This study introduces a novel investigation into the entanglement dynamics of two-proton decay in 6Be and 12O, using a three-body model to explore quantum correlations in nuclear systems. For 6Be, we measure entanglement using the von Neumann entropy and observe a decline from 0.70 to 0.35–0.40 within 1 ps due to decoherence driven by spatial separation, proton-proton interactions, and core dynamics. In the heavier 12O, the CHSH indicator reveals strong quantum correlations, reaching 2.282 close to the Tsirelson bound (2√(2)≈ 2.828) , but limited by model simplifications and environmental effects. Through time-dependent simulations with realistic nuclear potentials, we uncover the critical roles of proton-proton interactions and core structure in sustaining entanglement. These findings not only advance our understanding of quantum phenomena in nuclear decay but also address a key gap in connecting nuclear physics with quantum information science, paving the way for future experimental exploration of entanglement in proton-rich nuclei using coincidence measurements.
Spinels possess excellent properties for use in advanced applications. Here in this study, using density functional theory (DFT) calculations, we have studied the structural, electronic and optical properties (dielectric function, electron energy loss, extinction coefficient, reflectivity and refractive index, absorption coefficient, optical conductivity) of spinel compounds of the form MgA2X4 (A = Sc/Y; X = S, Se) under the effect of applied pressure. Interesting physical variations were observed in these materials under the application of pressure. The generalised gradient approximation (GGA) method was performed to figure out structure optimisation. By adopting the modified Becke–Johnson (mBJ) exact exchange technique, electronic and optical properties were computed. The energy band gap is shrunken from 2.9 to 1.6 eV and 0.736 to 0.084 eV for MgA2X4 (A = Sc/Y; X = S, Se) compounds under the effect of pressure. A noticeable variation was seen in the lattice parameters, band gap, electronic and optical properties via exceeding the pressure from 0 to 20 GPa, featuring a prominent absorption coefficient and higher optical conductivity in the visible and UV region, showing greater potential for their use in high-frequency devices. The compounds have the appropriate band gaps for water splitting through redox reactions.
In this article, the mixed convection (natural and forced) heat transfer of non-Newtonian nanofluid ( Fe_3O_4 -water) steady-state, 2D flow, laminar, with the influence of a magnetic field in a baffled, U-shaped lid-driven cavity has been analyzed. The problem is modeled mathematically, and the resulting nonlinear partial differential equations are solved numerically using FEM. The cavity is heated by the baffles and cooled by the vertical walls (moving walls), while the other walls are adiabatic. Where Prandtl number (Pr=6) and Grashof number ( Gr=10000 ) are assumed to be fixed. While the Richardson number is taken in the range of 0.01
This work investigates the invariant subspace method for time-fractional nonlinear evolution equations of second order with x-dependent coefficients. The study focuses on identifying invariant subspaces admitted by these equations and provides a systematic framework for constructing explicit solutions. Applying this method, explicit solutions are found for the nonlinear reaction-diffusion-advection equation, the coupled Burgers equation, the coupled advection–diffusion equation, and many other scalar and coupled nonlinear partial differential equations with x-dependent coefficients and a time-fractional derivative. In particular, x-dependent coefficients involving polynomial functions are considered, and a classification of the time-fractional nonlinear partial differential equations is obtained based on the invariant subspaces admitted by them. The investigation demonstrates that the invariant subspace method is a powerful tool for obtaining exact solutions of time-fractional partial differential equations with variable coefficients, thereby revealing novel solution structures.
According to Ref. [11], in bipartite qubit systems, a matrix A exists such that Det A = 0 indicates unentanglement, whereas Det A 0 indicates entanglement, and there exists an underlying SU(2) algebra. Here, we show that this algebra does not imply any internal degrees of freedom. Physical interpretation of the underlying algebras is given for the SU(2) case in the context of two entangled electrons. We also show that under a certain redefinition of matrices, the Clifford algebra satisfied by the usual 4-dimensional Dirac matrices is obtained. This redefinition is related to time reversal. In Ref. [11] it was shown that for qutrits there is a matrix P for which Det P =0 simultaneously with Tr P = ± 1 implies unentanglement. Any departure from these conditions implies entanglement, and there exists an underlying SU(3) algebra. The new results in this work are analytical solutions for the eigenvalues of the reduced density matrix corresponding to arbitrary bipartite qutrit states. The SU(3) algebra is obtained after a redefinition of variables. Here, we also obtain the entanglement entropy for both qubits and qutrits. For qubits, the entropy is in terms of Det A . For qutrits the entropy is expressed in terms of Det P and Tr P .
This study investigates the dynamical behavior of lump-type solutions in an extended ( 2+1 )-dimensional Kadomtsev–Petviashvili (KP) model. The analysis begins with the derivation of the bilinear form of the model using the Cole–Hopf transformation. By employing a suite of ansatz methods, diverse solution structures are derived, including lump-rogue wave interactions, periodic waveforms, kink and multi-kink solutions, and lump-breather molecular states. The influence of key parameters on these structures is systematically examined. Numerical visualizations of 3D, contour, and line plots illustrate the effect of parameter variations on wave dynamics. These results are of great interest across several applied areas, including oceanography, plasma dynamics, and nonlinear optics.
This paper investigates a three-component lattice equation that generalizes classical nonlinear lattice systems such as the Volterra and Toda lattice equations. This equation integrates features of discrete structure and multi-component coupling and has wide-ranging applications in condensed matter physics, plasma physics, biological modeling, and engineering sciences. By imposing a continuous limit, we establish its correspondence with several continuous nonlinear equations. Subsequently, an infinite set of conservation laws is constructed from the Lax pair, revealing the underlying integrability of this system. Furthermore, starting from constant amplitude waves, we analyze the conditions for modulational instability (MI) and examine the parameter dependence of perturbation growth. Based on the associated linear spectral problem, the generalized ( n, N-n )-fold Darboux transformation (DT) is constructed. Applying this transformation yields rational solutions and mixed solutions on a non-zero seed background, and asymptotic analysis is performed to elucidate the dynamical behavior of rational solutions. These results contribute to a deeper understanding of nonlinear wave dynamics in multi-component lattice systems.
The main emphasis of this study is to explore the relevance of invisible neutrino decay within the frameworks of both the Deep Underground Neutrino Experiment (DUNE) and the NuMI off-axis ν _e appearance (NO ν A) experiments. Under the normal mass hierarchy, we suppose that ν _3 is unstable and will eventually decay into a sterile state. In this work, we have studied the potential of these combinations to constrain the decay parameter. We have observed that the true value of θ _23 can significantly affect the constraint on the decay parameter. A true value of θ _23 in the HO can significantly improve the constraint. At the HO, for τ _3/m_3=2× 10^-11 s/eV, DUNE and the combination of DUNE and NO ν A can rule out the no decay scenario at 3 σ CL. For the given τ _3/m_3 , DUNE and the combination can measure τ _3/m_3 at 3 σ , in the range [ 7.22× 10^-11>τ _3/m_3> 1.16× 10^-11 ] s/eV and [ 6.10× 10^-11>τ _3/m_3>1.19× 10^-11 ] s/eV, respectively. This precision measurement of τ _3/m_3 improves significantly for the value of θ _23 in the HO compared to the lower octant (LO). Our analysis also yields measurements of CP sensitivity for DUNE, NO ν A, and DUNE+NO ν A in the context of invisible neutrino decay. In this work, we consider three values of the decay parameter to illustrate the analysis.
Controlled remote implementation of an operator (CRIO) is a global quantum protocol for executing an unknown unitary operator on a distant, unknown quantum state under the control of a remote controller, using a quantum resource shared in advance between the implementers and the controller. One implementer (Alice) has a photon in an unknown state to everyone. The other implementer (Bob) has a general unitary operator that he can execute, but no one else can. The controller (Charlie) does not need to know the explicit forms of both Alice’s state and Bob’s operator, but reserves the right to decide when the CRIO completes, i.e., when the remote implementation of Bob’s operator on Alice’s state is complete. Such protocols are fundamentally needed for controllable, scalable quantum distributed computing and cloud-based applications across remote nodes within a quantum network. In this paper, we extend our work (An and Bich, J. Phys. A: Math. Theor. 55, 225307 (2022)), in which a maximally hyperentangled state was used as the quantum resource, to the case of non-maximal hyperentanglement. The parameters identifying the non-maximally hyperentangled state of the quantum resource are deliberately configured to be known exclusively to the controller, ensuring a high level of security. We show that, although the shared hyperentangled state is non-maximal, the controller can still effectively govern the CRIO protocol, achieving unit fidelity at the expense of a finite success probability. This success probability is proportional to the degree of entanglement of the quantum resource, which can be flexibly tuned by appropriate channel engineering. Furthermore, we derive the average fidelity of classical remote implementation of the operator and calculate the average non-conditioned fidelity of the quantum CRIO without the controller’s participation. Then we evaluate the relevance of the quantum protocol in terms of the so-called quantumness power and the controller’s power.
The generalised Vaidya spacetime has several important applications in gravity. We study the embedding of an N-dimensional generalised Vaidya spacetime into an (N+1) -dimensional pseudo-Euclidean spacetime. The Gauss–Codazzi–Ricci equations reduce to a single condition, a Riccati equation, containing components of the Riemann tensor that can be solved in general in terms of elementary functions. The generalised mass function is found, representing the gravitational potential, which has a unique representation in terms of elementary functions. Our results have important geometrical and dynamical consequences. This mass function does not allow for the existence of a strong curvature singularity. The embedding in the Vaidya geometry generates a model of a radiating star with concentric layers.
This study investigates the fractional-order Benjamin–Ono equation by constructing a comprehensive set of analytical solutions based on Jacobi elliptic functions. Utilizing a wave transformation approach, eleven distinct exact solutions are derived, each corresponding to a different Jacobi elliptic function, including ‘sn’, ‘cn’, ‘dn’, ‘sc’, ‘sd’, and others. The resulting solutions are not only presented analytically but also examined through detailed graphical representations and physical interpretations. These analyses reveal the underlying dynamics of periodic, solitary, and blow-up type wave structures governed by fractional nonlocality. The diversity of wave profiles obtained highlights the flexibility and strength of the Jacobi elliptic framework in modeling complex, memory-driven behaviors in nonlinear fractional systems. This work provides a systematic and physically meaningful classification of solution types, contributing to the theoretical understanding of fractional wave phenomena and offering potential for future applications in dispersive and nonlocal media.
Conical disk systems play a crucial role in biomedical engineering, rheometer, viscometry, and advanced thermal devices due to their ability to regulate flow and transport processes. In this study, we investigate the nonlinear behavior of tangent hyperbolic nanofluid flow across an inclined conical disk configuration, which uniquely combines a stretchable disk with a rotatable cone under the influence of magnetohydrodynamic (MHD) effects. By employing similarity transformations, the governing nonlinear partial differential equations are reduced to a system of dimensionless ordinary differential equations, which are then solved numerically using MATLAB’s boundary value solver bvp5c. To further improve computational efficiency and predictive capability, a feed-forward backpropagation neural network is trained on the numerical results for heat and mass transfer rates. The results demonstrate that increasing the disk inclination angle intensifies radial flow, while simultaneously reducing thermal and solutal transfer rates by 34.47
This work provides an exact analytical solution for a particle with position-dependent mass in a generalized Morse-type potential. Using a Hulthén-type mass distribution and the von Roos symmetrization scheme, the model captures both molecular short-range effects and operator-ordering ambiguities. The problem is elegantly solved using supersymmetric quantum mechanics (SUSYQM), yielding closed-form energy spectra and bound-state wavefunctions expressed in terms of hypergeometric functions and Jacobi polynomials. The role of ambiguity parameters is clarified, with precise conditions ensuring the existence of bound states and the preservation of supersymmetry. Beyond its theoretical rigor, the framework offers a versatile tool for studying realistic systems such as heterostructures and molecules, and can be extended to other mass distributions and potentials.
We study the shell closure, alpha-decay and cluster-decay ( ^8 Be, ^12 C, ^14 C, ^16 O) of even-even ^238–338Hs_108 isotopes using relativistic mean field (RMF) model within an axially deformed oscillator basis with two force parameter sets like NL3* and NL-SH. In this article, the bulk properties such as binding energy (BE), rms charge radius, quadrupole deformation, neutron skin thickness, three neutron pairing gap for charge radius, two neutron separation energies ( S_2n ), differential variation of two neutron separation energy ( dS_2n ) and neutron pairing gap using three-, four- and five-point formulae have also been investigated thoroughly for the above mentioned isotopic series. Half-life periods are determined using the Viola-Seaberg, Royer, MUDL, UDL-1, UDL-2, Santosh et al. and unified formula by Ni et al. using calculated and experimentally accessible Q-values. For the prediction of the favorable decay mode of the isotopic series, the spontaneous fission half-life is also calculated by using two different formulas that are independent of force parameters. All the outcomes are compared with available experimental data. We found ^270 Hs is a comparably stable isotope of Hs with other possible shell closures at N =138 , 142, 154, 162, 166, 182, 184, 186, 210, 220, 222. This study helps us to understand the shell and subshell closures of even-even Hassium isotopes and their preferred decay modes.
The interaction of nonlinear waves in an inhomogeneous medium generally leads to temporal evolution in velocity, shape, or amplitude. Therefore, the study of solitary waves is prominent for re-emerging feature to its permanent structure after interaction. This work addresses the propagation dynamics of solitary waves for the NNV equation. It is a highly nonlinear two dimensional isotropic Lax integrable generalization of the well-known KdV equation. The symmetry reductions under infinitesimals and the generalized exact solutions of the NNV equation have been well investigated using the Lie symmetry method. The infinitesimals under a one-parameter group of transformations preserve invariance of the test equation and yield symmetry reductions. The twice implementation of symmetry reductions results in a system of ODEs. This system of ODEs is integrated under parametric constraints and provides exact solutions. These solutions are entirely new and more general than previously reported results, owing to arbitrary functions f_1(t) , f_2(t) , and f_3(t) , as well as several constants. The generalness of derived results are ensured with deductions of previous results [8, 10–12]. To understand the propagation properties of wave phenomena, these solutions are extended to include a graphical representation, which reveals a novel class of solitons and lump solutions. Moreover, adjoint equations and conserved vectors are derived under the Lagrangian formulation using Ibragimov’s method for each generator.
The Estevez–Mansfield–Clarkson (EMC) equation is a model equation that can be used to study and explain shallow water waves in fluid dynamics. This paper analyzes the Estevez–Mansfield–Clarkson equation, discusses its analytical solutions (including soliton solutions and lump solutions), and uses the Physics-Informed Neural Network (PINN) and the proposed Extension Physics-Informed Graph Neural Network (EGPINN) to learn the solved soliton solutions, respectively, with a comparison of the prediction results. Firstly, the multi-soliton solutions of the equation, including one-soliton, two-soliton, and three-soliton structures, are successfully derived using the Hirota bilinear method. The formation mechanism and propagation characteristics of the soliton solutions are analyzed in detail, and the laws governing the interaction between solitons are revealed. Then, the lump solutions of the equation are obtained using the positive quadratic function method, with in-depth analysis of the morphological evolution laws of the lump solutions under multivariate conditions and their physical connotations. Finally, PINN and EGPINN are used to learn the soliton solutions derived by the Hirota bilinear method. The research conclusions deepen the theoretical understanding of the solution space characteristics of the Estevez–Mansfield–Clarkson equation, provide a theoretical basis for understanding nonlinear phenomena such as the propagation, interaction, and waveform evolution of shallow water waves, and show application prospects in cutting-edge fields such as plasma physical processes, fluid turbulence mechanisms, and nonlinear optical effects.
This study investigates the Higgs-strahlung process e^+e^- → Z'H in the context of the SU(3)_C ⊗ SU(3)_L ⊗ U(1)_X (3-3-1) model with the extended electroweak sector, focusing on the role of the extra neutral gauge boson Z' . The total scattering cross-section is determined at tree level and its dependence on critical model parameters, such as the Z' boson mass and the Mandelstam variables. Compared to the standard model process e^+e^- → ZH , the extended gauge structure of the 3-3-1 model introduces modified couplings that can enhance production rates and lead to detectable deviations at high-energy colliders. The results of this study highlight the scope of the Higgs-strahlung process as a feasible channel for confirming the existence of new gauge bosons and exploring the symmetry-breaking patterns inherent to the 3-3-1 model.
The thermodynamics and magnetic properties of a one-dimensional Ising model defined by a Cantor set are examined in this article. Under various boundary conditions and with finite system sizes, we examine these properties. In our study, we analyze the free and internal energy, heat capacity, and entropy of the model using both deterministic and random metrics. We discover that the Bernoulli trial for forward and backward spins, the boundary conditions, and the system’s finite size affect the model’s properties.
A linear dust acoustic wave has been studied in an inhomogeneous dusty plasma, taking into account the presence of nonthermal ions. The hydrodynamic model is considered to study the wave dynamics. Due to density inhomogeneities, a variable-coefficient second-order ordinary differential equation is derived. Theoretical and numerical results discover the formation of amplifying linear waves due to gradient instability. Due to the presence of Cairns-distributed nonthermal ions, a modification to the theoretical result obtained using the WKB approximation has been observed for the linear dust acoustic wave in a multisized inhomogeneous dusty plasma. The effect of nonthermal ions on wave propagation in the region has been investigated. The numerical solution of the variable coefficient evolution equation is in good agreement with the analytical results obtained by the WKB approximation, especially in the presence of a smaller number of nonthermal (fast) ions in a slowly varying medium. The effect of the ions-to-electrons temperature ratio on the wavelength of the linear dust acoustic wave is also observed.
