Modern Physics Letters A

The purpose of this paper is to find proper homothetic vector fields in plane symmetric perfect fluid static spacetimes in the $f(R,T)$ theory of gravity by using direct integration technique. In this study, there exist six cases. Studying each case in detail, we found that in four cases proper homothetic vector fields exist while in the other two cases homothetic vector fields become Killing vector fields.

In this paper, we consider the quantum mechanics with Dunkl derivative. We use the Dunkl derivative to obtain the coordinate representation of the momentum operator and Hamiltonian. We introduce the scalar product to find that the momentum is Hermitian under this inner product. We study the one-dimensional box problem (the spin-less particle with mass m confined to the one-dimensional infinite wall). Finally, we discuss the harmonic oscillator problem.

Examining composite operators in non-commutative (NC) spaces, we show that these operators do not have a simple gauge transformation which can be attributed to the effective total charge of the composite particle. Using this result, along with the known constraint on charges permitted in NC quantum electrodynamics, we place a limit on the scale of non-commutativity to be at most smaller than current LHC limits for compositeness. Furthermore, this also suggests that a substructure at still smaller scales is necessary if such spaces are to be a physical reality.

To investigate the energy of Bianchi type-II cosmological model, I used the energy–momentum complexes of Einstein and Møller and obtained the zero total energy in these two prescriptions. This result reinforces the viewpoint of Albrow and Tryon that the universe must have a zero net value for all conserved quantities and be equivalent to the previous works of Nester et al. [Phys. Rev. D 78], 044035 (2008) and Aydogdu et al.

In this study, a novel quantum-based multi-objective is proposed using Schrödinger equations. The two new operations namely weighted cluster centroid computation and threshold setting are also introduced to refine cluster centroids. A novel fitness function strategy is also proposed for efficient searching. The proposed technique is compared with various well-known approaches. Experimental outcomes show that the proposed quantum approach outperforms other existing approaches.

Standard Big Bang Nucleosynthesis (SBBN) represents one of the basic tools to understand the early evolution of the universe. In this paper, we reanalyze this process to focus on the so-called lithium problem. ⁷Li is overproduced during SBBN compared to its primordial abundance as obtained from observations. For this reason, we extend the scenarios of SBBN in two directions: (i) equating all neutrino chemical potentials and including more neutrino families, (ii) varying neutrino chemical potentials independently. Since the so-called cosmological lithium problem is not resolved on nuclear/astrophysical ground, we argue that this problem should be examined by invoking nonstandard assumptions.

Analytical solutions of the Schrödinger equation with a singular, fractional-power potential, referred to as the second Exton potential, are derived and analyzed. The potential is defined on the positive half-axis and supports an infinite number of bound states. It is conditionally integrable and belongs to a biconfluent Heun family. The fundamental solutions are expressed as irreducible linear combinations of two Hermite functions of a scaled and shifted argument. The energy quantization condition results from the boundary condition imposed at the origin. For the exact eigenvalues, which are solutions of a transcendental equation involving two Hermite functions, highly accurate approximation by simple closed-form expressions is derived. The potential is a good candidate for the description of quark–antiquark interaction.

Quantum private query (QPQ) is a cryptographic application that protects the privacy of both users and databases while querying the database secretly. In most existing QPQ protocols, the protection of user privacy can only be cheat-sensitive. Cheat-sensitive means that Bob will be found later with a certain probability if he tries to get the address queried by Alice. On the premise of cheat-sensitivity, although Alice can discover Bob’s malicious behavior after a query (transaction), the secret information of Alice was leaked in the completed query, which is likely to be a fatal blow to Alice. Or, to prevent Bob’s malicious behavior, Alice executes one or more additional queries to test Bob’s honesty. However, to bypass Alice’s honesty test, Bob can also provide several honest queries before performing dishonest queries. Therefore, cheat-sensitive should not be the ultimate goal of user privacy protection in QPQ. In this paper, we propose a practical QKD-based QPQ protocol with better user privacy protection than cheat-sensitivity based on order rearrangement of qubits. The proposed QPQ protocol can resist the Trojan horse attack even without wavelength filter and photon number splitter (PNS) equipped with auxiliary monitoring detectors.

Recent astrophysical datasets have implied that the universe has entered a speedy expansion phase. The Polytropic gas model, which describes a unified formulation of dark contents (matter plus energy), is one of the most reasonable definitions of this mysterious phenomenon. This interesting formulation allows to simulate the dark contents in the cosmic form of the perfect fluid and gives an interesting point of view in the discussion of fundamental theories of physics. In the first step of our investigation, we discuss the thermal equation-of-state (EoS henceforth) and obtain the EoS and deceleration parameters as explicit functions of temperature. Subsequently, we obtain a relation for the thermal efficiency of the Carnot heat engine which depends on free parameters given in the cosmological Polytropic gas description and the limits of maximal and minimal temperatures imposed on the Carnot cycle.