Momentum Eigensolutions of Feinberg-Horodecki Equation with Time-Dependent Screened Kratzer-Hellmann Potential

We obtain an approximate value of the quantized momentum eigenvalues, Pn, together with the space-like coherent eigenvectors for the space-like counterpart of the Schrödinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.

Photodetachment dynamics of H^- ion in a harmonic potential plus a time-dependent oscillating electric field

The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cross section of this system is put forward. It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength, but oscillates complicatedly when the oscillating electric field strength turns strong. In addition, the frequency of the harmonic potential and the oscillating electric field （the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper, unless otherwise stated.） can also affect the photodetachment dynamics of this system. With the increase of the frequency in the harmonic potential and the oscillating electric field, the number of the closed orbits for the detached electrons increased, which makes the oscillatory structure in the photodetachment cross section much more complex. Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint. This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.

Solution of Dirac Equation with the Time-Dependent Linear Potential in Non-Commutative Phase Space

In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation is presented by Lewis-Riesenfield invariant method.

Negative Phase Time Effectin Potential-Well Passing

The properties of phase time taken for particles to pass through a quantum potential well are investigated. It is found in a 1 dimensional quantum mechanical problem that the phase time is negative when the incident energy and the thickness of potential well satisfy certain conditions. Similar results are also found in a 2 dimensional fully relativistic optical analog. It is shown that the expression of the la teral shift of transmitted optical waves is similar to that of the phase time in the 1 dimensional quantum mechanical problem. The phase time in the 2 dimensional optical problem is also shown to be negative under certain conditions.

Feinberg-Horodecki Exact Momentum States of Improved Deformed Exponential-Type Potential

We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponential-type potential with its momentum eigenvalues for few quantized states against the screening parameter.

A Generalized Gibbs Potential Model for Materials Degradation

It is well known that work done on a material by conservative forces (electrical, mechanical, chemical) will increase the Gibbs Potential of the material. The increase in Gibbs Potential can be stored in the material and is free/available to do work at some later time. However, it will be shown in this paper that while in this state of higher Gibbs potential, the material is metastable and the material will degrade spontaneously/naturally with time in an effort to reach a lower Gibbs Potential. A generalized Gibbs Potential Model is developed herein to better understand its impact on a materials degradation rate. Special attention will be given to dielectrics degradation.

Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model

We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schrödinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.

含时线性Klein-Gordon方程的解

把K-G方程通过变量代换化简成对时间一阶求导的形式,即薛定谔方程的形式.然后运用不变量方法求解含时线性情况下K-G方程的解.并讨论2种相关的情况:相对论非含时和非相对论含时情况下解的形式.

Quantum dynamics of dissociative adsorption of H_2 and D_2:The time-dependent wave packet method

A time dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H 2 and D 2 on a flat and static surface. The molecule surface interaction is described using a modified London Eyring Polanyi Sato (LEPS) type potential for the H 2/Ni(100) system. The three dimensional (3 D) dissociation probabilities were calculated for different initial rovibrational states as a function of initial incident energies. Our results show that the dissociation of the diatomic rotational states whose quantum numbers satisfy j+m =odd is forbidden at low energies for the homonuclear H 2 and D 2 due to the selection rule. The effect of the rotational orientation of diatoms on adsorption predicts that the in plane rotation (m=j) is more favorable for dissociation than the out of plane rotation (m=0) . Enhanced dissociation for vibrationally excited molecules and the significant enhancement of the dissociation probability of H 2 when compared to D 2 were explained reasonably in terms of quantum mechanical zero point energies, the tunneling effect and the reflection from an activation barrier.

Modeling and Simulations in Symmetrical Supercapacitors Using Time Domain Mathematical Expressions

This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of constant electric potential in time ε and the curve of the discharge process through two fixed resistors. The first resistor RCo is a control that aims to prevent sudden variations in the intensity of the electric current i1(t) present at the terminals of the electrochemical supercapacitor at the beginning of the charging process. The second resistor is the internal resistance RA of the ammeter used in the calculation of the intensity of the electric current i1(t) over time in the charging and discharging processes. The mathematical equations generated were based on a 2R(C + kUC(t)) electrical circuit model and allowed to simulate the effects of the potential-dependent capacitance (kUC(t)) on the charge and discharge curves and hence on the calculated values of the fixed capacitance C, the equivalent series resistance (ESR), the equivalent parallel resistance (EPR) and the electrical potential dependent capacitance index k.

Electron localization of linear symmetric molecular ion H3-(2＋)

Electron localization in the dissociation of the symmetric linear molecular ion H3-（2＋） is investigated. The numerical simulation shows that the electron localization distribution is dependent on the central frequency and peak electric field amplitude of the external ultrashort ultraviolet laser pulse. When the electrons of the ground state are excited onto the 2pσ-2Σu-＋ by a one-photon process, most electrons of the dissociation states are localized at the protons on both sides symmetrically. Almost no electron is stabilized at the middle proton due to the odd symmetry of the wave function. With the increase of the frequency of the external ultraviolet laser pulse, the electron localization ratio of the middle proton increases, for more electrons of the ground state are excited onto the higher 3pσ-2Σu-＋ ustate. 50.9% electrons of all the dissociation events can be captured by the middle Coulomb potential well through optimizing the central frequency and peak electric field amplitude of the ultraviolet laser pulse. Besides, a direct current（DC） electric field can be utilized to control the electron motions of the dissociation states after the excitation of an ultraviolet laser pulse, and 68.8% electrons of the dissociation states can be controlled into the middle proton.

Exploring the effect of aggregation-induced emission on the excited state intramolecular proton transfer for a bis-imine derivative by quantum mechanics and our own n-layered integrated molecular orbital and molecular mechanics calculations

We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonomethyl)-naphthalene-2-ol and 1-pyrenecarboxaldehyde. Especially, the density functional theory(DFT) and time-dependent density functional theory(TDDFT) methods for HNP monomer are introduced. Moreover, the "our own n-layered integrated molecular orbital and molecular mechanics"(ONIOM) method(TDDFT:universal force field(UFF)) is used to reveal the aggregation-induced emission(AIE) effect on the ESIPT process for HNP in crystal. Our results confirm that the ESIPT process happens upon the photoexcitation for the HNP monomer and HNP in crystal, which is distinctly monitored by the optimized geometric structures and the potential energy curves. In addition, the results of potential energy curves reveal that the ESIPT process in HNP will be promoted by the AIE effect. Furthermore, the highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) for the HNP monomer and HNP in crystal have been calculated. The calculation demonstrates that the electron density decrease of proton donor caused by excitation promotes the ESIPT process. In addition, we find that the variation of atomic dipole moment corrected Hirshfeld population(ADCH) charge for proton acceptor induced by the AIE effect facilitates the ESIPT process. The results will be expected to deepen the understanding of ESIPT dynamics for luminophore under the AIE effect and provide insight into future design of high-efficient AIE compounds.

一类带有时变系数的分数阶扩散方程解的爆破性

该文主要研究了一类带有时间系数的分数阶扩散方程初边值问题解的爆破性.采用位势阱理论,Nehari流形,凹凸性等方法,结合各种微分不等式技巧,分别证明了次临界初始能级,负初始能级和任意正初始能级的情况下解的爆破性,并且给出了爆破时间的上界估计.特别地,由于能量泛函和位势阱深与时变系数f(t)有关,所以在次临界初始能级的情况下,爆破时间的上界会随着时变系数f(t)的变化而变化.

一个保证波函数在含时的势场中幺正演化的算法

数值求解波函数的演化是量子力学研究的重要内容.很多数值算法针对不含时的势能而发展;然而有很多物理问题其势能是含时的,在这种情况下,以前发展的算法不能保证波函数幺正演化.为此,针对含时的势场发展了保证幺正演化的Crank-Nicolson算法,同时采用四阶精度的Numerov算法实现了高精度的空间离散差分.数值结果证明,这个新算法能保证波函数演化的幺正性和稳定性.

西秦岭北缘断裂破裂分段与地震危险性评估

根据最新地质考察和历史地震考证结果,西秦岭北缘断裂带从东到西可划分为宝鸡、天水、武山、漳县、黄香沟和锅麻滩共6个次级断裂段。上述断裂既具有单段破裂,又具有多段组合破裂的特征。利用时间相依的地震潜势概率评估方法,对这6个单段分别进行地震危险性概率评估,其中黄香沟段和漳县段发生单段破裂的可能性最大,天水段发生单段破裂的概率次之。若发生组合破裂,黄香沟段和漳县段组合破裂可能性大。同时,根据沿断裂带的b值扫描图像分析结果显示,黄香沟段和天水附近应力积累较高,这两个地区应是未来发生强震的主要段落,值得关注。

煤柱稳定性的时间相关性分析

利用最小势能原理,在分析了煤柱与顶板的相互关系以及煤柱受力状况后,建立了考虑顶板刚度及煤柱软化与流变特性的煤柱时间相关稳定性分析模型,引入煤岩体的蠕变本构关系,对煤柱的长期变形和稳定性进行了分析,得到了煤柱保持长期稳定的必要条件以及煤柱保持稳定的最小时间计算公式.在利用短壁开采方法控制地表沉陷的工程中,对煤柱变形与稳定性进行了预测,其结果与现场实测一致.

陇南市活断层地震危险性评估

在甘肃省陇南市活断层探测与地质填图研究的基础上,归纳了开展地震危险性评估所需的主要活动断裂的基本活动性参数;采用震级—破裂尺度关系、震级—频度关系等方法评估了陇南市相关断裂(带)的潜在最大震级和平均复发间隔;利用时间相依的地震潜势概率模型和泊松分布模型评估了各断裂或断层小区在未来50、100、200年内发生破坏性地震的概率。同时利用b值空间图像扫描的方法给出了研究区的b值图像,分析了高应力区的地震危险性。通过对以上结果的综合分析,结果表明盖山—迭山断裂或光盖山—迭山断层小区的西端表现为高应力累积区,且发生破坏性地震的概率较高,是未来危险程度较高的断裂段。。

现代引潮位质疑与调和分析方法评论

一些现代引潮位展开的潮波振幅中包含时间项 ,即振幅具有时间依赖性 ,它们不属于完全调和展开。由于潮波振幅的时间依赖性 ,振幅或发散或收敛 ,使得远离起始历元的潮波振幅变得毫无确定意义 ,不仅失去了坐标组合滤波的基础 ,而且使Venedikov调和分析方法的应用出现理论障碍 ,难以为用。按照平差变换理论 ,只有满秩变换 ,才能得到与原观测完全等价的平差结果。Venedikov调和分析方法中的数字滤波过程并非满秩变换 ,自然不能得到完全等价的平差结果。凡是预先采用数字滤波的调和分析方法 。

考虑板状颗粒间相互作用的黏土强度时效性的微观解释

为了探寻黏土强度时效性的微观机理,将时效强度与板状黏土颗粒搭接方式和相互作用势能联系起来,颗粒间的相互作用力使颗粒朝着势能较低的位置搭接,当颗粒间相互作用势能最低时,时效强度达到稳定值。提出了可考虑两板状颗粒间夹角θ和距离d影响的颗粒相互作用总势能公式,可用Zeta电位代替表面电位来计算势能,计算结果与实际情况相吻合。通过计算可知:①黏土时效强度与电解质浓度有很大关系,电解质浓度较低时(≤10^(-3)mol/L),两颗粒相互垂直时的总势能最低;电解质浓度较高时(≥10^(-1)mol/L),两颗粒相互平行时的总势能最低,时效强度几乎不变,甚至会减小;中间电解质浓度是过渡状态;②两黏土颗粒的稳定搭接方式主要是垂直和平行,两颗粒之间总会趋于向稳定搭接方式转化,这也是时效强度经历一定时间而达到稳定值的过程;③解释了黏土触变强度恢复的原因,即颗粒会一直趋于搭接强度最高的垂直稳定搭接。

一维时间周期势的量子隧穿

研究了一维时间周期势的量子隧穿,建立了周期势的两种物理模型,并分别在不同情况下对其进行理论研究和推导,证明了一维周期势下的量子隧穿可统一由一种模型处理.