meaningful deviations in the strong-field regime. A central and remarkable feature of the geometry is the regularization of the classical singularity: curvature invariants remain finite near the minimal radius <math altimg='si2.svg'><mrow><mi>r</mi><mo linebreak='goodbreak'>=</mo><mi>&#951;</mi></mrow></math>, effectively replacing the divergent core with a smooth and well-behaved region. This behavior naturally introduces a minimal length scale into the spacetime structure, offering a geometrically motivated resolution of the singularity problem. The deformation modifies the horizon structure, shifts the event horizon location, and alters the mass-radius relation. It also reduces the surface gravity, leading to a lower Hawking temperature and a slower evaporation process, thereby enhancing the thermodynamic stability of the black hole. Photon dynamics are correspondingly affected, resulting in a displaced photon sphere and modified strong-lensing characteristics. While the shadow remains perfectly circular due to spherical symmetry, its size depends sensitively on <italic>&#951;</italic>. Observational constraints can be expressed through <math altimg='si30.svg'><mrow><mrow><mo stretchy='true'>|</mo><msub><mi>R</mi><mrow><mi>s</mi><mi>h</mi></mrow></msub><mrow><mo>(</mo><mi>&#951;</mi><mo>)</mo></mrow><mo linebreak='badbreak'>&#8722;</mo><msub><mi>R</mi><mrow><mi>o</mi><mi>b</mi><mi>s</mi></mrow></msub><mo stretchy='true'>|</mo></mrow><mi>&#10877;</mi><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><msub><mi>R</mi><mrow><mi>o</mi><mi>b</mi><mi>s</mi></mrow></msub><mo>,</mo></mrow></math> which places an upper bound on the deformation parameter. In the weak-field limit, the deflection angle acquires a quadratic correction proportional to <italic>&#951;</italic> 2, ensuring consistency with precision tests while allowing potentially detectable deviations in strong-gravity observations. These features make the model both theoretically appealing and observationally testable.

South Africa

Azerbaijan

A. Errehymy

Y. Khedif

Italy

M. Daoud

Uzbekistan

B. Turimov

S. Usanov

Z. Yasakov

Z. Avezmuratova

Observational constraints on Kazakov-Solodukhin quantum deformed black holes from M87* and Sgr A* shadows

We investigate the structure of strange quark stars (SQSs) in the color–flavor–locked (CFL) phase in the presence of scalar bosonic dark matter within a two–fluid formalism. The quark matter equation of state (EOS) is obtained from perturbative QCD, incorporating the latest Particle Data Group values for the running coupling and strange quark mass, while the dark matter component is modeled as a self-interacting Bose–Einstein condensate. By considering different dark matter masses and varying the pairing gap Δ and the central dark matter pressure fraction <italic>f<inf>r</inf></italic>, we analyze the impact of dark matter on the structural properties of SQSs, including the maximum gravitational mass <italic>M</italic> <inf>TOV</inf>, the ratio of dark matter to strange-quark-matter radii <italic>R</italic> <inf>DM</inf>/ <italic>R</italic> <inf>SQM</inf>, and the dimensionless tidal deformability &#923;. We further examine the compatibility of the resulting mass&#8211;radius relations with the recent NICER measurements of compact stars. Within the parameter space considered in this study, we find that <italic>M</italic> <inf>TOV</inf> exhibits a non-monotonic dependence on the dark matter mass, with a critical value beyond which <italic>M</italic> <inf>TOV</inf> decreases. We also show that some pure CFL strange quark star configurations, particularly those associated with very stiff EOSs and larger maximum masses, may not simultaneously remain compatible with the &#923; range inferred from GW170817 while occupying the lower mass&#8211;gap region. In contrast, the inclusion of dark matter allows two-fluid CFL strange quark star configurations to reproduce the observed properties of massive compact objects in the lower mass&#8211;gap region, such as the secondary component of GW190814, while remaining qualitatively compatible with the &#923; range inferred from GW170817. We note, however, that the GW170817 constraints were originally inferred within single-fluid compact-star frameworks and therefore provide only qualitative guidance for the present two-fluid halo configurations. Our results suggest that exotic compact-star configurations may populate part of the conventionally defined lower mass&#8211;gap region.

Iran

J. Sedaghat

G.H. Bordbar

M. Haghighat

S.M. Zebarjad

Two–fluid CFL strange quark stars with scalar dark matter: Critical mass and mass–gap implications

We establish a new PBW basis for <math altimg='si1.svg'><msub><mi mathvariant='script'>A</mi><mi>q</mi></msub></math>, the alternating central extension of the <italic>q</italic>-Onsager algebra. Terwilliger showed that the alternating generators form a PBW basis in the block order <math altimg='si2.svg'><mrow><mi mathvariant='script'>G</mi><mo linebreak='goodbreak'>&lt;</mo><msup><mi mathvariant='script'>W</mi><mo>&#8722;</mo></msup><mo linebreak='goodbreak'>&lt;</mo><msup><mi mathvariant='script'>W</mi><mo>+</mo></msup><mo linebreak='goodbreak'>&lt;</mo><mover accent='true'><mrow><mi mathvariant='script'>G</mi></mrow><mo stretchy='true'>&#732;</mo></mover></mrow></math>. We prove that they also form a PBW basis in the different block order <math altimg='si3.svg'><mrow><msup><mi mathvariant='script'>W</mi><mo>&#8722;</mo></msup><mo linebreak='goodbreak'>&lt;</mo><mi mathvariant='script'>G</mi><mo linebreak='goodbreak'>&lt;</mo><mover accent='true'><mrow><mi mathvariant='script'>G</mi></mrow><mo stretchy='true'>&#732;</mo></mover><mo linebreak='goodbreak'>&lt;</mo><msup><mi mathvariant='script'>W</mi><mo>+</mo></msup></mrow></math>. Consequently, multiplication induces a vector-space isomorphism <display><formula id='ueq0001'><math altimg='si4.svg'><mrow><msup><mi mathvariant='script'>W</mi><mo>&#8722;</mo></msup><mi>&#8855;</mi><mi mathvariant='script'>G</mi><mi>&#8855;</mi><mover accent='true'><mrow><mi mathvariant='script'>G</mi></mrow><mo stretchy='true'>&#732;</mo></mover><mi>&#8855;</mi><msup><mi mathvariant='script'>W</mi><mo>+</mo></msup><mo>&#10230;</mo><msub><mi mathvariant='script'>A</mi><mi>q</mi></msub><mo>,</mo></mrow></math></formula></display>thereby confirming a conjecture of Terwilliger.

Singapore

Haoran Zhu

A new PBW basis for the alternating central extension of the <italic>q</italic>-Onsager algebra

In this work, two analytical solutions are proposed to characterize compact star configurations containing an effective negative-pressure fluid in the <italic>f</italic>( <italic>R, T</italic>) gravity paradigm that admit spherically symmetric geometry. We derive a system of modified field equations by taking into account a static interior spacetime, which consists of both negative-pressure fluid and ordinary matter sources. In order to investigate the interactions between the fluid components, we solve the field equations using two different equations of state. As the gravitational equations still contain more unknowns, we further use the Finch-Skea and Tolman IV spacetimes which lead us to two distinct models. The junction conditions are also applied to compute the constants associated with these solutions. Afterwards, our developed models&#8217; feasibility is explored by contrasting them with the observed characteristics of two particular stars, SAX J1808.4&#8211;3658 and Her X-1. Under certain parametric values, our results demonstrate that both the developed fluid configurations are physically realistic in this minimally coupled gravity framework.

Pakistan

M. Sharif

Tayyab Naseer

Aqsa Bashir

Examining the behavior of exotic compact stars within the <italic>f</italic>( <italic>R, T</italic>) gravity under Finch-Skea and Tolman IV spacetimes

Homogeneous and isotropic equilibrium states of strongly coupled <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills charged plasma in <math altimg='si3.svg'><msup><mrow><mi mathvariant='double-struck'>R</mi></mrow><mn>3</mn></msup></math> with equal chemical potentials for the maximal Abelian subgroup of the <italic>R</italic>-symmetry group become dynamically unstable below some critical temperature. The instabilities arise in the <italic>R</italic>-symmetry charge transport, precisely when the equilibrium state becomes thermodynamically unstable. We study the fate these correlated instabilities when the theory is placed on <italic>S</italic> 3. The curvature of the three-sphere affects the onset of the dynamical and the thermodynamic instabilities differently: increasing the curvature at low temperatures can stabilize its transport, but leave the plasma thermodynamically unstable. Thermodynamic stability is never recovered provided the <italic>S</italic> 3 volume is allowed to fluctuate. <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> SYM is always thermodynamically unstable in the fixed-pressure ensemble on <italic>S</italic> 3 as well.

Canada

Alex Buchel

Instability in <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills theory on <italic>S</italic> 3 at finite density