PDM-charged particles in PD-magnetic plus Aharonov–Bohm flux fields: Unconfined “almost-quasi-free” and confined in a Yukawa plus Kratzer exact solvability

Using azimuthally symmetrized cylindrical coordinates, we consider some position-dependent mass (PDM) charged particles moving in position-dependent (PD) magnetic and Aharonov–Bohm flux fields. We focus our attention on PDM-charged particles with $m\left(\overrightarrow{r}\right)=g\left(\rho \right)=\eta f\left(\rho \right)\exp (-\delta \rho )$ (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fields $\overrightarrow{B}=B_{\circ }(\mu /{\rho }^{\sigma })\widehat{z}$. Under such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential, $V\left(\overrightarrow{r}\right)=0$) endowed with $g\left(\rho \right)=\eta /\rho$ and $g\left(\rho \right)=\eta /{\rho }^2$. Both yield exactly solvable Schrödinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle with $g\left(\rho \right)=\eta \exp (-\delta \rho )/\rho$ moving not only in the vicinity of the PD-magnetic and Aharonov-Bohm flux fields but also in the vicinity of a Yukawa plus a Kratzer type potential force field $V\left(\rho \right)=-V_{\circ }\exp (-\delta \rho )/\rho -V_{{}_1}/\rho +V_{{}_2}/{\rho }^2$. For this particular case, we use the Nikiforov-Uvarov (NU) method to come out with exact analytical eigenvalues and eigenfunctions. Which, in turn, recover those of the almost-quasi-freePDM-charged particle with $g\left(\rho \right)=\eta /\rho$ for $V_{\circ }=V_{{}_1}=V_{{}_2}=0=\delta$. Energy levels crossings are also reported.     

Modeling of anisotropic spheres in extended teleparallel theory with matter coupling

This work is devoted to investigate the structures of compact stars by using spherically static symmetric space-time in the background of $f(\tau ,T)$ gravity, where $\tau$ represents the torsion scalar and $T$ represents the trace of the energy momentum tensor. We develop the field equations by using the concept of quintessence to discuss the motion by using anisotropic fluid distribution with a spherically symmetric metric. We use the convention of junction conditions to evaluate the unknown parameters used in the study of the compact stars. In this study we use the available data of three different compact objects $4U1608-52,$ $CenX-3$ and $EXO1785-240$. We discuss the physical and analytical existence of compact stars by satisfying some standard properties of compact stars like the behavior of the energy density, quintessence density, radial and tangential pressures, anisotropy, to elaborate the anisotropic nature of the star. We discuss the sound speeds and casuality conditions to show the stability of the system. Equilibrium of the star is justified by the TOV equation. Red-shift function, compactness, and mass function states the physical existence of the star. It is examined that all these parameters show the viability and stability of the model used in the effects of $f(\tau ,T)$ gravity.     

Conserved spin current with a perpendicular magnetic field

Previous theoretical studies show that the spin current in spin-orbit coupled systems can be effectively conserved. In this study, we show that in the presence of an external magnetic field B perpendicular to the surface without causing Landau levels, the spin-Hall conductivity, including the conventional spin and spin-torque Hall currents exhibit an interesting symmetry, ${\sigma }_{xy}^c(B)={\sigma }_{xy}^c(-B)$ valid for k-linear and k-cubic Rashba systems. The phenomenon where the electric field generated spin z component is unaltered under $B\to -B$ is attributed to the fact that the spin precession is locked in spin-orbit coupled systems. The perpendicular magnetic field generates spin x and y components, which are linear to B, and thus, there is no time-reversal symmetry. This result provides evidence for the detection of the bulk spin-Hall current. Furthermore, the applied magnetic field breaks the degenerate point of the two-band model, and the resulting spin-Hall conductivity does not vanish even for systems with linear momentum, which implies that the Berry phase is not the principal mechanism in k-linear systems. The non-zero charge-Hall conductivity generated by the perpendicular magnetic field is discussed here.     

CNN-aided multiple PU spectrum sensing in uncalibrated massive antennas SU system

This paper deploys the Convolutional Neural Network (CNN) to learn and set the statistical test in Spectrum Sensing (SS) task of multiple primary user (PU) sources in massive uncalibrated antennas of secondary users (SU) sharing the same spectrum resources. The proposed deep learning-based SS method (DL-SS) is based on the CNN architecture that has the capability of extracting features of the sample covariance matrices (SCMs) that are given as the network input, improving the overall performance and robustness. The proposed CNN-SS method is compared with nine recent multiple-antennas SS methods, namely the arithmetic–geometric detector (AGM), John’s detector (JD), sphericity detector (SD), generalized likelihood test (GLRT), locally most powerful invariant test (LMPIT), maximum–minimum eigenvalue detector (MME), covariance detector (CAV), Hadamard detector (HD) and volume detector (VD) methods; besides, the proposed method is also compared with five recent state-of-art CNN-based SS methodologies. Performance-complexity trade-off of the proposed and reference SS methods are corroborated via Monte Carlo Simulations (MCS). The proposed CNN-SS method under uncalibrated massive antennas reveals substantial benefits w.r.t. the reference methods and is competitive with others CNN-SS methodologies, both in terms of complexity and performance, achieving detection probability of $P_d=0.9$ $(@SNR=-20\mathrm{dB})$ under very low false alarm probability $P_f=0.1$. Under different figures of merit, the performance of the CNN-based SS detector has revealed to be indubitably superior regarding the state-of-art SS detectors. However, the proposed CNN-based SS detector presents relative computational complexity increases. Hence, to be effective, such a superior operational performance requires a very efficient processing structure in the SU base stations.     

Theoretical study of the effect of the Coulomb blockade and Kondo resonance in the density of states using self-consistent field approximation

In a recent paper, we theoretically investigated the density of states of the composite channel–contact system in the Coulomb and Kondo regimes using the self-consistent field approximation. There are the main experimental observations of vibration features in the Coulomb blockade [H. Park et al., Nature (London) 407, 57 (2000)] and Kondo [L. H. Yu et al., Phys. Rev. Lett. 93, 266802 (2004)] regimes. In the Kondo regime, our results show that one peak at $E=\mu$ can be observed in the density of states at low temperatures (0.0026 eV ≤ k_BT ≤ 0.0000026 eV). Also, the real part of ∑₃ has one minimum peak at $E=-\mu$ and the real par of ∑₂ has one maximum peak at $E=-\mu$ for 0.01 ≤ μ ≤ 0.07 in the Kondo regime at low temperatures.     

On the redox reactions between allyl radicals and NOx

NO_x mitigation is a central focus of combustion technologies with increasingly stringent emission regulations. NO_x can also enhance the autoignition of hydrocarbon fuels and can promote soot oxidation. The reaction between allyl radical (C₃H₅) and NO_x plays an important role in the oxidation kinetics of propene. In this work, we measured the absolute rate coefficients for the redox reaction between C₃H₅ and NO_x over the temperature range of 1000–1252 K and pressure range of 1.5–5.0 bar using a shock tube and UV laser absorption technique. We produced C₃H₅ by shock heating of C₃H₅I behind reflected shock waves. Using a Ti:Sapphire laser system with frequency quadrupling, we monitored the kinetics of C₃H₅ at 220 nm. Unlike low-temperature chemistry, the two target reactions, C₃H₅ + NO → products (R1) and C₃H₅ + NO₂ → products (R2), exhibited a strong positive temperature dependence for this radical-radical type reaction. However, these reactions did not show any pressure dependence over the pressure range of 1.5–5.0 bar, indicating that the measured rate coefficients are close to the high-pressure limit. The measured values of the rate coefficients resulted in the following Arrhenius expressions (in unit of cm³/molecule/s):$k_1\left({\mathrm{C}}_3{\mathrm{H}}_5+\text{NO}\right)=1.49\times {10}^{?10}\exp \left(?6083.6\frac{\mathrm{K}}{T}\right)\left(1017?1252K\right)$$k_2\left({\mathrm{C}}_3{\mathrm{H}}_5+\mathrm{N}{\mathrm{O}}_2\right)=1.71\times {10}^{?10}\exp \left(?3675.7\frac{\mathrm{K}}{T}\right)\left(1062?1250K\right)$To our knowledge, these are the first high-temperature measurements of allyl + NO_x reactions. The reported data will be highly useful in understanding the interaction of NO_x with resonantly stabilized radicals as well as the mutual sensitization effect of NO_x on hydrocarbon fuels.     

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

The exact solvability and impressive pedagogical implementation of the harmonic oscillator's creation and annihilation operators make it a problem of great physical relevance and the most fundamental one in quantum mechanics. So would be the position-dependent mass (PDM) oscillator for the PDM quantum mechanics. We, hereby, construct the PDM creation and annihilation operators for the PDM oscillator via two different approaches. First, via von Roos PDM Hamiltonian and show that the commutation relation between the PDM creation ${\hat{A}}^{+}$ and annihilation $\hat{A}$ operators, $[\hat{A},{\hat{A}}^{+}]=1\iff \hat{A}{\hat{A}}^{+}-1/2={\hat{A}}^{+}\hat{A}+1/2$, not only offers a unique PDM-Hamiltonian ${\hat{H}}_1$ but also suggests a PDM-deformation in the coordinate system. Next, we use a PDM point canonical transformation of the textbook constant mass harmonic oscillator analog and obtain yet another set of PDM creation ${\hat{B}}^{+}$ and annihilation $\hat{B}$ operators, hence an “apparently new” PDM-Hamiltonian ${\hat{H}}_2$ is obtained. The “new” PDM-Hamiltonian ${\hat{H}}_2$ turned out to be not only correlated with ${\hat{H}}_1$ but also represents an alternative and most simplistic user-friendly PDM-Hamiltonian, $\hat{H}={(\hat{p}/\sqrt{2m\left(x\right)})}^2+V\left(x\right)$; $\hat{p}=-iħ{\partial }_x$, that has never been reported before.