Modern Physics Letters A

Classical geometry can be described either in terms of a metric tensor $g_{ab}(x)$ or in terms of the geodesic distance ${\sigma }^2(x,x^{\prime })$. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum structure of spacetime. This is because one can incorporate some of the key quantum effects by replacing ${\sigma }^2$ by another function $S[{\sigma }^2]$ such that $S[0]=L_0^2$ is nonzero. This allows one to introduce a zero-point-length in the spacetime. I show that the geodesic distance can be an emergent construct, arising in the form of a correlator $S[{\sigma }^2(x,y)]=〈J(x)J(y)〉$, of a pregeometric variable $J(x)$, which can be interpreted as the quantum density of spacetime events. This approach also shows why null surfaces play a special role in the interface of quantum theory and gravity. I describe several technical and conceptual aspects of this construction and discuss some of its implications.

For the generalized parton distribution (GPD) E, extracted from hard exclusive processes and the Pauli form factor of the nucleon, the second moments for quarks and gluons at $t=0$ are calculated and their scale dependence analyzed. The parton angular momenta are subsequently determined and compared with other results.

We study Brans–Dicke cosmology with an inverse power-law effective potential. By using dynamical analyses, we search for fixed points corresponding to the radiation-like matter and dark energy-dominated era of our Universe, and the stability of fixed points is also investigated. We find phase space trajectories which are attracted to the stable point of the dark energy-dominated era from unstable fixed points like matter-dominated era of the Universe. The dark energy comes from effective potentials of the Brans–Dicke field, whose variation (related to the time-variation of the gravitational coupling constant) is shown to be in good agreement with observational data.

In this paper, we study a Bianchi type-I model of universe filled with barotropic and dark energy (DE) type fluids. The present values of cosmological parameters, such as Hubble constant $H_0$, DE and anisotropy energy parameters ${({\mathrm{\Omega }}_m)}_0$, ${({\mathrm{\Omega }}_{\mathrm{\text{de}}})}_0$ and ${({\mathrm{\Omega }}_{\sigma })}_0$ and Equation of State (EoS) parameter for DE $({\omega }_{\mathrm{\text{de}}})$, are statistically estimated in two ways by taking 38 point data set of Hubble parameter $H(z)$ and 581 point data set of distance modulus of supernovae in the range $0\le z\le 1.414$. It is found that the results agree with the Planck result [Planck Collab. (P. A. R. Ade et al.), Astron. Astrophys. 594, A14 (2016)] and more latest result obtained by Amirhashchi and Amirhashchi [H. Amirhashchi and S. Amirhashchi, arXiv:1811.05400v4]. Various physical properties such as age of the universe, deceleration parameter, etc. have also been investigated.

Gravitational collapse of a spherically symmetric homogeneous perfect barotropic fluid with linear as well as polytropic-type Equation of State (EoS) has been investigated in the framework of a linear model of $f(R,T)$ gravity. This modified gravity has the potential to explain the observed cosmic acceleration. The calculations have been done taking the transformed time coordinate $t\to \sqrt{\frac{{\rho }_0}{3}}t$, where ${\rho }_0$ is the initial density of the fluid. For linear EoS $p=\omega \rho$, the condition for being a true singularity, along with sufficient condition for the formation of apparent horizon covering the singularity has been derived. For a polytrope having the EoS $p=K{\rho }^{1+\frac{1}{n}}$, the scale factor $(A)$ as a function of fluid density $(\rho )$ has been obtained which is then used to study the dynamics of the fluid. Role of the polytropic index $(n)$ and the constant of proportionality $(K)$ in the dynamics of the fluid is also studied. A new type of exotic matter field having varied dependence of scale factor on the density, and having the potential to give rise to bouncing cosmology, provided it is the dominating fluid in the universe, is obtained in this domain and is investigated. Energy conditions are discussed.

This paper is devoted to formulating exact solutions of axially symmetric spacetime through gravitational decoupling technique. For this purpose, we first evaluate an exact solution in the framework of cosmic strings by assuming some additional constraints on the metric coefficients and extend it to obtain two concrete anisotropic cosmological models. We investigate energy conditions as well as the speed of sound constraint to ensure the physical viability of the developed solutions. It is concluded that both anisotropic models meet all the energy bounds as well as stability criterion. The expanding behavior of the universe is also confirmed through different cosmological parameters.

We present an explicit proof that a minimal model of rank-2 antisymmetric field with spontaneous Lorentz violation and a classically equivalent vector field model are also quantum equivalent by calculating quantum effective actions of both theories. We comment on the issues encountered while checking quantum equivalence in curved spacetime.

In this work, we study the spectral properties of electron quantum dots (QDs) confined in 2D parabolic harmonic oscillator influenced by gravity, external uniform electromagnetic field together with an Aharonov–Bohm (AB) flux field. Our calculations are based on the Nikiforov–Uvarov method and we obtain exact solutions for the energy levels and normalized wave functions. The interband optical absorption QDs of the parabolic spherical shape in GaAs is studied theoretically and the total optical absorption coefficient has been calculated by using the energy eigenvalues spectra and the corresponding wave functions.

The equation of the $\gamma$-unstable Bohr Hamiltonian, with particular forms of the sextic potential in the $\beta$ shape variable, is exactly solved for a finite number of states. The shape of the quasi-exactly solvable potential is then defined by the number of exactly determined states. The effect of exact solvability order on the spectral characteristics of the model is closely investigated, especially, concerning the critical point of the phase transition from spherical to deformed shapes. The energy spectra and the $B(E2)$ transition probabilities, up to a scaling factor, depend only on a single-free parameter, while for the critical point, parameter-free results are available. Several numerical applications are done for nuclei undergoing a $\gamma$-unstable shape phase transition in order to identify critical nuclei based on the most suitable exact solvability order.

A systematic study of dynamical aspects associated with heavy-ion-induced ${}^{16}\mathrm{\text{O}}+{}^{89}\mathrm{\text{Y}}$ reaction is carried out at center-of-mass energy $E_{\mathrm{\text{c.m.}}}=89$ MeV. The complete fusion (CF) and incomplete fusion (ICF) contributions are estimated by using the dynamical cluster-decay model (DCM). The incomplete fusion component is examined by normalizing the incident beam energy for each of the breakup fragment. The fusion evaporation cross-sections that emerged from CF and ICF channels are duly addressed using the optimized value of neck-length parameter $\mathrm{\Delta }R$. Further, the mass yield of compound nuclei (CN) formed in the CF and ICF processes is analyzed with respect to angular momentum $\ell$ values. The DCM-based calculations indicate the possible contribution of deep inelastic collision (DIC) in the decay of ${}^{105}{\mathrm{\text{Ag}}}^{\ast }$ at higher $\ell$ values, and DIC cross-sections are predicted which call for future validation.

Working within the framework of parity-time-symmetric quantum mechanics, we look into the possibility of entanglement generation and demonstrate that the feature of non-violation of no-signaling principle may hold for the simplest nontrivial case of bipartite systems. Basically, our arguments are based on the computation of the reduced density matrix of one party to justify that the entropy of the other does not change.

Recently, it was found that after imposing a helix boundary condition on a scalar field, the Casimir force coming from the quantum effect is linearly proportional to r, which is the ratio of the pitch to the circumference of the helix. This linear behavior of the Casimir force is just like that of the force obeying Hooke’s law on a spring. In this paper, inspired by some complex structures that live in the cells of human body like DNA, protein, collagen, etc., we generalize the helix boundary condition to a more general one, in which the helix consists of a tiny helix structure, and makes up a hierarchy of helix. After imposing this kind of boundary condition on a massless and a massive scalar, we calculate the Casimir energy and force by using the so-called zeta function regularization method. We find that Hooke’s law with the generalized helix boundary condition is not exactly the same as the usual one. In this case, the force is proportional to the cube of r instead. So, we regard it as a generalized Hooke’s law, which is complied by a generalized quantum spring.