Modern Physics Letters A

In this paper, we deal with spacetimes allowing a semi-symmetric connection whose metric tensor is recurrent. We investigate the impact of this connection on spacetimes and establish a nontrivial example. We physically explain the properties of spacetime that we obtained. Under a certain condition, we demostrate that a spacetime admitting such a connection becomes the GRW spacetime as well as the anti-de Sitter and represents the dark matter era. Finally, we scrutinize in case such a spacetime admits a Ricci soliton and generalized Ricci soliton.

This paper is related to the dynamics of stellar structure under the influence of modified gravity (in particular $f(T)$ gravity, where T is associated with a torsion scalar). We contemplate non-static plane geometry equipped with fluid dissipation in the form of diffusion limit. The suitable variables to handle the analysis are explored. To comprehend the dynamics of the system, we acquire the dynamical equations with the aid of Bianchi identities. We calculate the Taub mass for our structure and develop the relations of mass in the form of collapsing velocity, derivative of proper radial, and time. The scalars to comprehend the evolution and structure are explored for non-static plane geometry. These scalars have a novel existence for this structure. We find that the homogeneous expansion and homologous ways of evolution interrelate with each other. We perform the investigation for two cases that is dissipative and non-dissipative. The nature of the fluid in the dissipative case is shear and geodesic. We calculate the variety of solutions in this case. The analysis is concluded by analyzing the stability of the vanishing $Y_{\mathrm{\text{TF}}}$ constraint.

Modeling the worldsheets along the trajectory (a string) of a point particle (a 0-brane) as two timelike surfaces in 3-subspace of Minkowskian spacetime, respectively, the work aims at analyzing the topological structures of these two worldsheets along the trajectory of the point particle from the view point of singularity theory. Different from the regular curves, the traveling trajectory (modeled as framed timelike curve) of the particle is allowed to be singular, two worldsheets are generated by the traveling trajectories of the particle. As applications of singularity theory, we classify the singularities of these two worldsheets along the traveling trajectory of the particle. Using the approach of the unfolding theory in singularity theory, we find two new geometric invariants which are useful for characterizing the local topological structures of singularities of these two worldsheets along the particle. It is revealed that there exist cuspidal edge type and swallowtail type of singularities for these two worldsheets under the appropriate conditions of geometric invariants. Meanwhile, it is also pointed out that the types of singularities of these two worldsheets have a close relationships to the order of contacts between these two worldsheets and two timelike planes, respectively. Finally, some examples are presented to interpret our theoretical results.

In this paper, we investigate the non-relativistic limit of the Dirac equation for relativistic spin-1/2 particles within the framework of the conformable fractional derivative (CFD) using the Foldy–Wouthuysen (FW) transformation. This approach leads to the derivation of a conformable fractional Schrödinger–Pauli equation. We propose and employ a conformable fractional version of the FW transformation, thoroughly examining its efficacy and behavior in the non-relativistic limit. Additionally, based on perturbation theory, we compute the energy shifts within the context of CFD and derive a conformable fractional fine structure of the hydrogen spectrum.

In this paper, within the three-dimensional non-relativistic non-commutative phase–space (3D-NR(NCPS)) symmetries, we examined the 3D deformed Schrödinger equation (3D-DSE) using the improved Coshine Yukawa potential (ICYP) model composed from Coshine Yukawa potential (CYP) ($-4d_e\frac{a}{r}exp(-\alpha r)cosh(\alpha r)$) and other terms produced from the effect of phase–space deformation ($\frac{a{d}_e}{r^3}L.\mathrm{\Theta }+2d_{e}a\alpha \frac{exp(-2\alpha r)}{r^2}L.\mathrm{\Theta }$ and $d_{e}a\frac{exp(-2\alpha r)}{r^3}L.\mathrm{\Theta }$). For this study, the 3D-DSE in the 3D-NR(NCPS) symmetry is solved and discussed with standard independent time perturbation theory and the generalized Bopp’s shifts method. For the homogeneous (H₂ and N₂) and heterogeneous (LiH, ScH, and HCL) diatomic molecules, it is obtained that the improved non-relativistic energy equation and eigenfunction for the ICYP in the presence of deformation phase–space are dependent on the discrete atomic quantum numbers ($j,l,s$,m), the dissociation energy $d_e$, the equilibrium bond length the screening parameter $r_e$, the deformation phase parameters ($\eta ,\overline{\chi },\overline{\zeta }$) and the deformation space parameters ($\mathrm{\Phi },\chi ,\zeta$). Additionally, the thermal properties of the CYP and ICYP with 3D Schrödinger equation (3D-SE) and 3D-DSE are thoroughly examined in the three-dimensional non-relativistic quantum mechanics (3D-NR(QM)) known in the literature symmetry and 3D-NR(NCPS) symmetries, including the partition function, mean energy, free energy, specific heat, and entropy. Furthermore, we discussed particular cases of thermodynamic characteristics for the ICYP model. In our study, we have shown that all the physical values related to energy and thermodynamic properties within the framework of the 3D(NR)NCPS symmetry are equal to the corresponding values within the framework of 3D-NR(QM) symmetry known in the literature, in addition to minor effects resulting from their interaction with the topological properties of the deformed phase–space. This study has multiple applications in various domains, including atomic and molecular physics.

In this study, we present a novel extension to the Klinkhamer vacuum-defect model by incorporating a fifth spatial dimension. This modification results in the formulation of a comprehensive five-dimensional wormhole space-time. Crucially, this extension preserves its classification as a vacuum solution to the field equations, thereby automatically satisfying all energy conditions. We demonstrate that this five-dimensional vacuum-defect space-time can be expressed in a pure canonical form, and thus, locally reduces to five-dimensional Minkowski space. Finally, we explore the geodesic equations in the vicinity of this five-dimensional vacuum-defect wormhole, offering insights into its intriguing properties.

In this paper, we study the dissipative dynamics of interferometric power as a discord-like measure in Markovian environments such as dephasing, depolarizing, and generalized amplitude damping. Moreover, we compare the dynamics of interferometric power and entanglement by choosing the proper initial conditions. Our study shows that interferometric power decays asymptotically in all cases where the sudden death of entanglement appears. Therefore, quantum metrology based on interferometric power is more robust than entanglement.

This study aims to examine the phenomenological consequences of the constant-roll condition on the $f(R,\varphi ,X)$ gravity in the context of a non-canonical scalar field. In this regard, two periods of inflation are investigated, specifically the slow-roll and quintessence phases, within the context of the non-canonical scalar field. We will make two assumptions: first, the slow-roll condition is imposed on the first slow-roll parameters, and second, the scalar field evolves according to the constant-roll condition. We provide a comprehensive explanation of the gravitational equations of motion that govern the behavior of the cosmological system. We consider the constant-roll condition and use a specifically chosen potential to simplify analytical calculations. By doing so, we express the slow-roll indices and the resulting observational indices of the theory as functions of the e-foldings number. Our analysis demonstrates that the existence of constant-roll inflation with non-canonical scalar fields aligns with observed results across a wide range of model parameters. Furthermore, we establish an equation that combines the fundamental equations of the theory. By using a differential operator, we convert this equation into a linear form, yielding the effective equation of state (EoS) parameter. The value of this parameter is dependent upon the exponential $\alpha$ parameter of the kinetic term, as well as to the first slow-roll parameter and the constant-roll parameter $\sigma$. Under the assumption of a fixed $\sigma$ field, we demonstrate that the early universe has the ability to experience a two-stage inflation, as described by the EoS parameter.

In this paper, we study the quantum-corrected Schwarzschild AdS black hole surrounded by quintessence matter in two folds: its thermal quantities and shadows. For this purpose, first, we present a detailed analysis of the influences of the quintessence matter field on Hawking temperature, mass, Gibbs free energy, and specific heat functions. Then, we examine the shadows by following Carter’s approach. We find that the shadow radius value takes smaller values for greater quintessence state parameter values. On the other hand, we see that the shadow radius takes greater values for greater values of the normalization parameter. Finally, in a brief section, we discuss the energy emission rate and show that the Gaussian-type plots’ peak values are also affected by the quintessence matter field parameters.

Our main objective is to explore the shape and geometry of the limiting curves of the structures that define the escape properties of a particle from a lobular domain in a multiwell potential. For this purpose, we examine the lower umbilical catastrophe $D_5$, for $\alpha =1$, by calculating the Lyapunov orbit at the entrance of the lobular region as well as the set of incoming asymptotic trajectories to it and the set of successive intersections of this set with a proper surface of section.