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.     

Time-periodic quantum states of weakly interacting bosons in a harmonic trap

We consider quantum bosons with contact interactions at the Lowest Landau Level (LLL) of a two-dimensional isotropic harmonic trap. At linear order in the coupling parameter g, we construct a large, explicit family of quantum states with energies of the form $E_0+g{E}_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. Any superposition of these states evolves periodically with a period of $8\pi /g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ may become relevant. These quantum states provide a counterpart to the known time-periodic behaviors of the corresponding classical (mean field) theory.     

Resonance studies using the contour deformation method in the complex momentum plane

A contour deformation method (CDM) in the complex momentum plane has been successfully extended and implemented to probe resonances in atomic and molecular systems. Specifically, solution of the Schrödinger equation is performed in momentum space with momentum deformed on a contour in the complex plane. The bound, resonant, and complex continuum states could be directly revealed from the eigenvalues of the Schrödinger equation in the complex momentum plane. The calculations of shape resonances in electron scattering with Na⁺ in Debye plasmas (one channel), and in the charge transfer process ${\mathrm{H}}^{?}(1s^2)+\mathrm{Li}(1s^{2}2s)$ ($1^2{\Sigma }^{+}$) $\to \mathrm{H}(1s)+{\mathrm{Li}}^{?}(1s^{2}2s^2)$ ($2^2{\Sigma }^{+}$) (coupled channels) are given as illustrative examples. It is shown that calculated results from CDM agree very well with those extracted from the eigenphase sum of scattering theories. The effectiveness of CDM is also demonstrated by comparing its results with those obtained by the complex rotation scaling and exterior complex scaling methods. The convergence of CDM results can be obtained by increasing the momentum integration region and the number of integration points. The studied examples demonstrate that CDM could be a powerful tool for studies of resonances in complex atomic and molecular systems.     

Co-thickness and oxidation states effect on magnetic anisotropy in Co/MgO heterostructure

Interfacial magnetism and magnetic anisotropy constant ($K_i$) in Co/MgO heterostructure have been studied using ab-initio density functional calculations. It is found that interfacial Co spin magnetic moment shows a strong interdependence on Co-O bond lengths and a reasonable spin-polarization of ～80% is established as a function of Co layers. Our results revealed a saturated positive (out-of-plane) $K_i$ of +2.80 mJ/m² at ≥12 Co layers (～1.6 nm Co thickness), which is associated with orbital magnetic moment difference in [100] and [001] direction along with a strong hybridization between $d_{xy}$ and $d_{x^2?y^2}$ orbitals through orbital angular momentum operator $\stackrel{?}{L_z}$. Furthermore, it is shown that the $K_i$ magnitude almost remains constant and weakens in the case of under- and over-oxidations in the interfacial MgO and Co layers, respectively. Interestingly, $K_i$ improved for oxygen migrated interface due to enhanced $d_{xy}$ and $d_{x^2?y^2}$ orbitals coupling. The disordered interfaces stability is checked by analyzing the formation energy. Hence, the present findings disclose that the higher Co thickness in ordered Co/MgO structure supports to out-of-plane [001] (positive) $K_i$, which could be useful for its technological implementation in high-density magnetic data storage devices with high thermal stability.     

Comparison of information-theoretic products and inequalities for the lowest bound and unbound electronic states of H2+ based on exact calculation

A study of information-theoretic properties of molecular bond on the example of the ground (bound) $1s{\sigma }_g$ and the lowest excited (unbound) $2p{\sigma }_u$ states of H${}_2^{+}$ was conducted. Data about general information-theoretic measures, information products (Cramér-Rao, Fisher-Shannon information, and LMC complexity) and their inequalities in position and momentum spaces as a function of internuclear distance $R=0.2$–20 a.u. were obtained by an exact numerical calculation of the wave function. A systematic correlation between these information products was established. It was found that LMC complexity is most sensitive and detailed among these information products. A clear correlation between accuracy of determination of energy and information products in the simplest LCAO model compared to results of the exact calculation was observed.     

Thermalization of electron–positron plasma with quantum degeneracy

The non-equilibrium electron–positron–photon plasma thermalization process is studied using relativistic Boltzmann solver, taking into account quantum corrections both in non-relativistic and relativistic cases. Collision integrals are computed from exact QED matrix elements for all binary and triple interactions in the plasma. It is shown that in non-relativistic case (temperatures $k_{B}T\le 0.3m_e{c}^2$) binary interaction rates dominate over triple ones, resulting in establishment of the kinetic equilibrium prior to final relaxation towards the thermal equilibrium, in agreement with the previous studies. On the contrary, in relativistic case (final temperatures $k_{B}T\ge 0.3m_e{c}^2$) triple interaction rates are fast enough to prevent the establishment of kinetic equilibrium. It is shown that thermalization process strongly depends on quantum degeneracy in initial state, but does not depend on plasma composition.     

Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal,radiation and encapsulating shell damping at various excitation pressures

This study presents the fundamental equations governing the pressure dependent disipation mechanisms in the oscillations of coated bubbles. A simple generalized model (GM) for coated bubbles accounting for the effect of compressibility of the liquid is presented. The GM was then coupled with nonlinear ODEs that account for the thermal effects. Starting with mass and momentum conservation equations for a bubbly liquid and using the GM, nonlinear pressure dependent terms were derived for power dissipation due to thermal damping (Td), radiation damping (Rd) and dissipation due to the viscosity of liquid (Ld) and coating (Cd). The pressure dependence of the dissipation mechanisms of the coated bubble have been analyzed. The dissipated energies were solved for uncoated and coated 2–20 $\mathrm{\mu }\text{m}$ in bubbles over a frequency range of $0.25f_r-2.5f_r$ ($f_r$ is the bubble resonance) and for various acoustic pressures (1 kPa-300 kPa). Thermal effects were examined for air and C3F8 gas cores. In the case of air bubbles, as pressure increases, the linear thermal model looses accuracy and accurate modeling requires inclusion of the full thermal model. However, for coated C3F8 bubbles of diameter 1–8 $\mathrm{\mu }\text{m}$, which are typically used in medical ultrasound, thermal effects maybe neglected even at higher pressures. For uncoated bubbles, when pressure increases, the contributions of Rd grow faster and become the dominant damping mechanism for pressure dependent resonance frequencies (e.g. fundamental and super harmonic resonances). For coated bubbles, Cd is the strongest damping mechanism. As pressure increases, Rd contributes more to damping compared to Ld and Td. For coated bubbles, the often neglected compressibility of the liquid has a strong effect on the oscillations and should be incorporated in models. We show that the scattering to damping ratio (STDR), a measure of the effectiveness of the bubble as contrast agent, is pressure dependent and can be maximized for specific frequency ranges and pressures.     

Magnetic anisotropy of ferromagnetic metals in low-symmetry systems

We have constructed an analytic formula to treat the perpendicular magnetic anisotropy energy in ferromagnetic metals with low symmetry, such as $C_{4\mathrm{V}}$ and $C_{3\mathrm{V}}$. We find that the anisotropy energy is proportional to a part of the expectation values of the orbital angular momentum and magnetic dipole operator. Although the result is similar to the model proposed by Laan (1998) [2], we have derived a concrete expression for the spin-flip virtual excitation process term, which can be dominant in atoms with small magnetic moments and/or small exchange splitting. Pt monatomic layer with proximity-induced spin polarization grown on Fe is an example of this. Other multilayer systems such as Co/Pd and Co/Ni, and bilayer systems such as Fe(CoB)/MgO can be discussed similarly. Moreover, the relation between perpendicular magnetic anisotropy energy and measurable physical parameters is discussed based on X-ray magnetic circular dichroism spectroscopy.     

An alternative form of Hooge's relation for 1/f noise in semiconductor materials

Single quantum dots and other materials exhibit irregular switching between on and off states; these on–off states follow power-law statistics giving rise to 1/f noise. We transfer this phenomenon (also referred to as on–off intermittency) to the generation and recombination (= g–r) process in semiconductor materials. In addition to g–r noise we obtain 1/f noise that can be provided in the form of Hooge's relation. The predicted Hooge coefficient is ${\alpha }_H={\alpha }_X{\alpha }_{im}$ whereby ${\alpha }_X$ depends on the parameters of the g–r noise and ${\alpha }_{im}$ on the parameters of the intermittency. Due to the power-law distribution of the on-times, the coefficient ${\alpha }_{im}$ shows a smooth dependence on time t. We also suggest an alternative form of Hooge's 1/f noise formula relating the 1/f noise to the number of centers (such as donor or trap atoms) rather than to the number of charge carriers as defined by Hooge.     

Spin-orbital coupling and magnetic properties of Ir-based double perovskites with different 5dn (n = 3, 4, 5) states

We have investigated the spin and orbital moments of Ir-based double perovskites with $5d^n$ (n = 3, 4, 5) states by local spin-density approximation with spin-orbital coupling and Hubbard correlation (LSDA+SOC+U). Our calculations reveal that the ratio of orbital to spin momentum $L_z/S_z$ approaches to certain values for the double perovskites with different 5dⁿ (n = 3, 4, 5) shell fillings. Based on d orbits, a spin-orbital coupling model with exchange splitting is proposed and it can well describe the ratio of angular momentums for the compounds. Our model calculations reveal that $L_z/S_z$ is determined by the exchange splitting, spin-orbital coupling as well as the state of shell filling. Our model is well corroborated by the experiments and density-functional calculations.