Modern Physics Letters A

Uncertainties in flavor and mass eigenstates of neutrinos are considered within the majorization approach. Nontrivial bounds reflect the fact that neutrinos cannot be simultaneously in flavor and mass eigenstates. As quantitative measures of uncertainties, both the Rényi and Tsallis entropies are utilized. Within the current amount of experience concerning the mixing matrix, majorization uncertainty relations need to put values of only two parameters, viz. ${𝜃}_{12}$ and ${𝜃}_{13}$. That is, the majorization approach is applicable within the same framework as the Maassen–Uffink relation recently utilized in this context. We also consider the case of detection inefficiencies, since it can naturally be incorporated into the entropic framework. Short comments on applications of entropic uncertainty relations with quantum memory are given.

By analyzing the energy–momentum relationship of the absorbed fermions dropping into a Reissner–Nordstöm–anti-de Sitter black hole surrounded by dark matter, the laws of thermodynamic and weak cosmic censorship conjecture in the extended phase space are investigated. We find that the first law of thermodynamics is valid. However, the validity of the second law of thermodynamics depends on the density $\alpha$ of the perfect fluid dark matter. In addition, we also find that when the fermions are absorbed, the structures of black hole surrounded by dark matter would not change. Therefore, weak cosmic censorship conjecture holds for the extreme black holes and the non-extreme black holes.

In this paper, we have adopted a new approach to study the Killing vector fields of locally rotationally symmetric and general Bianchi type I spacetimes. Instead of directly integrating the set of Killing’s equations, an algorithm is developed in Maple which converts these equations to the reduced involutive form (Rif) and consequently it imposes some restrictions on the metric functions in the form of a tree, known as Rif tree. The set of Killing’s equations is then solved for each branch of the Rif tree, giving the explicit form of the Killing vector fields. The structure of Lie algebra is presented for each set of the obtained Killing vector fields and some physical implications of the obtained metrics are discussed.

In this paper, we consider a static black hole in $f(R)$ gravity. We recapitulate the expression for corrected thermodynamic entropy of this black hole due to small fluctuations around equilibrium. Also, we study the geometrothermodynamics (GTD) of this black hole and investigate the adaptability of the curvature scalar of geothermodynamic methods with phase transition points of this black hole. Moreover, we study the effect of correction parameter on thermodynamic behavior of this black hole. We observe that the singular point of the curvature scalar of Ruppeiner metric coincides completely with zero point of the heat capacity and the deviation occurs with increasing correction parameter.

Starting from a regular, static and spherically symmetric spacetime, we present a stellar model formed by two sources of ordinary and quintessence matter both with anisotropic pressures. The ordinary matter, with density $\rho$, is formed by a fluid with a state equation type Chaplygin $P_r(\rho )=\mu c^2\rho -\nu /(c^2\rho )$ for the radial pressure. And the quintessence matter, with density ${\rho }_q$, has a state equation $P_r({\rho }_q)=-c^2{\rho }_q$ for the radial pressure and $P_r({\rho }_q)=-(1+3w)c^2{\rho }_q/2$ for the tangential pressure with $-1<w<-\frac{1}{3}$. The model satisfies the required conditions to be physically acceptable and additionally the solution is potentially stable, i.e. $v_t^2-v_r^2<0$ according to the cracking concept, and it also satisfies the Harrison–Zeldovich–Novikov criteria. We describe in a graphic manner the behavior of the solution for the case in which the mass is $1.3M_{\odot }$ and radius $R=8.849$km which matches the star EXO 1785-248, from where we obtain the maximum density ${\rho }_c=1.206510^{18}\mathrm{\text{kg}}/{\mathrm{\text{m}}}^3$ for the values of the parameters $\mu =0.15535$, $w=-0.33334$.

In this paper, the thermal quantum correlations along with the thermal entropic uncertainty in a two neighboring XYZ Heisenberg spin-1/2 particles subjected to a transverse external magnetic field with the interplay of both antisymmetric Dzyaloshinskii–Moriya and symmetric Kaplan–Shekhtman–Entin–Wohlman–Aharony are investigated. The quantum consonance and uncertainty-induced quantum nonlocality as well as the entropic uncertainty with quantum memory for the considered system are specified and the thermal behaviors of them in terms of the system parameters are examined. The expected decrease of quantum correlations for higher absolute temperatures is confirmed while the inflation of the uncertainty is generated. Moreover, we show that the stronger spin-spin and spin-orbit exchange couplings can enhance the thermal quantum correlations and suppress the uncertainty. Accordingly, our remarks are expected to be beneficent in illustrating the dynamical quantum correlations and entropy-based uncertainty in a general Heisenberg spin-chain model and thus would be useful for practical quantum information processing.

In this paper, exactly solvable model of the quantum harmonic oscillator is proposed. Wave functions of the stationary states and energy spectrum of the model are obtained through the solution of the corresponding Schrödinger equation with the assumption that the mass of the quantum oscillator system varies with position. We have shown that the solution of the Schrödinger equation in terms of the wave functions of the stationary states is expressed by the pseudo Jacobi polynomials and the mass varying with position depends from the positive integer $N$. As a consequence of the positive integer $N$, energy spectrum is not only non-equidistant, but also there are only a finite number of energy levels. Under the limit, when $N\to \infty$, the dependence of effective mass from the position disappears and the system recovers known non-relativistic quantum harmonic oscillator in the canonical approach where wave functions are expressed by the Hermite polynomials.