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In this paper, we present some monotonicity rules for the ratio of two power series $x\mapsto \sum_{k=0}^\infty a_k x^k / \sum_{k=0}^\infty b_k x^k$ under the assumption that the monotonicity of the sequence ${a_k/b_k}$ changes twice. Additionally, we introduce a local monotonicity rule in this paper.

The main objective of this paper is to establish the $Y$-function and L'Hospital-type monotonicity rules with nabla and diamond-alpha derivatives on time scales.

The variance of quantum channels involving a mixed state gives a hybrid of classical and quantum uncertainties. We seek certain decomposition of variance into classical and quantum parts in terms of the Wigner-Yanase skew information. Generalizing the uncertainty relations for quantum observables to quantum channels, we introduce a new quantity with better quantum mechanical nature to describe the uncertainty relations for quantum channels. We derive several uncertainty relations for quantum channels via variances and the Wigner-Yanase skew information., Comment: 11 pages, 1 figure

As an efficient mathematical tool, monotonicity rules play an extremely crucial role in the real analysis field. In this paper, we explore some monotonicity rules for quotient of Delta, Nabla and Diamond-Alpha integrals with variable upper limits and parameters on time scales, respectively. Moreover, we consider the monotonicity rules for quotient of the product of multiple Delta integrals with parameters on time scales. Power series is also concerned for being a special case of integral with parameters on time scales.

In this paper, we investigate the monotonicity of the functions $t \mapsto \frac{\sum_{k=0}^\infty a_k w_k(t)}{\sum_{k=0}^\infty b_k w_k(t)}$ and $x \mapsto \frac{\int_\alpha^\beta f(t) w(t,x) \textrm{d} t}{\int_\alpha^\beta g(t) w(t,x) \textrm{d} t}$, focusing on case where the monotonicity of $a_k/b_k$ and $f(t)/g(t)$ change once. The results presented also provide insights into the monotonicity of the ratios of two power series, two $\mathcal{Z}$-transforms, two discrete Laplace transforms, two discrete Mellin transforms, two Laplace transforms, and two Mellin transforms. Finally, we employ these monotonicity rules to present several applications in the realm of special functions and stochastic orders., Comment: 15 pages

Here we study the quark orbital angular momentum of the ground octet baryons employing an extended chiral constituent quark model, within which the baryon wave functions are taken to be superposition of the traditional $qqq$ and the $qqqq\bar{q}$ higher Fock components. Coupling between the two configurations is estimated using the $^3P_{0}$ quark-antiquark creation mechanism, and the corresponding coupling strength is determined by fitting the sea flavor asymmetry of the nucleon. The obtained numerical results show that the quark angular momentum of the nucleon, $\Sigma$, $\Lambda$ and $\Xi$ hyperons are in the range $0.10$-$0.30$. In addition, the quark angular momentum of all the hyperons are a little bit smaller than that of the nucleon. And the octet baryons spin fractions taken by the intrinsic quark orbital angular momentum could be up to $60\%$ in present model., Comment: 9 pages, 3 figures, 3 tables

The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We establish a series of parameterized uncertainty relations in terms of the parameterized norm inequalities, which improve the exiting variance-based uncertainty relations. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is a common eigenvector of all the observables. Detailed examples are provided to illustrate the tightness of our uncertainty relations., Comment: 13 pages, 3 figures

Understanding the mechanisms and spatial correlations of crystallographic symmetry breaking in ferroelectric materials is essential to tuning their functional properties. While optical second harmonic generation (SHG) has long been utilized in ferroelectric studies, its capability for probing complex polar materials has yet to be fully realized. Here, we develop a SHG spectral imaging method implemented on a home-designed laser-scanning SHG microscope, and demonstrate its application for a model system of (K,Na)NbO3 single crystals. Supervised model fitting analysis produces comprehensive information about the polarization vector orientations and relative fractions of constituent domain variants as well as their thermal evolution across the polymorphic phase transitions. We observe an unexpected persistence of the orthorhombic phase at low temperatures, pointing to the phase competitions. Besides, we show that unsupervised matrix decomposition analysis can quickly and faithfully reveal domain configurations without a priori knowledge about specific material systems. The SHG spectral imaging method can be readily extended to other ferroelectric materials with potentials to be further enhanced., Comment: 16 pages, 4 figures

Fano effect arising from interference between two dissipation channels to the radiation continuum enables to tune the photon statistics. Understanding the role of Fano effect and exploiting to achieve strong photon correlations are of both fundamental and applied significance. We present an analytical description of Fano-enhanced photon correlations based on cavity quantum electrodynamics to show that, the Fano effect in atom-cavity systems can improve the degree of antibunching by over four orders of magnitude. The enhancement factors and the optimal conditions are explicitly given, and found related to the Fano parameter $q$. Remarkably, the Fano enhancement manifests robustness against the decoherence processes, and can survive in the weak coupling regime. We expect our work to provide insight in tuning the photon statistics through Fano effect, which offers a new route to enhance the photon correlations, as well as the possibility of generating nonclassical light in a wider diversity of systems without the need of strong light-matter interaction., Comment: 6 pages, 3 figures

The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner-Yanase-Dyson skew information and the quantum Fisher information are the special cases of the metric-adjusted skew information corresponding to different Morozova-Chentsov functions, our results generalize some existing uncertainty relations. Detailed examples are given to illustrate the advantages of our methods., Comment: 14 pages, 3 figures

We investigate the single-photon blockade (1PB) in the quasichiral regime of atom-photon interaction that mediates via dissipative environment, where the effective atom-photon interaction is asymmetrical but achiral. The synthetic magnetic current in the closed-loop coupling breaks down the reciprocity of atom-photon interaction, resulting in an asymmetrical and even completely unidirectional effective coupling between two selected quantum states. As an example, we couple the single-atom cavity-QED (cQED) system to a strongly dissipative auxiliary cavity. We find that in the quasichiral regime, the unconventional photon blockade (UPB) always incorporates with the conventional photon blockade (CPB) in the condition of maximum chirality. Furthermore, we show that 1PB in the quasichiral regime combines the advantages of UPB and CPB, demonstrating the perfect single-photon purity, higher efficiency, smooth time dynamics as well as lower requirement of modes coupling to achieve UPB. Our work paves the way for 1PB towards practical applications and reveals the intriguing quantum-optics phenomena in the quasichiral light-matter interaction., Comment: 9 pages, 6 figures

Uncertainty principle plays a vital role in quantum physics. The Wigner-Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum channels to arbitrary N quantum channels based on Wigner-Yanase skew information. We illustrate that these uncertainty inequalities are tighter than the existing ones by detailed examples. Especially, we also discuss the uncertainty relations for N unitary channels, which could be regarded as variance-based sum uncertainty relations with respect to any pure state., Comment: 12 pages, 2 figures

Flexoelectricity (coupling between polarization and strain gradients) is a property of all dielectric materials that has been theoretically known for decades, but it is only relatively recently that it has begun to attract experimental attention. As a consequence, there are still entire families of materials whose flexoelectric performance is unknown. This is the case, for example, of antiferroelectrics: materials with an antipolar but switchable arrangement of dipoles. And yet, these materials could be flexoelectrically relevant because it has been hypothesised that the origin of their antiferroelectricity might be flexoelectric. In this work, we have measured the flexoelectricity of two different antiferroelectrics (PbZrO3 and AgNbO3) as a function of temperature, up to and beyond their Curie temperature. Neither flexoelectricity nor the flexocoupling coefficients are anomalously high, but the flexocoupling shows a sharp peak at the antiferroelectric phase transition., Comment: 12 pages, 3 figures

Let $f$ and $g$ be both continuous functions on $\left( 0,\infty \right) $ with $g\left( t\right) >0$ for $t\in \left( 0,\infty \right) $ and let $ F\left( x\right) =\mathcal{L}\left( f\right) $, $G\left( x\right) =\mathcal{L }\left( g\right) $ be respectively the Laplace transforms of $f$ and $g$ converging for $x>0$. We prove that if there is a $t^{\ast }\in \left( 0,\infty \right) $ such that $f/g$ is strictly increasing on $\left( 0,t^{\ast }\right) $ and strictly decreasing on $\left( t^{\ast },\infty \right) $, then the ratio $F/G$ is decreasing on $\left( 0,\infty \right) $ if and only if \begin{equation*} H_{F,G}\left( 0^{+}\right) =\lim_{x\rightarrow 0^{+}}\left( \frac{F^{\prime }\left( x\right) }{G^{\prime }\left( x\right) }G\left( x\right) -F\left( x\right) \right) \geq 0, \end{equation*} with \begin{equation*} \lim_{x\rightarrow 0^{+}}\frac{F\left( x\right) }{G\left( x\right) } =\lim_{t\rightarrow \infty }\frac{f\left( t\right) }{g\left( t\right) }\text{ \ and \ }\lim_{x\rightarrow \infty }\frac{F\left( x\right) }{G\left( x\right) }=\lim_{t\rightarrow 0^{+}}\frac{f\left( t\right) }{g\left( t\right) } \end{equation*} provide the indicated limits exist. While $H_{F,G}\left( 0^{+}\right) <0$, there is at leas one $x^{\ast }>0$ such that $F/G$ is increasing on $\left( 0,x^{\ast }\right) $ and decreasing on $\left( x^{\ast },\infty \right) $. As applications of this monotonicity rule, a unified treatment for certain bounds of psi function is presented, and some properties of the modified Bessel functions of the second are established. These show that the monotonicity rules in this paper may contribute to study for certain special functions because many special functions can be expressed as corresponding Laplace transforms., Comment: 24 pages

In this paper, we present a very accurate approximation for gamma function: \begin{equation*} \Gamma \left( x+1\right) \thicksim \sqrt{2\pi x}\left( \dfrac{x}{e}\right) ^{x}\left( x\sinh \frac{1}{x}\right) ^{x/2}\exp \left( \frac{7}{324}\frac{1}{ x^{3}\left( 35x^{2}+33\right) }\right) =W_{2}\left( x\right) \end{equation*} as $x\rightarrow \infty $, and prove that the function $x\mapsto \ln \Gamma \left( x+1\right) -\ln W_{2}\left( x\right) $ is strictly decreasing and convex from $\left( 1,\infty \right) $ onto $\left( 0,\beta \right) $, where \begin{equation*} \beta =\frac{22\,025}{22\,032}-\ln \sqrt{2\pi \sinh 1}\approx 0.00002407. \end{equation*}, Comment: 9 pages

In this paper, we develop Windschitl's approximation formula for the gamma function to two asymptotic expansions by using a little known power series. In particular, for $n\in \mathbb{N}$ with $n\geq 4$, we have \begin{equation*} \Gamma \left( x+1\right) =\sqrt{2\pi x}\left( \tfrac{x}{e}\right) ^{x}\left( x\sinh \tfrac{1}{x}\right) ^{x/2}\exp \left( \sum_{k=3}^{n-1}\tfrac{\left( 2k\left( 2k-2\right) !-2^{2k-1}\right) B_{2k}}{2k\left( 2k\right) !x^{2k-1}} +R_{n}\left( x\right) \right) \end{equation*} with \begin{equation*} \left| R_{n}\left( x\right) \right| \leq \frac{\left| B_{2n}\right| }{2n\left( 2n-1\right) }\frac{1}{x^{2n-1}} \end{equation*} for all $x>0$, where $B_{2n}$ is the Bernoulli number. Moreover, we present some approximation formulas for gamma function related to Windschitl's approximation one, which have higher accuracy., Comment: 14 pages

Based upon projected local density of states (PLDOS) for photons, we develop a local coupling theory to simultaneously treat the weak and strong interaction between a quantum emitter and photons in arbitrary nanostructures. The PLDOS is mapped by an extremely flexible and efficient method. The recent experiment observation for the photonic crystal slabs is very well interpreted by our ab-initio PLDOS. More importantly, a bridge linking the PLDOS and cavity quantum electrodynamics is for the first time established to settle quality factor, g factor and vacuum Rabi splitting. Our work greatly enriches the knowledge about the interaction between light and matter in nanostructures., Comment: 13 pages, 3 figures

Infrared spectroscopic techniques can provide a vital probe of the superconducting energy gap which is one of the most fundamental physical properties of superconductors. Currently, the central questions regarding the optical properties of superconductors are how the energy gap can be measured by infrared techniques and at which frequency the gap exists. An effective infrared spectroscopic method to investigate the superconducting energy gap, Eg, was developed by using the Bomem DA 3.01 Fourier Transformation Spectrophotometer. The reflectivity of a superconducting thin film of YBaCuO deposited on SrTiO3 was measured. A shoulder was observed in the superconducting state reflectance R(sub S) at 480/cm. This gives a value of Eg/kT(sub c) = 7.83, where k is the Boltzmann constant and T(sub c) is the superconducting transition temperature, from which, it is suggested that YBaCuO is a very strong coupling superconductor.