International Journal of Modern Physics A

The N-dimensional radial Schrödinger equation has been solved using the Nikiforov Uvarov (NU) method, in which we used the medium modified form of Cornell potential and quasi-particle Debye mass with strong magnetic field background. The binding energies and the mass spectra of heavy quarkonium have been studied in the N-dimensional space for different values of magnetic field, the binding energy decreases with increasing magnetic field, which shows early dissociation of heavy quarkonium system. The influence of dimensionality number has also been discussed on binding energies of $J/\psi$ and $\mathrm{\Upsilon }$ for fixed value of magnetic field. It is found that with an increase in dimensionality, the binding energy starts decreasing from a higher initial value. The results obtained are quite consistent with recent studies.

We show the need of the emergence of an invariant minimum speed in the space–time. So, we propose a deformed special relativity with two limits of speed so-called Symmetrical Special Relativity (SSR). It presents a universal minimum speed V that plays the role of a preferred reference frame $S_V$ associated with vacuum. This new paradigm of space–time allows us to understand the origin of the cosmological constant ${\mathrm{\Lambda }}_0$ starting from first principles given by a new kinematic invariance at low energies, which leads us to build a space–time metric with the presence of a minimum speed, so that such metric is equivalent to a de Sitter metric. In order to do that, we use a model of spherical universe with Hubble radius $R_H$ filled by a low vacuum energy density $ϵ$ that governs the accelerated expansion of the universe with negative pressure shown by the equation of state (EOS) of vacuum given by SSR-theory ($p=-ϵ$). Thus, we realize that such spherical universe made up of dark energy works like a black body with adiabatic expansion thermalized with a kind of dark gas that plays the role of the dark energy. From this model of virtual particles of dark gas that fills the sphere with dark energy, we are able to derive the law of universal gravitation, allowing us to understand the cosmological anti-gravity according to the EOS of vacuum in the space–time with a minimum speed. So, we estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this model, as the dark universe can be thought of as a black body with Hubble radius, we obtain its power and frequency of emission of radiation for a low temperature. We conclude that such radiation is a gravitational wave with an extremely low frequency and power due to the slight stretching of the fabric of space–time, since ${\mathrm{\Lambda }}_0$ is very small.

The variational method is used to study the hard confinement of a two-particle quantum system in two potential models, the Cornell potential and the global potential, with Dirichlet-type boundary conditions at various cut-off radii. The trial wave function is constructed as the product of the $1S$ free hydrogen atom wave function or $1S$ harmonic oscillator wave function times a linear cut-off function of the form $(r-z)$ to ensure hard entrapment within a sphere of radius z. The behavior of $|\psi {|}^2$, the wave function at the origin (WFO) and the mean radius $〈r〉$ are computed for different situations and compared for the two potential models.

The virial theorem is established in the framework of resolution-scale relativity for stochastic dynamics characterized by a diffusion constant $\mathcal{𝒟}$. It only relies on a simple time average just like the classical virial theorem, while the quantum mechanical virial theorem involves the expectation values of the observables. Nevertheless, by the emergence of a quantum-like potential term, the resolution-scale relativity virial theorem also encompasses quantum mechanical dynamics under the identification $\hslash \leftrightarrow 2m\mathcal{𝒟}$. This provides an illustration of the resolution-scale relativistic approach to the foundation of standard quantum mechanics. Furthermore, it is pointed out that if the resolution-scale relativity principle is implemented in macroscopic systems that are complex and/or chaotic, then the application of the classical virial theorem in the analysis of the dynamics of astrophysical systems neglects the contribution from a resolution-scale relativistic quantum-like potential. It is shown that this quantum-like potential could account for some fraction of the dark matter hypothesis.

Being the fountainhead of transverse distortion and asymmetries in accordance to “$\mathrm{\text{SSA}}=\mathrm{\text{GPD}}\ast \mathrm{\text{FSI}}$”, we study the spin-flip generalized parton distribution. We demonstrate this transverse deformation by using the quark-scalar diquark model and unveil a comparison among the low-lying strange baryons for distinct feasible combinations of quark–diquark pairs. Final-state interaction originating the correlation of a target spin and a virtual photon to the generated pion plane in semi-inclusive deep inelastic scattering has also been analyzed.

This paper explores the relativistic behavior of spin-half particles possessing an Electric Dipole Moment (EDM) in a curved space–time background induced by a spiral dislocation. A thorough review of the mathematical formulation of the Dirac spinor in the framework of quantum field theory sets the foundation for our investigation. By deriving the action that governs the interaction between the spinor field, the background space–time, and an external electric field, we establish a framework to study the dynamics of the system. Solving the resulting wave equation reveals a set of coupled equations for the radial components of the Dirac spinor, which give rise to a modified energy spectrum attributed to the EDM. To validate our findings, we apply them to the geometric phase and thermodynamics.

We propose a nonrelativistic fluid analogue model for a scalar field coupled to a classical source. The generic analogue gravity model involves the phonon-field which is coupled to the acoustic metric. We work in the special relativity limit of the acoustic analogue. By assuming a time-dependent external potential on the fluid system, we are able to model a source term for the scalar field. Upon quantization, phonon creation due to the source is studied.