Modern Physics Letters A

In this paper, we take the view that the area of a black hole’s event horizon is quantized, $A=l_P^2(4ln2)N$, and the associated degrees of freedom are finite in number and of fermionic nature. We then investigate general aspects of the entropy, $S_{\mathrm{\text{BH}}}$, our main focus being black hole self-similarity. We first find a two-to-one map between the black hole’s configurations and the ordered partitions of the integer $N$. Hence, we construct from there a composition law between the subparts making the whole configuration space. This gives meaning to black hole self-similarity, entirely within a single description, as a phenomenon stemming from the well-known self-similarity of the ordered partitions of $N$. Finally, we compare the above to the well-known results on the subleading (quantum) corrections, which necessarily require different (quantum) statistical weights for the various configurations.

We propose a new method for calculating the redshift in galaxies, according to which the amount of redshift in the spectrum of each galaxy consists of two parts: about 2/3 of the redshift is due to the speed of the galaxy moving away from us, and about 1/3 is due to the fact that photons moving in the expanding Universe acquire an additional (non-Doppler) redshift. The additional reddening of photons in the spectrum of the galaxy is due to photons coming to us from the past, when the gravitational potential of the universe was lower, and consequently, the frequencies of atomic spectra were also lower than at present. A scheme of a laboratory experiment is proposed that will allow direct measurement of a non-Doppler (additional) part of the cosmological redshift and demonstrate the very fact of the expansion of the universe in real time in about 15 min. The experiment also makes it possible to measure the expansion rate of the universe and its current gravitational potential. These results will help to significantly refine modern ideas about the age of the universe, and about the amount of dark energy and dark matter in it.

The mass spectrum of $b\bar{b}$ states has been obtained using the phenomenological relativistic quark model (RQM). The Hamiltonian used in the investigation has confinement potential and confined one gluon exchange potential (COGEP). In the framework of RQM a study of $M1$ and $E1$ radiative decays of $b\bar{b}$ states has been made. An overall agreement is obtained with the experimental masses and decay widths. The possibility that some of the excited $s$ wave $b\bar{b}$ states being exotic states is explored.

Since Dirac predicted in 1937 the possible variation of gravitational constant and other coupling constants from his large number hypothesis, efforts continue to determine such variation without success. Such efforts focus on the variation of one constant while assuming all others pegged to their currently measured values. We show that the variations of the speed of light $c$, the gravitational constant $G$, the Planck constant $h$, and the Boltzmann constant $k$ are interrelated: $G\sim c^3\sim h^3\sim k^{3/2}$. Thus, constraining any one of the constants leads to inadvertently constraining all the others. It may not be possible to determine the variation of a constant without concurrently considering the variation of others. We discuss several astrophysical observations that have been explained recently with the concomitant variation of two or more constants. We also analyze the reported and unexplained 35 $\mu$g decrease of 1 Kg Pt-Ir working standards over 22 years of measurements and show that they can be accounted for by allowing $G$, $c$, and $h$ to vary as predicted, provided such mass decrease can be confirmed with a Kibble balance used for determining the Planck constant and weighing test-masses with extreme precision.

By using the holographic hypothesis and Kaniadakis generalized entropy, which is based on relativistic statistical theory and modified Boltzmann–Gibbs entropy, we build Kaniadakis holographic dark energy (DE) model in the Brans–Dicke framework. We derive cosmological parameters of the Kaniadakis holographic DE model, with IR cutoff as the Hubble horizon, in order to investigate its cosmological consequences. Our study shows that even in the absence of an interaction between the dark sectors of the cosmos, the Kaniadakis holographic dark energy model with the Hubble radius as IR cutoff can explain the present accelerated phase of the universe expansion in the Brans–Dicke theory. The stability of the model, using the squared of sound speed, has been checked and it is found that the model is unstable in non-interacting case and can be stable for some range of model parameters within the interacting case.

In this paper, we consider the Coulomb crystals in linear ion trap with a nonlinear dissipative force induced by optical radiation. We discuss a relation between 2D and 3D ion crystals formation and the crystalline units’ initial conditions. A phase diagram of the Coulomb crystal configurations is constructed. We introduce a cross size and surface area metrics to define a Coulomb crystals dimension sensitivity to the initial conditions and show the hysteresis-like-type phase transition between 2D and 3D configurations.

Using the method of the “exact discretization” of the Schrödinger equation, we propose a particular discretized version of the $N=2$ Supersymmetric Quantum Mechanics (SQM). After defining the corresponding shape invariance condition, we show that the energy spectra and wave functions for discretized Quantum Mechanical systems can be found using the technique of $N=2$ Supersymmetric Quantum Mechanics exactly the same way as it is done for their continuous counterparts. As a demonstration of the present method, we find the energy spectrum for a discretized Coulomb potential and its ground state wave function.

This paper presents an analytical investigation of the teleportation and the thermal entanglement of two identical qubits in the ground state of graphene lattices. The elastic interaction between the two qubits is considered as a scattering process. The modified Hamiltonian and density matrix of the system were presented. The teleportation and the entanglement of two-qubit system are analyzed through the study of the average fidelity of teleportation $F_A$, the concurrence ${𝒞}$ and the entanglement of formation ${{ℰ}}_f$. The results depend on the temperature $T$ and also on the parameters of the system as the $\chi$ parameter of the interaction potential and $\gamma$ band parameter. The study shows that the teleportation and the entanglement decrease when the temperature $T$ increases but they become all the more important as the parameters $\chi$ and $\gamma$ increase.

A novel quantum private comparison (QPC) protocol with six-particle maximally entangled states is put forward, which can guarantee that the true content of secret messages from two users cannot be extracted by an illegal party. The entanglement correlation among different particles in one six-particle maximally entangled state is taken to realize the private comparison of secret messages from two users. Neither quantum entanglement swapping nor unitary operations are adopted. Third party (TP) only needs Bell basis measurements while two users only need Bell basis measurements and $Z$ basis measurements. The proposed protocol has no security loophole for the outside attack and the participant attack.