Modern Physics Letters A

This paper investigates the Noether versus Killing symmetries and their associated conservation laws of Bianchi type-V spacetimes. The study is carried out using the Maple RIFSIMP package, which converts a set of nonlinear differential equations into the reduced involutive form (RIF). This technique generates an RIF tree, where each branch is solved to obtain the explicit forms of Noether symmetries. Separate RIF trees are used to represent each group. We derive a general expression for the Noether symmetry connected to homothety, and then we investigate this Noether symmetry in each separate group. To explore whether dark energy is associated with Bianchi type-V spacetime, we examine the energy density of each spacetime obtained in association with the Ricci scalar. The symmetries of the larger groups, 11- and 17-dimensional, are presented separately in the tables.

It is argued, as a working hypothesis, that “normal” and dark matter interactions can only be $T$- and $CP$-violating. One way to implement this idea is to consider that time reversal in dark matter is implemented, not by an antiunitary operator, but by an unitary operator. It is shown how this occurs naturally in the context of complex spacetime with an extended symmetry group.

First, we illustrate that a conformally flat generalized Ricci recurrent spacetime is a perfect fluid spacetime. As a consequence, we prove that such a spacetime represents a dust matter fluid, stiff matter and dark energy era under certain restrictions on the Ricci scalar. Then we establish that such a spacetime is a Robertson–Walker spacetime. Also, we note that in a conformally flat generalized Ricci recurrent spacetime, the fluid is shear-free, vorticity-free and its flow vector is hypersurface orthogonal. We investigate a conformally flat generalized Ricci recurrent spacetime as a solution of curvature-squared gravity theory. In this study, various energy conditions in terms of the Ricci scalar are examined and state that the Universe is in an accelerating phase and satisfies the weak, null, dominant, and strong energy conditions.

We prove through path integral Monte Carlo that the covariant Euclidean scalar field theory, ${\phi }_n^r$, where $r$ denotes the power of the interaction term and $n=s+1$ with $s$ as the spatial dimension and 1 adds imaginary time, such that $r=12$, $n=3$ can be acceptably quantized using scaled affine quantization (AQ) and the resulting theory is nontrivial, unlike what happens using canonical quantization which finds it trivial.

In this paper, two novel schemes for bidirectional controlled remote state preparation (BCRSP) and asymmetric bidirectional controlled remote state preparation (ABCRSP) in four-dimensional systems are proposed. The first scheme uses a six-particle entangled state as the quantum channel. Under Charlie’s supervision, Alice and Bob can simultaneously create a single-particle four-dimensional equatorial state at each other’s location. Moreover, in the second scheme, using a seven-particle entangled state as the quantum channel, Alice remotely prepares a two-particle four-dimensional equatorial state for Bob, while Bob remotely prepares another single-particle four-dimensional equatorial state for Alice under the supervision of controller Charlie. Both schemes employ quantum operations such as control-not, projective measurement and unitary transformation in four-dimensional systems. It is worth noting that the proposed schemes have a total success probability of 100% in ideal environment. In addition, we also investigate the proposed two schemes in the noisy environment. The fidelities of output states are calculated and the effect factors are discussed. Finally, we give the advantages of these schemes compared to other schemes.

In this work, we study quantum teleportation, a fundamental protocol of quantum physics. In particular, we present a mathematical methodology to study the combined effects of noisy resource state and noisy classical communication on teleportation fidelity and its deviation. We describe a teleportation protocol where an arbitrary two-qubit state in canonical form is used as a resource. Thereafter, to teleport an unknown qubit, Alice measures her qubits in Bell basis and conveys the measurement outcome to Bob via noisy classical channel(s). We derive the exact formulae of optimal teleportation fidelity and corresponding fidelity deviation where the resource state and the classical communication, both can be noisy. To provide the proof of optimality, we provide a systematic method. We further find conditions for non-classical fidelity and dispersion-free teleportation for our teleportation protocol. In this way, we identify noisy environments where it is possible to achieve dispersion-free teleportation without compromising non-classical fidelity. We also demonstrate scenarios where the increase of entanglement in the resource state, may degrade the quality of teleportation — a counter-intuitive instance. Finally, we discuss about the minimum classical communication cost required to achieve non-classical fidelity for our protocol. Here we mainly focus on a possible way to optimize the classical communication cost.

In this paper, we study the Chaplygin gas equation in curvature-matter coupling gravity to describe the observed expansion of the universe. We consider the Chaplygin gas equation of state in terms of the energy density $\rho$ and pressure $p$, by the relationship $p=-\frac{A}{\rho }$ and the curvature-matter coupling gravity as $f(R,T)$, where $A$ is a positive constant, $R$ and $T$ denote, respectively, the Ricci scalar and the trace of energy–momentum tensor. Considering the gravitational lagrangian in the form $f(R,T)=R+h(T)$, where we used two forms of $h(T)$ and by assuming a perfect fluid as matter source, we determined through the modified Friedmann equations, the corresponding energy and pressure for each model. By using the free parameters of our models, we performed the numerical results of the energy conditions to study its viability. Furthermore, we have derived some cosmological parameters like deceleration parameter and statefinder parameters and graphically investigated the nature of these parameters in Chaplygin gas model.

In this paper, we introduced the deceleration parameter $(q)$ in a different manner by proposing a modern law. According to this law, we suggested a time-periodic $q$. Furthermore, we used this law to develop a model in which the universe oscillates with quintom matter in a four-dimensional FLRW metric background. Using this model, we obtained the oscillating Hubble parameter $(H)$, which remains positive. Consequently, the universe undergoes decelerating expansion and accelerating expansion periodically, avoiding singularities.