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.     

Graphdiyne-actinyl complexes as potential catalytic materials: A DFT perspective from their structural,bonding, electronic and redox properties

Versatile graphdiyne (GDY) substrate has been modified by numerous transition metals and resulting composites showed excellent photo/electro-catalytic performance. However, GDY materials modified by actinides that are stockpiled waste product due to large-scale use in nuclear industry, are particularly scarce and remains great challenge. To deeply understand the structural properties, GDY complexating actinyl (An^mO₂)ⁿ⁺ (An = U, Np, Pu; m = VI, V) species with its atomistic pore was investigated by relativistic density functional theory (DFT). The GDY pore was found suitable to hold actinyl species, by forming organometallic AnC dative bonds. This chemical coupling interaction was further confirmed by quantum theory of atoms-in-molecule and electronic structure calculations. The GDY-uranyl(V), for instance, shows a π(UC) bonding HOMO, which is anticipated to improve electron transfer between ligand and metal. Orbital structures and compositions of complexes suggest their implication towards catalysis, which were further corroborated by calculations on redox potentials of GDY-actinyl complexes. Hence, our results show the potential applications of GDY complexating actinyl species towards novel catalytic surfaces.     

Hetero-Polar Sextuple Bond: A Relativistic Quantum Chemical Study**

Number of bonds formed by sharing an electron pair between two atoms is not restricted to one, it can go beyond four and six is the maximum. While homopolar sextuple bond in Mo₂ and W₂ has been reported, such a high bond order in heteropolar diatomics has remained elusive. In the pursuit of the sextuple bond in polar diatomics, the present study depicts the existence of such multiple bonds in Rhodium-Scandium hetero-diatom based on relativistic quantum chemical calculations. The bonding comprises of three normal electron sharing covalent bonds and three dative covalent bonds.     

Frequency ratios of Sr,Yb, and Hg based optical lattice clocks and their applications

This article describes the recent progress of optical lattice clocks with neutral strontium (⁸⁷Sr), ytterbium (¹⁷¹Yb) and mercury (¹⁹⁹Hg) atoms. In particular, we present frequency comparison between the clocks locally via an optical frequency comb and between two Sr clocks at remote sites using a phase-stabilized fibre link. We first review cryogenic Sr optical lattice clocks that reduce the room-temperature blackbody radiation shift by two orders of magnitude and serve as a reference in the following clock comparisons. Similar physical properties of Sr and Yb atoms, such as transition wavelengths and vapour pressure, have allowed our development of a compatible clock for both species. A cryogenic Yb clock is evaluated by referencing a Sr clock. We also report on an Hg clock, which shows one order of magnitude less sensitivity to blackbody radiation, while its large nuclear charge makes the clock sensitive to the variation of fine-structure constant. Connecting all three types of clocks by an optical frequency comb, the ratios of the clock frequencies are determined with uncertainties smaller than possible through absolute frequency measurements. Finally, we describe a synchronous frequency comparison between two Sr-based remote clocks over a distance of 15 km between RIKEN and the University of Tokyo, as a step towards relativistic geodesy.     

Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

Quantum-corrected finite entropy of noncommutative acoustic black holes

In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1$2+1$-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.     

氩原子和类氩离子相对论修正

以相对论修正哈密顿(包括质量修正、单体和双体达尔文修正、自旋-自旋接触相互作用)的球张量形式为基础, 借助不可约张量理论导出了类氩体系基态能量的相对论修正的解析表达式. 在斯莱特表象中完成了所有的角向积分和自旋求和计算, 能量的相对论修正式用径向矩阵元的线性组合来表示.对类氩体系基态能量的相对论修正值进行了具体计算,相对误差均小于0.0459%