Hidden Quantum Effect in General Relativity

If the Planck length is chosen as the natural length scale of the Universe, the Penrose-Carter diagram associated with the classical gravitational collapse of a thin spherical shell of massless matter reveals, beyond and in agreement with the claimed non locality of the horizon, a quantum nature of the whole process.

Gedanken Experiment for Delineating the Regime for the Start of Quantum Effects, and Their End, Using Turok’s Perfect Bounce Criteria and Radii of a Bounce Maintaining Quantum Effects, as Delineated by Haggard and Rovelli

Haggard and Rovelli delineated an outer radius as to the range of quantum effects, which extends past the Schwartzshield radius. This is defined as 7/3 times the mass of the initial cosmological system. We also have a range of perturbative effects as delineated by Turok’s article which gives a range of values of for which second order perturbative terms in cosmological evolution may play a role, where we have second order perturbation terms for which . Right afterwards, there are no perturbative behavior and no perturbation if . This is the 2nd order term for perturbing term for GW (Gravitational wave) as denoted by , and near the “zero point” of cosmological expansion, and from there we determine the size of the quantum effects, i.e. when they initiate, the relevant initial entropy, so as to determine the radii of initial cosmology, so quantum gravity may initiate its activity, in our toy universe. The criteria of Turok is used to obtain the relevant mass, m, used in the initial radii so that it is 7/3 times the mass of the initial cosmological system. We use the “Criteria of Turok” to delineate the start of quantum gravity effects. Mass m is done via appealing to graviton mass, and that times initial entropy, which is commented upon in Equation (9).

Quantum Effect in the Mesoscopic RLC Circuits with a Source

The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of.the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.

Quantum Effects of Mesoscopic Inductance and Capacity Coupling Circuits

基于电的费用，非消散的 mesoscopicinductance 的有限差别的 Schroedinger 方程和能力联合电路的 discretenes 为一个 mesoscopic 电路使用量子论被完成。库仑封锁效果，被电的费用的组件引起，被学习。适当地在电路选择部件，有限差别的 Schroedinger 方程能在 prepresentation 被划分成二个 Mathieu 方程。与 WKBJ 方法，处于二个电路的扎根的状态的水流量变化是计算的。结果表演水流量二个电路的零点的变化是存在并且相关。

Quantum Effect in Mesoscopic Open Electron Resonator

The open electron resonator is a mesoscopic device that has attracted considerable attention due to its remarkable behavior:conductance oscillations.In this paper,using an improved quantum theory to mesoscopic circuits developed recently by Li and Chen,the mesoscopic electron resonator is quantized based on the fundamental fact that the electric charge takes discrete value.With presentation transformation and unitary transformation,the Schr(?)dinger equation becomes an standard Mathieu equation.Then,the detailed energy spectrum and wave functions in the system are obtained,which will be helpful to the observation of other characters of electron resonator.The average of currents and square of the current are calculated,the results show the existence of the current fluctuation,which causes the noise in the circuits,the influence of inductance to the noise is discussed.With the results achieved,the stability characters of mesoscopic electron resonator are studied firstly,these works would be benefit to the design and control of integrate circuit.

Quantum Effect in a Diode Included Nonlinear Inductance-Capacitance Mesoscopic Circuit

The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonic oscillator,due to diodesincluded in the circuit.In this paper,using the advanced quantum theory of mesoscopic circuits,which based on thefundamental fact that the electric charge takes discrete value,the diode included mesoscopic circuit is firstly studied.Schr(o|¨)dinger equation of the system is a four-order difference equation in (?) rep esentation.Using the extended perturbativemethod,the detail energy spectrum and wave functions are obtained and verified,as an application of the results,thecurrent quantum fluctuation in the ground state is calculated.Diode is a basis component in a circuit,its quantizationwould popularize the quantum theory of mesoscopic circuits.The methods to solve the high order difference equationare helpful to the application of mesoscopic quantum theory.

Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

基于电磁的相互作用和重力的相互作用的统一理论，一个为充电的迪拉克粒子在的运动的方程的非相对论的限制重力删除被学习。从从这 non-relativisticlimit 获得的 Schroedinger 方程，我们能看到古典牛顿的重力的潜力在 Schroedinger 方程作为潜力的部分出现，它能解释在奶牛实验发现的重力的阶段效果。并且因为这个牛顿的重力的潜力， theearth 的重力的领域里的一个量粒子可以形成一个引力联盟者绑使量子化的状态，它已经在实验被检测了。与重力的相互作用有关的阶段效果的三种不同类型在这篇论文被学习，并且这些阶段效果应该在一些天体物理学的过程是可见的。而且，在那里直接存在在 gravitomagnetic 之间联合这引起的领域和量纺纱，和放射联合能被用来直接在一颗星的表面上决定 thegravitomagnetic 地。

Quantum Effect on Elementary Process of Diffusion and Collective Motion of Brown Particles

The correlation between the Schrödinger equation and the diffusion equation revealed that the relation of material wave is not a hypothesis but an actual one valid in a material regardless of the photon energy. Using the relations of material wave and uncertain principle, the quantum effect on elementary process of diffusion is discussed. As a result, the diffusivity is obtained as a universal expression applicable to any problem of diffusion phenomena. The Gauss theorem in theory and the Kirkendall effect in experimentation reveal the necessity of the coordinate transformation for a diffusion equation. The mathematical method for solving an interdiffusion problem of many elements system is established. The phase shift of the obtained analytical solution indicates the correlation between the solutions of each diffusion equation expressed by a fixed coordinate system and by a moving coordinate system. Based on the coordinate transformation theory, some unsolved problems of diffusion theory are reasonably solved and also some new important findings are discussed in relation to matters in the existing diffusion theory.

Spin direction dependent quantum anomalous Hall effect in two-dimensional ferromagnetic materials

We propose a scheme for realizing the spin direction-dependent quantum anomalous Hall effect(QAHE)driven by spin-orbit couplings(SOC)in two-dimensional(2D)materials.Based on the sp^(3)tight-binding(TB)model,we find that these systems can exhibit a QAHE with out-of-plane and in-plane magnetization for the weak and strong SOC,respectively,in which the mechanism of quantum transition is mainly driven by the band inversion of p_(x,y)/p_(z)orbitals.As a concrete example,based on first-principles calculations,we realize a real material of monolayer 1T-SnN_(2)/PbN_(2)exhibiting the QAHE with in-plane/out-of-plane magnetization characterized by the nonzero Chern number C and topological edge states.These findings provide useful guidance for the pursuit of a spin direction-dependent QAHE and hence stimulate immediate experimental interest.

First-principles prediction of quantum anomalous Hall effect in two-dimensional Co2Te lattice

The quantum anomalous Hall effect(QAHE) has special quantum properties that are ideal for possible future spintronic devices. However, the experimental realization is rather challenging due to its low Curie temperature and small non-trivial bandgap in two-dimensional(2D) materials. In this paper, we demonstrate through first-principles calculations that monolayer Co2Te material is a promising 2D candidate to realize QAHE in practice. Excitingly, through Monte Carlo simulations, it is found that the Curie temperature of single-layer Co2Te can reach 573 K. The band crossing at the Fermi level in monolayer Co2Te is opened when spin–orbit coupling is considered, which leads to QAHE with a sizable bandgap of Eg= 96 me V, characterized by the non-zero Chern number(C = 1) and a chiral edge state. Therefore, our findings not only enrich the study of quantum anomalous Hall effect, but also broaden the horizons of the spintronics and topological nanoelectronics applications.

Coexistence of giant Rashba spin splitting and quantum spin Hall effect in H–Pb–F

Rashba spin splitting(RSS)and quantum spin Hall effect(QSHE)have attracted enormous interest due to their great significance in the application of spintronics.In this work,we theoretically proposed a new two-dimensional(2D)material H–Pb–F with coexistence of giant RSS and quantum spin Hall effec by using the ab initio calculations.Our results show that H–Pb–F possesses giant RSS(1.21 eV·A)and the RSS can be tuned up to 4.16 e V·A by in-plane biaxial strain,which is a huge value among 2D materials.Furthermore,we also noticed that H–Pb–F is a 2D topological insulator(TI)duo to the strong spin–orbit coupling(SOC)interaction,and the large topological gap is up to 1.35 e V,which is large enough for for the observation of topological edge states at room temperature.The coexistence of giant RSS and quantum spin Hall effect greatly broadens the potential application of H–Pb–F in the field of spintronic devices.

Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

Boltzmann Equations with Quantum Effects (2): Entropy Identity, Existence and Uniqueness of Spatial Decay Solutions

A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0<C<∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f ∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v).

Investigation of strain effect on the hole mobility in GOI tri-gate pFETs including quantum confinement

The strain impact on hole mobility in the GOI tri-gate pFETs is investigated by simulating the strained Ge with quantum confinement from band structure to electro-static distribution as well as the effective mobility. Lattice mismatch strain induced by HfO2 warps and reshapes the valence subbands, and reduces the hole effective masses. The maximum value of hole density is observed near the top comers of the channel. The hole density is decreased by the lattice mismatch strain. The phonon scattering rate is degraded by strain, which results in higher hole mobility.

Boltzmann Equations with Quantum Effects (1):Long Time Behavior of Spatial Decay Solutions

The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.

Effect of Bohm quantum potential in the propagation of ion–acoustic waves in degenerate plasmas

A theoretical investigation has been carried out on the propagation of the ion–acoustic(IA) waves in a relativistic degenerate plasma containing relativistic degenerate electron and positron fluids in the presence of inertial non-relativistic light ion fluid. The Korteweg-de Vries(K-dV), modified K-dV(m K-dV), and mixed m K-dV(mm K-dV) equations are derived by adopting the reductive perturbation method. In order to analyze the basic features(phase speed, amplitude, width,etc.) of the IA solitary waves(SWs), the SWs solutions of the K-dV, m K-dV, and mm K-d V are numerically analyzed. It is found that the degenerate pressure, inclusion of the new phenomena like the Fermi temperatures and quantum mechanical effects(arising due to the quantum diffraction) of both electrons and positrons, number densities, etc., of the plasma species remarkably change the basic characteristics of the IA SWs which are found to be formed either with positive or negative potential. The implication of our results in explaining different nonlinear phenomena in astrophysical compact objects, e.g.,white dwarfs, neutron stars, etc., and laboratory plasmas like intense laser–solid matter interaction experiments, etc., are mentioned.

Testing the quantum effects near the event horizon with respect to the black hole shadow

In recent years,the study of quantum effects near the event horizon of a black hole(BH)has attracted extensive attention.It has become one of the important methods to explore BH quantum properties using the related properties of a quantum deformed BH.In this work,we study the effect of a quantum deformed BH on the BH shadow in two-dimensional Dilaton gravity.In this model,quantum effects are reflected by the quantum correction parameter m.By calculation,we find that:(1)the shape of the shadow boundary of a rotating BH is determined by the BH spin a,the quantum correction parameter m,and the BH type parameter n;(2)when the spin a=0,the shape of the BH shadow is a perfect circle;when a≠0,the shape is distorted;if the quantum correction parameter m=0,their shapes reduce to the cases of a Schwarzschild BH and Kerr BH,respectively;(3)the degree of distortion of the BH shadow is different for various quantum correction parameters m;with an increase in the parameter m,the boundary of the BH shadow expands;(4)the size of the BH shadow varies greatly with respect to various quantum deformed BHs(n),and the change in BH shadow shape caused by parameter n is similar to that caused by parameter m,which indicates that there is a"degenerate phenomenon"between the two parameters.Because the value of m in actual physics should be very small,the current observations of the event horizon telescope(EHT)cannot distinguish quantum effects from the BH shadow.In future BH shadow measurements,it will be possible to distinguish quantum deformed BHs,which will help to better understand the quantum effects of BHs.

Effect of spin on the instability of THz plasma waves in field-effect transistors under non-ideal boundary conditions

Terahertz(THz) radiation can be generated due to the instability of THz plasma waves in field-effect transistors(FETs). In this work, we discuss the instability of THz plasma waves in the channel of FETs with spin and quantum effects under non-ideal boundary conditions. We obtain a linear dispersion relation by using the hydrodynamic equation, Maxwell equation and spin equation. The influence of source capacitance, drain capacitance, spin effects, quantum effects and channel width on the instability of THz plasma waves under the non-ideal boundary conditions is investigated in great detail. The results of numerical simulation show that the THz plasma wave is unstable when the drain capacitance is smaller than the source capacitance;the oscillation frequency with asymmetric boundary conditions is smaller than that under non-ideal boundary conditions;the instability gain of THz plasma waves becomes lower under non-ideal boundary conditions. This finding provides a new idea for finding efficient THz radiation sources and opens up a new mechanism for the development of THz technology.

Integer quantum Hall effect in Kekulé-patterned graphene

Y-shaped Kekulébond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed.In this paper,the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field.Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula.It is found that the Y-shaped Kekulébond texture lifts the valley degeneracy of all Landau levels except that of the zero mode,leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity.Consequently,the Hall conductivity is quantized as±ne^(2)/h for n=2,4,6,8,10,...,excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones.These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulébond texture amplitude.

Quantum Anti-Zeno Effect in Artificial Quantum Systems

In this paper, we study a quantum anti-Zeno effect (QAZE) purely induced by repetitive measurements foran artificial atom interacting with a structured bath.This bath can be artificially realized with coupled resonators in onedimension and possesses photonic band structure like Bloch electron in a periodic potential.In the presence of repetitivemeasurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy levelspacing outside of the energy band of the artificial bath.If there were no measurements, the decay would not happenoutside of the band.In this sense, the enhanced decay is completely induced by measurements through the relaxationchannels provided by the bath.Besides, we also discuss the controversial golden rule decay rates originated from the vanHove's singularities and the effects of the counter-rotating terms.