This study extends the Feshbach-Villars (FV) formalism to encompass spin-1/2 particles propagating in curved spacetime. Starting from the covariant Dirac equation, we derive its Hamiltonian form using a tetrad (vierbein) formulation and implement a diagonal FV transformation on the associated second-order (squared) equation.The resulting Schrödinger-type evolution equation is expressed in both block-matrix and Pauli-matrix representations, explicitly displaying gravitational and electromagnetic couplings, alongside spin-field interaction terms. We analyze this formalism in (1 + 2)-and (1 + 3)-dimensional settings and apply it to cosmic-string backgrounds (static and spinning, with and without oscillator couplings) to determine the corresponding energy spectra and exact wave functions. Although the FV reformulation is algebraically equivalent to the covariant Dirac dynamics-subject to the standard restriction that eliminates spurious solutions introduced by squaring-it offers a highly practical complementary perspective. Specifically: (i) the particle and antiparticle sectors are distinctly represented by two coupled components equipped with a simple (pseudo-)unitary inner product tied to the conserved charge; (ii) the physical distinction between stationary and static spacetimes is directly encoded in the FV operator Y, which is governed by the ADM shift vector, thus clearly diagnosing how frame-dragging modifies particle-antiparticle mixing; and (iii) the FV block structure provides a streamlined approach for solving spectral problems in topologically nontrivial geometries.
Double-well potentials are important potential models that underlie the study of macroscopic quantum tunneling in Bose-Einstein Condensates (BECs), which are most commonly constructed in the form of a combination of a finite square-well potential and a square potential barrier. We propose another possibility of constructing a double-well potential, which consists of the combination of a square-well potential and a movable Gaussian-type potential barrier, and by adjusting the width, height, symmetry, and position of the movable potential barrier, symmetric and asymmetric double-well potentials with rich structures can be constructed. By numerically solving the Gross-Pitaevskii equation (GPE), we give the ground state structures of the BEC in this double-well potential, and then study the tunneling dynamics in the BEC in this double-well potential. The results show that the parameters of the movable potential can control the ground state structure and tunneling dynamics of the BEC system very precisely, and the ground state structure and tunneling dynamics are more sensitive to the asymmetric Gaussian-type potential barrier.
In this study, we use the Mei symmetry technique to produce conserved quantities for a system of coupled Lane–Emden–Klein–Gordon–Fock equations with central symmetry. Compared with earlier results by Muatjetjeja (2017) (J. Differential Equations, 263 (2017) 8322–8328), we have discovered new types of conserved quantities using the Mei symmetry method. The system under consideration possesses a two-dimensional maximal Noether algebra and a three-dimensional maximal Lie algebra. We have shown that the maximal Mei algebra is four-dimensional, that is, the system admits more Mei symmetries than the classical Lie and Noether symmetry generators. Furthermore, we have used Mei symmetry reduction to produce several exact solutions for the corresponding system. The novel symmetries and conserved quantities that are derived here can be used to gain a deeper understanding of the physical interpretation of the system taken into account.
The Unified Standard Model with Emergent Gravity (USMEG-EFT) framework achieves Standard Model-gravity unification by treating 4D general relativity as an effective field theory (EFT). This work presents a comparative analysis of Einstein–Cartan (EC) theory and the USMEG-EFT against experimental constraints and theoretical consistency requirements, distinguishing minimal EC with algebraically determined torsion from variants in which the spin connection is an independent quantum field. The latter class includes the Faddeev–Popov quantization framework of Brandt, Frenkel, Martins-Filho, and McKeon, adopted in their unification proposal, and for which gravitational wave polarization measurements directly test the additional propagating degrees of freedom. General relativity’s spin-2 graviton produces exactly two tensor polarizations, while EC theory with independent dynamical spin connection predicts up to six modes. LIGO–Virgo–KAGRA null tests for GW170817 favor pure tensor over pure vector and pure scalar hypotheses at Bayes factors exceeding 1020:1, improved to approximately 1026:1 with a gamma-ray-burst jet-orientation prior. Complementary matter-sector constraints from the Standard Model Extension yield |b̃⊥n|<8.4×10−34 GeV, constraining background-torsion scenarios, while MICROSCOPE bounds equivalence principle violation at η < 1.5 × 10−15. For minimal EC theory, the four-fermion contact interaction generated upon coupling to fermions introduces nonrenormalizable divergence structures at two-loop order, a case not addressed by the Becchi–Rouet–Stora–Tyutin (BRST) framework established for the independent spin connection. We situate EC theory within the broader landscape of gauge gravity theories and acknowledge USMEG-EFT’s limitations, including sub-Planckian validity and currently untestable distinctive predictions. Taken together, these results render EC theory disfavored relative to USMEG-EFT as a unification framework, with distinct arguments applying to each variant: geometric extensions introducing independent torsion are neither required nor experimentally favored within currently testable parameter space.
This study investigates the onset of convective instabilities in a porous medium inhabited by gravitactic microorganisms, incorporating the effects of rotation and local thermal nonequilibrium. This system is confined between two horizontal parallel surfaces, heated from below. Microorganism behavior is modeled using Pedley’s framework, while fluid motion through the porous structure is described using the Darcy–Brinkman model. Density variations are incorporated through the Oberbeck–Boussinesq approximation. A linear stability analysis is carried out, yielding a system of ordinary differential equations obtained through normal mode analysis and addressed using the Galerkin method. Both stationary and oscillatory convection modes are examined to capture the full range of dynamic behavior. The results show that rotation and interphase heat transfer stabilize the system by suppressing buoyancy-driven motion, whereas permeability and microorganism motility promote instability by enhancing fluid transport and density variations. Additionally, oscillatory convection becomes significant under strong rotational effects, while boundary conditions play a key role in modulating the onset and nature of instability. Also, numerical results reveal that for free–free, rigid–rigid, and rigid–free boundaries, increasing the interphase heat transfer and rotation rate from 0 to 104 raises the critical Rayleigh–Darcy number by approximately 199%, 199%, 200% and 382%, 143%, 28%, respectively. These findings highlight the strong stabilizing influence of interphase heat transfer and rotation on porous bioconvection, offering valuable insights for optimizing systems such as microbial fuel cells and bio-reactors.
The present analysis investigated the stagnation dynamic of Maxwell fluid over a stretching surface, including the characteristics of variable thermal conductivity, variable viscosity, and induced magnetic field. The flow is examined under both prescribed surface temperature and concentration and prescribed surface heat and mass flux conditions. The study takes into account a system of highly nonlinear partial differential equations governing the behavior of considered flow. The inspection of these equations requires conversion into ordinary differential equations via suitable similarity transformations. These complex equations are solved by applying the bvp4c scheme in MATLAB, and a neural network-based analysis is implemented to enhance the prediction and generalization of key physical quantities. Results for Nusselt number and Sherwood number are analyzed concerning pertinent flow parameters. Profiles of velocity, temperature, and concentration are plotted. The numerical comparisons confirmed excellent agreement with previously published work validating the model. The study reveals that increasing Deborah number leads to a notable reduction in the fluid velocity near the surface. The integrated neural network framework provides additional insight into the nonlinear dynamics of Maxwell fluid flow under an induced magnetic field.
Based on the individual MoSi2N4 and SMoSiN2 monolayers, we design an AA-stacked MoSi2N4/SMoSiN2 heterojunction (AA-HJ) with enhanced stability, confirmed by phonon dispersion analysis. The pristine AA-HJ exhibits a 2.13 eV indirect Type-I bandgap. Under −2% strain, it transforms into a Type-II heterojunction with a widened bandgap of 2.60 eV. An interfacial electrostatic potential difference drives charge transfer from MoSi2N4 to SMoSiN2, establishing an intrinsic built-in electric field. This strain-induced band engineering facilitates efficient charge separation through built-in electric fields, making it a potential water splitting photocatalyst for oxygen evolution reaction in the SMoSiN2 layer and hydrogen evolution reaction in the MoSi2N4 layer. The AA-HJ (−2%) presents a good optical absorption in visible and ultraviolet regions, further confirming its potential as a sunlight-driven photocatalyst for water splitting applications.
The purpose of this study is to investigate the cosmological implications of the recently proposed gravity framework known as f(R, Σ, T). This framework extends modified gravity theories by incorporating the Ricci scalar R, a non-metricity-like scalar Σ, and the trace of the energy–momentum tensor T into the gravitational action. We take into consideration the particular functional form f(R, Σ, T) = R + Σ + 2πηT, where η is a free coupling parameter that determines the degree to which matter and geometry interact with one another. We derive the modified field equations and establish analytic expressions for cosmic energy density and pressure in terms of the Hubble parameter and its derivative. This is done under the assumption that the Friedmann–Robertson–Walker universe is isotropic, homogeneous, and spatially flat. A comparison is made between the cosmological model that was developed and the observational data obtained from the Pantheon + SH0ES Type Ia Supernovae sample as well as the 33 Hubble parameter measurements obtained from the Cosmic Chronometer technology. To constrain the model parameters H0, η, and b, we use a Bayesian statistical framework and run a Markov Chain Monte Carlo analysis with the emcee Python program. Our findings support an accelerating universe and suggest that the f(R, Σ, T) model could be a viable alternative to classic dark energy theories. This is accomplished by providing more complex gravitational dynamics through longer matter–geometry couplings.
Magnesium-based alloys, as the lightest metallic structural materials, have great potential for applications in the aerospace and automotive industries. Among these, Mg–Zn alloys have received considerable attention due to their significant precipitation strengthening effects. Although extensive experimental and theoretical studies have been conducted to investigate the crystal structures and mechanical properties of precipitates in Mg–Zn alloys, there remains considerable debate about the exact stoichiometry and crystal structures of these precipitates. In this study, the thermodynamic stability, crystal structure, mechanical properties, and electronic structure of intermetallic phases in the Mg–Zn binary system are systematically explored using the variable-composition evolutionary algorithm (USPEX) combined with first-principles calculations. Over 1700 possible crystal structures were generated by USPEX, and their formation energies were calculated. Four thermodynamically stable phases (Mg 2 Zn, MgZn, Mg 4 Zn 7 , and MgZn 2 ) and one metastable phase (MgZn 4 ) were found. The addition of Zn can significantly enhance the bulk, shear, and Young's moduli of Mg–Zn intermetallics relative to pure Mg, with MgZn 4 showing the highest shear and Young's moduli. Bader charge and density of states analysis reveal significant charge transfer from Mg to Zn, indicating the ionic bonding and metallic nature in the Mg–Zn system. The results of this study not only confirm the stoichiometries and crystal structures of Mg–Zn intermetallics but also provide theoretical insights into the strengthening mechanisms of Mg–Zn alloys and for the design of new high-performance alloys.
In this paper, we investigate vortex formation in spin–orbit-coupled (SOC) spin-1 dipolar Bose–Einstein condensates. We focus on the differences in time evolution of several physical quantities such as vorticity profiles, integrated vorticity, angular momentum, and compressible and incompressible kinetic energy. Numerical results show that the three components exhibit rich dynamical behaviors, depending on the competition between SOC and dipole–dipole interactions. Additionally, we also compare different rotation frequencies and contact interactions, showing that they play a significant role in these physical quantities.
The study of non-Markovian quantum processes has attracted significant interest in recent decades, giving rise to several competing notions of quantum non-Markovianity. These notes serve as an introduction to the topic for graduate students familiar with quantum mechanics and probability theory. Owing to the vastness of the literature, we focus on two prominent characterizations of quantum Markovianity based on the divisibility of quantum channels and monotonically decreasing state distinguishability. The correspondence between classical concepts (stochastic matrices, Chapman–Kolmogorov equation) and their quantum analogs (dynamical maps, completely positive-divisibility) is emphasized throughout.
Based on the multi-configuration Dirac–Hartree–Fock method, accurate atomic spectra data including the transition rates, line strengths, and oscillator strengths for the inner-shell excitation configuration 2s2p 2 ( 4 P)3d in N II ion are reported by taking into account the core–core, core–valence, and valence correlation effects as well as the Breit interaction. Good accordance can be found in the comparison with other calculations and measurements. Because the highly excited 2s2p 2 ( 4 P)3d configuration in N II is larger than the N III thresholds 2s 2 2p 2 P[Formula: see text] and 2 P[Formula: see text], there exists an autoionization phenomenon. Also, the autoionization rates of 2s2p 2 ( 4 P)3d are much larger than its radiative transition rates. This causes the energy levels of 2s2p 2 ( 4 P)3d configuration, especially for the triple states 3 P, 3 D, and 3 F, to become considerably instable. In addition, there is strong energy level mixing among the 2s2p 2 ( 4 P)3d configuration and the highly excited configurations 2s 2 2p nl ( n = 6; l = p, f, h) with same even parity. These enable the energy levels and their transition rates to become sensitive to core correlation effect and Breit interaction.
The work in hand presents the elastic, elastic anisotropy, and thermoelectric and thermophysical properties and the effect of pressure variation on them for RNi 5 H 6 (R = Sc, Y, or La), in which all calculations have been investigated by using the first-principles method within the full-potential linearized augmented plane wave method implemented in wien2k package. Both the framework of the generalized gradient approximation (GGA96) and the IReLast package implemented in Wien2k have been used to describe the exchange–correlation potential and to determine elastic constants and mechanical properties, respectively. Additionally, the quasi-harmonic Debye model is employed within Gibbs2. The calculated elastic constants and modulus satisfy Born’s mechanical stability criteria, meaning that the three hydrides in this study are mechanically stable. Meanwhile, their mechanical behaviors reveal that these hydrides have a ductile character and are elastically anisotropic, whereas ScNi 5 H 6 is considered highly ductile and relatively low hardness compared to others. In addition, we observed that the changeability of the properties related to the elastic constants increases with pressure, while mechanical stability remains valid. Due to these hydrides’ positive Cauchy pressure, the chemical bonds have metallic characteristics. The substitution led to a decrease in the anisotropy of the mechanical quantities. These hydrides’ bulk modulus and Debye temperatures decrease from ScNi 5 H 6 to LaNi 5 H 6 . As the atomic radius of rare earth atoms decreases, the substitution leads to an increase in both the Debye temperature and bulk modulus. In contrast, this led to a decrease in the volume, specific heat at constant pressure, heat capacity at constant volume, thermal expansion, thermal expansion coefficient, and entropy.
This study presents a comprehensive first-principles (DFT) investigation of the structural, electronic, optical, and thermodynamic properties of the LiSnI 3 perovskite. Structural optimization confirms a stable cubic LiSnI 3 perovskite phase with a lattice constant of 6.22 Å and a bulk modulus of 16.77 GPa, supported by a negative formation energy (−1.35 eV/atom). Electronic structure calculations show that LiSnI 3 is a direct-band-gap semiconductor, with band gaps of 0.33 eV (GGA-PBE) and 0.76 eV (HSE06). The optical properties of LiSnI 3 reveal a strong static dielectric response (ε₁ (0) = 8.08), a high refractive index (n (0) = 2.84), and a pronounced absorption edge at 0.81 eV, demonstrating suitability for infrared and UV optoelectronic applications. Thermodynamic results, combined with ab initio molecular dynamics simulations, confirm that the LiSnI 3 perovskite remains dynamically and thermally stable across broad pressure and temperature ranges. The combined findings highlight LiSnI 3 as a promising lead-free perovskite material for advanced optoelectronic and energy-related applications.
The mass spectrum of the S-wave positronium is considered in the framework of a non-relativistic model. A good agreement is obtained with the experimental masses of the 1S0, singlet state, the para-positronium, and the 3S1 state, the ortho-positronium. The role of one-photon exchange potential (OPEP) and the confinement potential is discussed. The mass difference between ortho- and para-positronium is attributed to the spin-dependent terms of OPEP.
We investigate the thermodynamics of the (2 + 1)-dimensional BTZ black hole in the presence of a nonperturbative exponential correction to the Bekenstein–Hawking entropy. Adopting an effective entropy deformation within a horizon thermodynamics framework, we reconstruct the corresponding corrected metric and derive the modified temperature, heat capacity, and free energies. The correction is exponentially suppressed for large black holes, ensuring recovery of the classical AdS 3 solution, while producing controlled deviations at small horizon radii. We find that exponential corrections generate a nontrivial intermediate thermodynamic regime and alter stability properties relative to the classical BTZ case. Our results provide a simple analytic model for exploring nonperturbative quantum effects in lower-dimensional gravity.
In this work, polymer gel electrolytes based on poly(vinyl alcohol) (PVA) incorporating the KI/I2 redox couple and different surfactants, sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB), and cocamidopropyl betaine (CAPB), were formulated and systematically characterized for application in dye-sensitized solar cells (DSSCs). The main objective was to overcome the intrinsic drawbacks of conventional liquid electrolytes, such as leakage, volatility, and poor mechanical stability. The gels were prepared via physical crosslinking of PVA in aqueous media, with surfactants introduced at concentrations below, at, and above their critical micelle concentration (CMC). Structural, electrochemical, and rheological properties were investigated using Fourier-transform infrared spectroscopy, zeta potential and ionic conductivity measurements, oscillatory rheology, and optical microscopy. The results show that surfactant incorporation strongly affects gel organization and ion transport. SDS increased ionic conductivity up to 5.98 mS/cm at the CMC, while CTAB induced ion trapping at sub-CMC levels and reduced conductivity down to 0.0152 mS/cm. CAPB provided a near-neutral electrostatic environment and achieved a peak conductivity of 9.22 mS/cm above the CMC, along with homogeneous microstructure. These findings demonstrate that surfactant-assisted PVA-based gel electrolytes, particularly SDS-and CAPB-containing systems, are promising candidates for stable, flexible, and efficient quasi-solid-state DSSCs.
Topological defect influence on molecular potential models has been significantly proven to shape the behaviour and interactions of different constituent quantum systems. Based on this fact, we employ the Nikiforov-Uvarov functional analysis method to solve the Schr & ouml;dinger equation with modified Kratzer plus generalized Morse potential, embedded with Aharonov-Bohm flux field and point-like global monopole defect. Rotation-vibrational energies of the combined potential have been presented numerically and graphically for various quantum states, flux field, and topological defect values. Ro-vibrational energies of carbon monoxide have been presented for modified Kratzer potential, as a special consideration. In addition, vibrational energy expression of the combined molecular potential considered is used to obtain some thermodynamic functions using arbitrary values, using Poisson summation formula. Graphical studies of these thermodynamic functions show high dependence on temperature, flux field, and topological defect parameters considered. Conventional results of this study in Minkowski space are realized as the topological defect parameter approaches unity, and their special cases agree with available results in literature. The result in this study also point relatively to some physical phenomena in chemical and molecular physics.
After a brief historical introduction of quantum thermodynamics, we present its main goal and objectives, from fundamental questions to practical applications in quantum technologies. We then introduce the standard thermodynamic framework for quantum systems, valid in the weak coupling limit and in thermal environments. Extensions to strong coupling and nonthermal baths are briefly mentioned. Then, using this standard thermodynamic framework, we describe the quantum version of the Otto cycle and Carnot cycle for heat-to-work conversion as well as for refrigeration. The analysis of their differences is used to introduce the concept of entropy production at the quantum level, which quantifies irreversibility and is responsible for loss of efficiency. Then, we present a simple description of an autonomous quantum refrigerator, a promising device for qubit re-initialisation in quantum technologies. Finally, we briefly mention some quantum effects in heat engines and refrigerators. We conclude with a perspective on the main goals of quantum thermodynamics.
We present a unified encoding approach for the generation and dynamic control of optical Airy beams using phase-only holography. By co-encoding a modified Airy beam Fourier spectrum together with an in situ Fresnel lens phase function into a single phase mask, the proposed method enables compact, lensless beam formation without external Fourier optics. While SLM-based implementations combining cubic and Fresnel phase profiles have been previously reported, the present work refines this strategy through an optimized 8-bit grayscale phase mapping procedure that improves phase accuracy and beam reconstruction quality. In addition to controlled spatial translation and angular steering, the method allows modulation of the beam’s effective acceleration through systematic adjustment of the cubic phase parameters, enabling dynamic reshaping of the parabolic propagation trajectory. Quantitative characterization of diffraction efficiency, beam fidelity, and background suppression confirms the improved optical performance of the proposed phase-only implementation relative to conventional phase–amplitude approaches. This digitally programmable and mechanically stable framework provides a compact and efficient platform for structured light generation and controlled beam shaping, with potential applications in optical manipulation and free-space optical communication.
