Asymptotic behavior of two-electron expectation values in two-electron excited states

Singly-excited states of the two-electron atom cease being bound when $Z\to 1$ (from above), the outer orbital becoming infinitely diffuse. The asymptotic relations$\underset{Z\to 1}{\lim }?{(Z?1)}^k〈{(1sns)}^{1,3}S\left|r_{12}^k\right|{(1sns)}^{1,3}S〉=〈(n?1)s^{(0)}\left|r^k\right|(n?1)s^{(0)}〉,$ where $k=?1,1,2,3,?$, are demonstrated to hold. Here, $(n?1)s^{(0)}$ is a hydrogenic s orbital with principal quantum number $(n?1)$. New, more nuanced light is shed on the already challenged dogma that the Pauli principle keeps the electrons further apart in the triplet than in the corresponding singlet.     

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.     

Duality between the SU(2) lattice gauge model and bosonic t − J model

We investigate the duality between the $SU(2)$ lattice gauge model and the bosonic $t-J$ model. We construct the relations between the gauge field operators and particle operators, and map the low-energy regime of the $SU(2)$ lattice gauge model to a $U(1)$ bosonic $t-J$ model coupled with a $U(1)$ gauge field. The mapped model can be interpreted as a bosonic $t-J$ model with particle-hole symmetry, or a mean-field form of the bosonic $t-J$ model with the coexistence of a two-particle pairing and four particle-pairing. The duality between the lattice gauge model and the bosonic $t-J$ model provides a direct connection between gauge theory and strongly correlated systems.     

Experimental determination of interfacial energy for solid Al in the Al-Sn-Mg eutectic system with Bridgman-type apparatus

The equilibrated grain boundary groove shape of solid Al in equilibrium with Al-Sn-Mg eutectic liquid was observed by using a Bridgman type directional solidification apparatus. The ratio of the thermal conductivity of the equilibrated liquid to the thermal conductivity of solid Al has been obtained as 0.91. In addition, the average Gibbs-Thomson coefficient, $\bar{\mathrm{\Gamma }}=(4.20\pm 0.35)\times {10}^{-8}\mathrm{Km}$, the solid-liquid interfacial energy, ${\sigma }_{SL}=180.68\pm 23.48\text{mJ}/{\text{m}}^2$ and the grain boundary energy, ${\sigma }_{GB}=309.30\pm 29.47\text{mJ}/{\text{m}}^2$, in the Al/Al-Sn-Mg system have been calculated from the measured grain boundary shapes.     

Investigating the thermoelectric properties of Na0.74Co1−xNbxO2 (x = 0.05,0.10) at high temperature region

Here, the thermoelectric (TE) properties of Na_0.74Co${}_{1-x}$Nb_xO₂ ($x=0.05,0.10$) compounds are investigated experimentally and computationally. The experimental measurements are conducted in $300-620$ K. Positive sign of Seebeck coefficient for both the compounds indicates the dominating p-type character. The maximum experimental values of ZT are observed as ∼ 0.12 and ∼ 0.19 at 620 K for $x=0.05$ and $x=0.10$, respectively. The experimental transport properties of these compounds are understood by employing spin-polarized GGA+U (= 4 eV) electronic structure calculations on $x=0.0625$ compound. On the basis of best experimental and computational matching of transport properties, we have estimated ZT till 1200 K computationally. The highest calculated values of ZT are ∼ 1.36 and ∼ 1.22 at 1200 K for $x=0.05$ and $x=0.10$, respectively. The optimum value of efficiency for $x=0.05$ is calculated as ∼ 6.4%, whereas it reaches ∼ 7.5% for $x=0.10$.     

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.     

Novel electron holes of Gaussian type due to second order,non-perturbative electron trapping and the general loss of identifiability of hole structures in experiments

A second order non-perturbative trapping scenario is employed to show the existence of a new Gaussian type of solitary electron holes. Use is thereby made of Schamel's pseudo-potential method, the only method that can guarantee the completeness of an equilibrium solution of the Vlasov-Poisson system in addition to its existence. The new potential is of the form $e^{-X{(x)}^2}$ where $X(x)=sinh(x)$ and is hence reminiscent of the Gaussian potential appearing in its “second generation”. The simultaneous presence of both trapping generations hence establishes a one-parametric continuum spectrum of solitary electron holes all of them being, through appropriate fitting, potential candidates for identifying structures in experimental observations and numerical simulations. Taking into account the possibility of many more trapping scenarios moreover, a unique identification of structures, the desired goal expressed in the current literature when interpreting structure formation, is therefore not achievable. Origin of this intrinsic ambiguity is the loss of mathematical stringency in the kinetic regime through chaos triggered by the ergodic particle trajectories in the resonant region of phase space in the single particle – coherent wave interaction process.     

Fractional spin-vortex states in F = 2 spinor Bose-Einstein condensates

Stable fractional vortices are numerically generated in the two-dimensional rotating $F=2$ spinor Bose-Einstein condensates. We demonstrate the existence of $\frac{1}{4}$-vortex state or $\frac{1}{2}$-vortex state in the biaxial nematic phase, and $\frac{1}{3}$-vortex state in the cyclic phase. At fast rotation a lattice of fractional vortex in the spin space emerges. Intriguingly, the integral spin-winding of the whole system does not increase with the rotation speed but equals to a simple fraction.     

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.