An integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind

In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind.Comment: 10 page

Trigonometric protocols for shortcuts to adiabatic transport of cold atoms in anharmonic traps

Shortcuts to adiabaticity have been proposed to speed up the "slow" adiabatic transport of an atom or a wave packet of atoms. However, the freedom of the inverse engineering approach with appropriate boundary conditions provides thousands of trap trajectories for different purposes, for example, time and energy minimizations. In this paper, we propose trigonometric protocols for fast and robust atomic transport, taking into account cubic or quartic anharmonicities. The numerical results have illustrated that such trigonometric protocols, particular cosine ansatz, is more robust and the corresponding final energy excitation is smaller, as compared to sine trajectories implemented in previous experiments.Comment: 5 pages, 5 figure

Studying the D1DD_1D molecule in the Bethe-Salpeter equation approach

We study the possible bound states of the $D_1D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_1D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_1D$ molecule, whereas the interpretation of $Z_2^+(4250)$ as a $D_1D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^+(4250)$ does not.Comment: 17 pages, 6 figures, and 4 table

Calculation of divergent photon absorption in ultrathin films of a topological insulator

We perform linear and non-linear photon absorption calculations in topological insulator ultra-thin films on a substrate. Due to the unique band structure of the coupled topological surface states, novel features are observed for suitable photon frequencies, including a divergent edge singularity in one-photon absorption process and a significantly enhancement in two-photon absorption process. The resonanct frequencies can be controlled by tuning the energy difference and coupling of the top and bottom surface states. Such unique linear and nonlinear optical properties make ultra-thin films of topological insulators promising material building blocks for tunable high-efficiency nanophotonic devices.Comment: 6 pages, 3 figure

Theoretical Modeling of Tribochemical Reaction on Pt and Au Contacts: Mechanical Load and Catalysis

Micro-electro-mechanical system and nano-electro-mechanical system (MEMS and NEMS) transistors are considered promising for size-reducing and power-maximizing electronic devices. However, the tribopolymer which forms due to the mechanical load to the surface contacts affects the conductivity between the contacts dramatically. This is one of the challenging problems that prevent widespread practical use of these otherwise promising devices. Here, we use density functional theory (DFT) to investigate the mechanisms of tribopolymer formation, including normal mechanical loading, the catalytic effect, as well as the electrochemical effect of the metal contacts. We select benzene select as the background gas, because it is one of the most common and severe hydrocarbon contaminants. Two adsorption cases are considered: one is benzene on the reactive metal surface, Pt(111), and the other is benzene on the noble metal, Au(111). We demonstrate that the formation of tribopolymer is induced both by the mechanical load and by the catalytic effect of the contact. First, benzene molecules are adsorbed on the Pt surfaces. Then, due to the closure of the Pt contacts, stress is applied to the adsorbates, making the C-H bonds more fragile. As the stress increases further, H atoms are pressed close to the Pt substrate and begin to bond with Pt atoms. Thus Pt acts as a catalyst, accelerating the dehydrogenation process. When there is voltage applied across the contacts, the catalytic effect is enhanced by electrochemistry. Finally, due to the loss of H atoms, C atoms become more reactive and link together or pile up to form tribopolymer. By understanding these mechanisms, we provide guidance on design strategies for suppressing tribopolymer formation.Comment: 14 pages, 7 figure

Some Bernstein functions and integral representations concerning harmonic and geometric means

It is general knowledge that the harmonic mean $H(x,y)=\frac2{\frac1x+\frac1y}$ and that the geometric mean $G(x,y)=\sqrt{xy}\,$, where $x$ and $y$ are two positive numbers. In the paper, the authors show by several approaches that the harmonic mean $H_{x,y}(t)=H(x+t,y+t)$ and the geometric mean $G_{x,y}(t)=G(x+t,y+t)$ are all Bernstein functions of $t\in(-\min\{x,y\},\infty)$ and establish integral representations of the means $H_{x,y}(t)$ and $G_{x,y}(t)$.Comment: 19 page

Second Order Linear Energy Stable Schemes for Allen-Cahn Equations with Nonlocal Constraints

We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn equation with nonlocal constraints that preserves the total volume of each phase in a binary material system. The energy quadratization strategy is employed to derive the energy stable semi-discrete numerical algorithms in time. Solvability conditions are then established for the linear systems resulting from the semi-discrete, linear schemes. The fully discrete schemes are obtained afterwards by applying second order finite difference methods on cell-centered grids in space. The performance of the schemes are assessed against two benchmark numerical examples, in which dynamics obtained using the volumepreserving Allen-Cahn equations with nonlocal constraints is compared with those obtained using the classical Allen-Cahn as well as the Cahn-Hilliard model, respectively, demonstrating slower dynamics when volume constraints are imposed as well as their usefulness as alternatives to the Cahn-Hilliard equation in describing phase evolutionary dynamics for immiscible material systems while preserving the phase volumes. Some performance enhancing, practical implementation methods for the linear energy stable schemes are discussed in the end

Negative refraction index of the quantum lossy left-handed transmission lines affected by the displaced squeezed Fock state and dissipation

Quantum lossy left-handed transmission lines (LHTLs) are central to the miniaturized application in microwave band. This work discusses the NRI of the quantized lossy LHTLs in the presence of the resistance and the conductance in a displaced squeezed Fock state (DSFS). And the results show some novel specific quantum characteristics of NRI caused by the DSFS and dissipation, which may be significant for its miniaturized application in a suit of novel microwave devices.Comment: 11 pages,5 figure

Studying the bound state of the BKˉB\bar{K} system in the Bethe-Salpeter formalism

In this work, we study the $B\bar{K}$ molecule in the Bethe-Salpeter (BS) equation approach. With the kernel containing one-particle-exchange diagrams and introducing two different form factors (monopole form factor and dipole form factor) in the vertex, we solve the BS equation numerically in the covariant instantaneous approximation. We investigate the isoscalar and isovector $B\bar{K}$ systems, and we find $X(5568)$ cannot be a $B\bar{K}$ molecule