Fisher information and quantum state estimation of two-coupled atoms in presence of two external magnetic fields

We consider a quantum system of an atom-atom interaction in the presence of two external magnetic and classical fields in x, and z directions. The dynamical behavior of single atom quantum quantifiers such as the atomic Wehrl entropy, atomic Fisher information and quantum entropy are investigated. The quantum entanglement degradation in regard to the atomic state estimation are discussed through the evolution of the atomic Fisher information flow, and the effects of the external classical fields and types of time dependent coupling between the two atoms are examined. We explore the relationship between different statistical quantities in the absence and presence of classical field during the time evolution. The results show that the creation and manipulation of entanglement by external fields greatly benefit within the suitable choice of the kind of time dependent coupling among the two atoms and external. Keywords: Atomic Wehrl entropy, Atomic Fisher information, Atom-atom interaction, Single atom entanglement, Time dependent couplin

Thermo-viscoelastic orthotropic constraint cylindrical cavity with variable thermal properties heated by laser pulse via the MGT thermoelasticity model

Abstract In the past few decades, many models have been proposed to address the shortcomings found in the classical theories of thermoelasticity and to allow limited speeds of heat waves. In this context, in the current paper a new generalized model of thermoelasticity based on the Moore–Gibson–Thompson (MGT) equation has been introduced. This new model can be derived by introducing the relaxation time factor into the third type of Green–Naghdi model (GN-III). In contrast to the previous works, it was taken into account that the physical properties of the material are dependent on temperature and on the viscous type. The viscoelastic medium has been assumed to obey the Kelvin–Voigt model. On the basis of the present model, thermo-viscoelastic interactions have been investigated in an unbounded orthotropic body with a cylindrical cavity. The surface of the cavity is restricted and exposed to a pulse-formed heat flow that dissolves exponentially. The characteristic thermal modulus of the material is assumed to be a linear function of temperature. The Laplace transform can be used to eliminate time dependency from control equations. Using a suitable approximate method, the transformed equations have been finally inverted by numerical inversion of the Laplace transform. Certain comparisons have been introduced to estimate the effects of the viscosity, pulsed heat, and thermal temperature-independent properties on all studied fields. A comparison with previous models of thermoelasticity is also performed in tables to verify the accuracy of the proposed model. We found from the results that the physical fields strongly depend on the viscoelastic parameter, the change of the thermal conductivity, and pulsed heat, so it is not possible to neglect their effect on the manufacturing process of machines and devices

The fractional comparative study of the non-linear directional couplers in non-linear optics

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Statistical inferences with jointly type-II censored samples from two Pareto distributions

In the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method

Influence of dipole interaction on the quantum correlation detection and teleportation in a qubit-field system

This study examines the analysis of the teleportation process in a two-qubit state, particularly scrutinizing the interplay of atomic dipole coupling interaction, the detuning parameter, photon count, and the surrounding environment. Our investigation assumes the existence of a teleportation channel comprising two-qubit systems interacting with a photon field enveloped by the dephasing environment. Within this framework, we closely examine the quantum correlations exhibited by the teleported state, encompassing dimensions of entanglement, steering, and non-locality. Our results underscore the pivotal role played by the initial state of the atomic and field subsystems in shaping quantum relations. The dipole coupling has a profound impact, significantly enhancing the three quantifiers. Particularly, the entanglement changes from a de-entangled state to a partially entangled state. On the other hand, the detuning parameter introduces distortion in the quantum correlations, a phenomenon that can be effectively mitigated by controlling the dipole coupling

The estimations for parameter of Suja distribution with application

Strong relation between reliability studies and product quality. And reliability analysis deals with failure time of units and there are many well-known lifetime distributions. In this paper, we adopt the statistical inference of one more flexible one parameter distribution called Suja lifetime distribution. We primarily take into account four methods to estimate the distributional parameter other than the maximum likelihood estimation. The approximate confidence interval and two bootstrap confidence intervals have also been determined. The point and interval estimators of the Suja’ parameter are assessed and compared throughout the Monte Carlo simulation study. Finally, the Suja distribution is used to modeled and analyzed three real data sets

Competing Risks Model with Partially Step-Stress Accelerate Life Tests in Analyses Lifetime Chen Data under Type-II Censoring Scheme

The experiment design may need a stress level higher than use condition which is called accelerate life tests (ALTs). One of the most ALTs appears in different applications in the life testes experiment is partially step stress ALTs. Also, the experiment items is failure with several fatal risk factors, the only one is caused to failure which called competing risk model. In this paper, the partially step-stress ALTs based on Type-II censoring scheme is adopted under the different risk factors belong to Chen lifetime distributions. Under this assumption, we will estimate the model parameters of the different causes with the maximum likelihood method. The two, asymptotic distributions and the parametric bootstrap will be used to build each confidence interval of the model parameters. The precision results will be assessed through Monte Carlo simulation study

Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method

In this study, we use a new approach, known as the Aboodh residual power series method (ARPSM), in order to obtain the analytical results of the Black–Scholes differential equations (BSDEs), which are prime for judgment of European call and put options on a non-dividend-paying stock, especially when they consist of time-fractional derivatives. The fractional derivative is considered in the Caputo sense. This approach is a combination of the Aboodh transform and the residual power series method (RPSM). The suggested approach is based on a new version of Taylor’s series that generates a convergent series as a solution. The advantage of our strategy is that we can use the Aboodh transform operator to transform the fractional differential equation into an algebraic equation, which decreases the amount of computation required to obtain the solution in a subsequent algebraic step. The primary aspect of the proposed approach is how easily it computes the coefficients of terms in a series solution using the simple limit at infinity concept. In the RPSM, unknown coefficients in series solutions must be determined using the fractional derivative, and other well-known approximate analytical approaches like variational iteration, Adomian decomposition, and homotopy perturbation require the integration operators, which is challenging in the fractional case. Moreover, this approach solves problems without the need for He’s polynomials and Adomian polynomials, so the small size of computation is the strength of this approach, which is an advantage over various series solution methods. The efficiency of the suggested approach is verified by results in graphs and numerical data. The recurrence errors at various levels of the fractional derivative are utilized to demonstrate the convergence evidence for the approximative solution to the exact solution. The comparison study is established in terms of the absolute errors of the approximate and exact solutions. We come to the conclusion that our approach is simple to apply and accurate based on the findings

Different Method Estimations of the Three Parameters of Exponentiated Gompertz Distribution

This article discusses the maximum likelihood, least squares, weighted least squares, and percentiles estimates of three parameters of an exponentiated Gompertz distribution based on complete sample. By using the mean square error through Monte Carlo simulation, this study compares the performances of estimates. Real data set is used as an example of the methods of estimations for the three parameters of exponentiated Gompertz distribution

Influence of an External Classical Field on a ♢ Four-Level Atom Inside a Quantized Field

In this paper, we study the effect of detuning parameters and driven external classical field parameters on a quantum system consisting of a ♢-configuration four-level atom inside a quantized cavity field. Under some canonical conditional of dressed states, the exact solution of the Schrödinger equation is obtained. The occupation of atomic levels and statistical population inversion is studied. Our results show that the classical field parameter dissolved the collapse periods and increased the maximum bounds of the upper state, while decreasing the lower bounds of the lower state. The detuning parameters reduce the minimum bounds of atomic levels and their inversion. On the other hand, the linear entropy and l1 norm of coherence are employed to measure the temporal evolution of the mixedness and coherence. It is found that the driven classical field improves the temporal evolution of the mixedness and lower bounds of coherence. However, the detuning parameters have a destructive effect on the mixedness and lower bounds of coherence. The intensity of the external classical field is regarded as a control parameter with different values of detuning parameters