Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.     

Harmonic Noise-Induced Resonant Passing in an Inverse Harmonic Potential

The dynanfics of a particle passing over the sad- dle point plays a crucial role in many branches of physics and chemistry.Previous studies on the saddle-point passing problem mostly considered par- ticles that are subjected to a random force. Noise- induced transport has been studied in many fields including mathematics, physics, chemistry, biology, and economics. A classic example is the fusion reaction of massive nuclei, in which the fusion is in- duced by diffusion. In previous works, the fusion probability was obtained by determining the passing probability of a Brownian particle over the top of an inverse harmonic potential. Great progress has been achieved by regarding the study of passing prob- lems since tile pioneering work published by Kramers. The simplest situation assumes a Brownian particle driven by white noise, which however is not satisfied due to the multiple spectral density of the realistic ran- dora force. One of the realistic models of random force is the Gaussian colored noise, which requires the study of the motion of a particle driven by structured noise, such as harmonic noise which can be generated by the coordinate of a harmonic oscillator driven by white noise. This type of colored noise allows the consideration of resonance phenomena due to the fact that a peak in its spectrum is presented here.     

An effective method to improve the robustness of small-world networks under attack

In this study, the robustness of small-world networks to three types of attack is investigated. Global efficiency is introduced as the network coefficient to measure the robustness of a small-world network. The simulation results prove that an increase in rewiring probability or average degree can enhance the robustness of the small-world network under all three types of attack. The effectiveness of simultaneously increasing both rewiring probability and average degree is also studied, and the combined increase is found to significantly improve the robustness of the small-world network.Furthermore, the combined effect of rewiring probability and average degree on network robustness is shown to be several times greater than that of rewiring probability or average degree individually. This means that small-world networks with a relatively high rewiring probability and average degree have advantages both in network communications and in good robustness to attacks. Therefore, simultaneously increasing rewiring probability and average degree is an effective method of constructing realistic networks. Consequently, the proposed method is useful to construct efficient and robust networks in a realistic scenario.     

Detection of ordered wave in the networks of neurons with changeable connection

The probability of long-range connection among neurons could be changeable in biological neuronal networks. In this paper, the probability of long-range connection between neurons is not fixed at a constant but varies in a numerical region (≤p0 ), and then the collective behaviors of neurons are detected. A statistical factor in the two-dimensional space is used to detect the phase transition and robustness of spiral wave in the active network of neurons. It is found that the development of spatiotem-poral pattern depends on the numerical region (≤p0 ) for the probability of long-range connection. Coherence resonance-like behavior is observed due to the fluctuation in the long-range probability. Spiral waves emerge to occupy the network of neurons under an optimized probability of long-range connection, and it shows certain robustness in weak channel noise.     

Generation of nonclassical states in a large detuning cavity

By using the theory of cavity QED, we study the system in which a two-level atom interacts with a cavity in the case of large detuning. Through the selective detecting of atomic state, Schrodinger cat states and entangled coherent states are easily generated. When the atom is driven by a weak classical field and the cavity field is in the Schrodinger cat state, we study the conditions of generating the Fock states and the maximal success probability. The maximal success probability in our scheme is larger than the previous one.     

重核熔合耗散动力学

用双中心核态参数描写重核熔合过程,以一个布朗粒子通过二次势位垒的简化模型得到了熔合几率的解析表达式.在两碰撞核的接触处,颈部变量的变化遵守高斯分布,而沿拉长方向的初始平均动能由表面摩擦模型所确定.计算了几个对称和近似对称的反应系统的熔合激发函数,并与实验结果进行了比较.讨论了颈部增长和初始能量损失对熔合障碍产生的效应. Dissipative dynamics of fusion of massive nuclei is studied in terms of the two center shape parameterization. Fusion probability is obtained analytically from a Brownian particle passing over a parabolic potential barrier along the elongation coordinate. The neck variable at the initial contact shape is supposed to be a Gaussian distribution. Fusion probabilities of several symmetric or nearly symmetric systems in central collisions are calculatedand compared with experimental data. Effects of neck folding...     

Extinction Effects of Multiplicative Non-Gaussian L′evy Noise in a Tumor Growth System with Immunization

The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.     

Interlayer transport of an electron in bilayer graphene with phonon-induced lattice distortion in the presence of biased potential

The interlayer transport of an electron in bilayer graphene influenced by a phonon in the presence of a biased potential is investigated using the tight-binding approach. The in-plane optical mode E2g and out-of-plane optical mode B1g associated with the applied biased potential are considered to compute and discuss the interlayer transport probability of an electron initially localized on the bottom layer at the Dirac point in the Brillouin zone. Without the biased potential, the interlayer transport probability is equal to 0.5 regardless of the phonon displacement except for a few special cases. Applying a biased potential to the layers, we find that in different phonon modes the function of the transport probability with respect to the applied biased potential and phonon displacement is complex and various, but on the whole the transport probability decreases with the increase in the absolute value of the applied biased potential. These phenomena are discussed in detail in this paper.     

Transmission Probability of an Ultracold Atom in the Presence of Atomic Coherence

We investigate the transmission probability of an ultracold V-type three-level atom passing through a micromaser cavity,in the presence of atomic coherence which is established by a coherent driving field.We show that the transmissibility of this micromaser system with the atomic coherence is better than that of the ordinary micromaser system without atomic coherence.When the driving field is strong enough,for any cavity length the ultracold atom can pass through the micromaser cavity freely.     

Generation of an N-qubit phase gate via atom--cavity nonidentical coupling

A scheme for approximate generation of an N-qubit phase gate is proposed in cavity QED based on nonidentical coupling between the atoms and the cavity. The atoms interact with a highly detuned cavity-field mode, but quantum information does not transfer between the atoms and cavity field, and thus the cavity decay is negligible. The gate time does not rise with an increase in the number of qubits. With the choice of a smaller odd number l （related to atom-cavity coupling constants）, the phase gate can be generated with a higher fidelity and a higher success probability in a shorter time （the gate time is much shorter than the atomic radiative lifetime and photon lifetime）. When the number of qubits N exceeds certain small values, the fidelity and success probability rise slowly with an increase in the number of qubits N. When N→∞, the fidelity and success probability infinitely approach 1, but never exceed 1.     

Modified fusion probability by reflection boundary

We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.     

重核熔合与裂变位垒的动力学回流现象

用实验粒子多次通过位垒的方法计算重核熔合与裂变过程中的熔合几率和裂变速率,结果发现位垒附近存在着一种强烈的回流现象.研究还表明当鞍点后势变得平滑,则回流变大.这种效应降低了以往所用的实验粒子首次通过位垒方法得到的熔合几率和裂变速率,从而给出这两种量的正确描述     

量子非欧姆阻尼环境中的重核熔合概率及热核裂变速率

考虑处于量子非欧姆阻尼环境下的重核熔合及热核裂变系统的动力学,给出了数值模拟相应c数量子广义朗之万方程的方法。其中提出的产生任意关联量子色噪声的数值方法,适用于任意非马尔科夫过程噪声的产生。利用此方法计算了重核熔合概率,结果表明量子涨落对重核熔合具有“低抬高压”的效应:当粒子的初始动能小于（大于）临界初始动能时,量子涨落会增大（减小）粒子鞍点通过概率。非欧姆阻尼环境中粒子稳定通过概率随δ值的变化是非单调的,且当粒子初始动能小于（大于）临界初始动能,量子涨落会使稳定通过概率随δ值变化曲线的极大值位置向右（向左）漂移。此外,在热核裂变系统中,超欧姆阻尼环境会增大裂变速率,而量子涨落不仅显著增大裂变速率,还使裂变速率随δ值变化曲线的极大值位置发生漂移。Dynamics of heavy-ion fusion and nuclear fission system in a quantum non-Ohmic environment have been considered and a numerical simulation method to solve the corresponding c-number quantum generalized Langevin equation is proposed. The method of generating quantum colored noise with arbitrary correlation can be applied to generate noise of arbitrary non-Markov process. Calculating fusion probability of heavy nuclei with this method, the result has shown that the passing probability is enlarged (decreased) by the quantum fluctuation when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Steady passing probability of particle in non-Ohmic environment versus is nonmonotonic. Quantum fluctuation makes the maximum position of the curve drift towards right (left), when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Furthermore, nuclear fission rate is larger in super-Ohmic environment. Quantum fluctuation enlarges nuclear fission rate and makes the the maximum position of nuclear fission rate versus δ drift.     

Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.     

Minimum measurement time interval to estimate a reliable sound pressure level of road traffic noise using two types of dynamic statistics

A new method to determine the minimum measurement time interval needed to obtain the equivalent continuous A-weighted sound pressure level with a designated reliability is presented. This method considers variations in the noise emission from passing vehicles. To verify the validity and availability, simulation experiments based on our dynamic model are examined under various traffic conditions. A statistic quantity, the mean time interval between two maximum sound pressure levels consecutively observed during the reference measurement time interval, is introduced in the experimental analysis. Additionally, the theoretical analysis includes another statistic quantity corresponding to the mean time interval, the mean recurrence time of the maximum sound pressure level, when the transition probability, rate of heavy vehicles, and probability distribution of vehicles passing the observation point during the reference measurement time interval are known.     

重力场中原子的衍射态及其概率分布

使用量子力学中Feynman的路径积分方法,导出了重力场中原子经单缝、双缝及多缝衍射后的量子态及其概率分布.在一定近似条件下,证明了干涉条纹的移动与重力加速度有关,而条纹间隔与重力加速度无关.     

南中国海海域存在孤立子内波条件下的 声场统计特性*

利用南海浅海海域低频声传播起伏实验中获取的水文数据，结合二维平流模型重构出声传播路径上的动态声速场，使用蒙特卡洛方法研究了有、无孤立子内波经过声传播路径条件下的声传播损失统计特性，并与实验结果进行了对比分析。仿真和实验结果表明：当孤立子内波经过声传播路径时，声传播损失起伏剧烈；与“下发上收”相比，“下发下收”情况下传播损失的概率分布更加分散。     

A residual-based message passing algorithm for constraint satisfaction problems

Message passing algorithms, whose iterative nature captures complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in tackling hard computational tasks in optimization, inference, and learning problems. In the context of constraint satisfaction problems (CSPs), when a control parameter (such as constraint density) is tuned, multiple threshold phenomena emerge, signaling fundamental structural transitions in their solution space. Finding solutions around these transition points is exceedingly challenging for algorithm design, where message passing algorithms suffer from a large message fluctuation far from convergence. Here we introduce a residual-based updating step into message passing algorithms, in which messages with large variation between consecutive steps are given high priority in the updating process. For the specific example of model RB (revised B), a typical prototype of random CSPs with growing domains, we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost. Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.     

Diffusion dynamics in external noise-activated non-equilibrium open system-reservoir coupling environment

The diffusion process in an external noise-activated non-equilibrium open system-reservoir coupling environment is studied by analytically solving the generalized Langevin equation. The dynamical property of the system near the barrier top is investigated in detail by numerically calculating the quantities such as mean diffusion path, invariance, barrier passing probability, and so on. It is found that, comparing with the unfavorable effect of internal fluctuations, the external noise activation is sometimes beneficial to the diffusion process. An optimal strength of external activation or correlation time of the internal fluctuation is expected for the diffusing particle to have a maximal probability to escape from the potential well.