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.     

Study of the q-Gaussian distribution with the scale index and calculating entropy by normalized inner scalogram

In this paper, we discuss a method based on wavelet analysis for the study of the q-index of the Gaussian distribution. We derive q-index from the scale index, $i_{\mathit{scale}}$, using the expression; $q\equiv 1+2i_{\mathit{scale}}$ where $i_{\mathit{scale}}$ is a wavelet based tool for measuring the degree of aperiodicity of a dynamical system in the range of $0\le i_{\mathit{scale}}\le 1$. We show that this expression gives consistent results with the numerical approach of q-Gaussian distribution which determines the degree of non-extensivity of a dynamical system in the range of $1<q<3$. We also suggest a new entropy calculation method based on the normalized inner scalogram for studying the chaotic characteristics of nonlinear dynamical systems.     

Glauber gluons in annihilation amplitudes for heavy meson decays

We investigate the Glauber divergences in nonfactorizable annihilation amplitudes for two-body hadronic heavy meson decays in the $k_T$ factorization theorem at one-loop level. These divergences can be absorbed into the Glauber factors in the dominant kinematic regions of small parton momenta, which modify the interference between a nonfactorizable annihilation amplitude and other amplitudes by rotating it with a phase. We postulate that only the Glauber effect associated with a pion is significant, due to its special role as a $q\bar{q}$ bound state and as a pseudo Nambu–Goldstone boson simultaneously. It is elaborated that the data of the $D\to \pi \pi$ and $\pi K$ branching ratios have revealed prominent Glauber effects. This work provides a solid theoretical ground for the factorization-assisted topological-amplitude parametrization of two-body hadronic $D$ meson decays.     

Moment of inertia of superconductors

We find that the bulk moment of inertia per unit volume of a metal becoming superconducting increases by the amount $m_e/(\pi r_c)$, with $m_e$ the bare electron mass and $r_c=e^2/m_e{c}^2$ the classical electron radius. This is because superfluid electrons acquire an intrinsic moment of inertia $m_e{(2{\lambda }_L)}^2$, with ${\lambda }_L$ the London penetration depth. As a consequence, we predict that when a rotating long cylinder becomes superconducting its angular velocity does not change, contrary to the prediction of conventional BCS-London theory that it will rotate faster. We explain the dynamics of magnetic field generation when a rotating normal metal becomes superconducting.     

Modeling the non-Arrhenius ignition behavior of 2‐butanol: A detailed theoretical and experimental study

2-butanol is a promising alternative to fossil fuels for which production pathways are already established and which was proven to be suitable for usage within modern internal combustion engines. It is a potential octane booster for gasoline fuels, can be used in diesel engines to reduce soot production, and is applicable as a stand-alone fuel. In the present study, the previously not discussed non-Arrhenius ignition behavior of 2-butanol was revealed by recalculating and adjusting the thermodynamic properties of the fuel and its most important radicals. All relevant fuel consumption reaction rate coefficients were replaced by a consistent set of analogies without any further modifications of the rate parameters. The existing spectrum of validation targets for 2-butanol was extended by new high-pressure Rapid Compression Machine (RCM) experiments for end-of-compression pressures of $p_{eoc}$ =  20, 30, 40, and 50 bar with high resolution of temperature to highlight the non-Arrhenius ignition behavior and to study the model performance in more detail. The kinetic model proposed in the present study can reproduce the observed non-Arrhenius behavior within the RCM regime. Kinetic analysis demonstrated that simulated Ignition Delay Times (IDTs) are very sensitive to the equilibria of the $\stackrel{.}{\text{R}}$ + ${\text{O}}_2$ reactions for all 2-hydroxybutyl radicals. With the newly determined thermodynamic properties, the equilibria of the $\stackrel{.}{\text{R}}$ + ${\text{O}}_2$ reactions are moved towards lower temperatures, enabling low-temperature chain branching. The shift of the equilibrium from the R${\stackrel{.}{\text{O}}}_2$ side to $\stackrel{.}{\text{R}}$ + ${\text{O}}_2$ within the temperature regime covered by the RCM experiments could be identified as the main reason for the observed non-Arrhenius behavior.     

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.     

An existence of universality in the dynamics of two types of glass-forming liquids - fragile liquids and strong liquids

By employing a simplified nonlinear memory function proposed recently by the present author, a universal equation for a collective-intermediate scattering function derived based on the time-convolutionless mode-coupling theory is numerically solved to study the dynamics of glass-forming liquids. The numerical calculation is done based on the simulation results performed on two types of liquids, fragile liquids and strong liquids. Those are then shown to be uniquely determined by the long-time collective diffusion coefficient $D(q_m)$, where $q_m$ is a first peak position of a static structure factor for a whole system. Thus, there exists such a universality that there is only one solution for different liquids of a same type at a given value of D. This may be consistent with the fact that strong liquids are structurally quite different from fragile liquids. Finally, it is emphasized that such a universality must be helpful to predict $q_m$ from experimental data.     

True spin and pseudo spin entanglement around Dirac Points in graphene with Rashba spin–orbit interaction

We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin–orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the $\delta \overrightarrow{k}$-contour. Due to the spin–orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin–orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum $\overrightarrow{k}$ is independent of the Rashba coupling strength.