非高斯噪声驱动下一维双稳系统的逻辑操作

本文以成功率作为逻辑随机共振的测度, 主要研究了非高斯噪声激励下一维双稳系统的逻辑随机共振现象, 并用平均首次通过时间的方法对此现象的机理进行了解释. 研究结果表明: 只有在适当的噪声强度带或关联时间带上, 成功率才会达到共振峰值. 通过对系统参数进行优化, 提高了系统实现逻辑操作的可靠性. 关键词： 逻辑随机共振 一维双稳系统 非高斯噪声 平均首次通过时间     

Mean first-passage time of quantum transition processes

In this paper, we consider the problem of mean first-passage time (MFPT) in quantum mechanics; the MFPT is the average time of the transition from a given initial state, passing through some intermediate states, to a given final state for the first time. We apply the method developed in statistical mechanics for calculating the MFPT of random walks to calculate the MFPT of a transition process. As applications, we (1) calculate the MFPT for multiple-state systems, (2) discuss transition processes occurring in an environmental background, (3) consider a roundabout transition in a hydrogen atom, and (4) apply the approach to laser theory.     

色关联噪声驱动的非对称双稳系统中平均首次穿越时间的研究

研究了由色关联的乘性白噪声和加性白噪声驱动的非对称双稳系统中，色关联及非对称性对平均首次穿越时间的影响.数值结果表明乘性噪声强度α和加性噪声强度D及互相关时间τ对首次穿越时间T的影响是一致的，加性和乘性噪声间的互关联强度λ及势阱的非对称性r对T的影响是一致的.τ的增加能提高粒子的逃逸率，λ的增加则减小逃逸率.     

色噪声驱动的非对称双稳系统的平均首次穿越时间

研究了由关联乘性色噪声及加性白噪声驱动的非对称双稳系统中势阱的非对称性及噪声对系统两个方向平均首次穿越时间的影响. 首先利用一致有色噪声近似推导了系统的稳态概率密度的表达式，根据最速下降法推导了平均首次穿越时间的表达式. 数值结果表明：势阱的非对称性对两个方向的平均首次穿越时间的影响是不同的；由于噪声的关联性，即使对于关联乘性色噪声及加性白噪声驱动的对称双稳系统，两个方向的平均首次穿越时间也不再相等；在lnT₊-r和lnT_{-关键词： 平均首次穿越时间 非对称双稳系统 乘性色噪声 加性白噪声}     

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises: Mean First-Passage Time

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter (measures deviation from Gaussian character) r, the delay time τ, the noise correlation time τ₀, the intensities D and α of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ₀, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.     

交叉关联噪声对光学双稳系统平均首通时间的影响

研究了乘性色噪声和加性白噪声驱动的光学双稳系统中噪声对系统两个方向平均首通时间T₊（x_s1→x_s2）和T_-（x_s2→x_s1）的影响（平均首通时间是指从一稳态出发越过势垒到另一稳态所用时间的平均值）.通过Novikov定理和Fox近似方法得到相应的Fokker-Planck方程,利用最速下降法得到T₊（x_s1→x_s2）和T_-（x_s2→x_s1）的表达式.研究发现：乘性噪声强度Q和加性噪声强度D对T₊（x_s1→x_s2）的影响相同,对T_-（x_s2→x_s1）的影响不同;T₊（x_s1→x_s2）随乘性色噪声自关联时间τ的增大而增大,但随噪声间的交叉关联强度λ的增大而减小;T_-（x_s2→x_s1）随τ的增大而减小,随λ的增大而增大. 关键词： 平均首通时间 光学双稳系统 乘性色噪声 加性白噪声     

The quantum acoustomagnetoelectric field in a quantum well with a parabolic potential

The acoustomagnetoelectric (AME) field in a quantum well with a parabolic potential (QWPP) has been studied in the presence of an external magnetic field. The analytic expression for the AME field in the QWPP is obtained by using the quantum kinetic equation for the distribution function of electrons interacting with external phonons. The dependence of the AME field on the temperature T of the system, the wavenumber q of the acoustic wave and external magnetic field B for the specific AlAs/GaAs/AlAs is achieved by using a numerical method. The problem is considered for both cases: The weak magnetic field region and the quantized magnetic field region. The results are compared with those for normal bulk semiconductor and superlattices to show the differences, and we use the quantum theory to calculate the AME field in the QWPP.     

Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

<正>The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C(s).Three cases including linear delay,cubic delay and global delay in the system are considered respectively.The simulation results indicate that the linear delay enhances the fluctuation of the system (reduces the stability of the system) while the cubic delay and global delay weaken it(enforce the stability of the system),and the effect of cubic delay is more pronounced than the linear delay and global delay.     

Diffusive corrections to asymptotics of a strong-field quantum transport equation

The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number ?, evolution equations are derived for the terms of zeroth and first order in ?. In particular, a quantum drift-diffusion equation for the position density of electrons, with an ?-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order ?², uniformly in time and for arbitrary initial data is given.     

Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T _c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T _c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T _c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.      

Quantum kinetic theory of confined electrons in a strong time dependent field

A gauge-invariant Green’s function approach to the quantum transport of spatially confined electrons in strong electromagnetic fields is presented. The theory includes mean field and exchange effects, as well as collisions and initial correlations. It allows for a self-consistent treatment of spectral properties and collective effects (plasmons), on one hand, and nonlinear field phenomena, such as harmonic generation and multiphoton absorption, on the other. It is equally applicable to electrons in quantum dots, ultracold ions in traps and valence electrons of metal clusters.     

Reaction kinetic model of height selection in heteroepitaxial growth of quantum dots

A reaction kinetic model is proposed for height selection of heteroepitaxially growing nanometer-thick quantum dots. The model describes the growth by a set of rate equations for the combined size and height distributions of the dots. In addition to nucleation and growth, the model includes a coarse-grained conversion rate incorporating kinetics of height changes. With suitably chosen rate coefficients the model reproduces qualitatively the experimentally observed height-selected size distributions and their evolution. The results support the view that the height selection and the form of the size distribution both result from the oscillating energy barrier for the transformation of dots of different heights, and this transformation barrier is considerably larger in magnitude than oscillations in the electronic energy due to quantum well states in the dot.     

Possible corrections to quantum mechanical predictions in a hidden variable model

We derive possible corrections to the statistical predictions of quantum mechanics in measurement over an ensemble of identically prepared systems based on a hidden variable model of quantization developed in the previous work. The corrections are characterized by a dimensionless parameter σ$\sigma$ and the prediction of quantum mechanics is reproduced in the formal limit σ→0$\sigma \to 0$. Quantum mechanics is argued to be reliable for a sufficiently low quantum number.     

A semi-detailed kinetic model of char combustion with consideration of thermal annealing

The present paper presents a semi-detailed kinetic model of coal char combustion which embodies consideration of thermal annealing as a mechanism leading to the loss of char combustion reactivity along burn off. The distinctive feature of this model is that deactivation induced by thermal annealing is followed along with combustion. Thermodeactivation is modelled according to the power-law equation proposed by Senneca and Salatino [1]. A semi-detailed combustion mechanism was taken after Hurt and Calo [2] and includes three steps: formation of carbon–oxygen complexes (chemisorption), switch-over of surface oxides and desorption of oxygen complexes to yield combustion products. Computation results allow to discuss the impact of thermal annealing on char combustion under conditions of practical interest.     

Detecting entanglement by the mean value of spin on a quantum computer

We implement a protocol to determine the degree of entanglement between a qubit and the rest of the system on a quantum computer. The protocol is based on results obtained in paper [Frydryszak et al. (2017) [23]]. This protocol is tested on a 5-qubit superconducting quantum processor called ibmq-ourense provided by the IBM company. We determine the values of entanglement of the Schrödinger cat and the Werner states prepared on this device and compare them with the theoretical ones. In addition, a protocol for determining the entanglement of rank-2 mixed states is proposed. We apply this protocol to the mixed state which consists of two Bell states prepared on the ibmq-ourense quantum device.     

Quantum corrections to the thermodynamic properties of a two-dimensional fluid with hard-core potential

A simple theory, based on the physical interpretation of the reciprocal of activity, is developed to evaluate the thermodynamic properties of a two-dimensional fluid in the semi-classical limit. The theory is applied to calculate the quantum corrections to the equation of state and excess free energy of two-dimensional fluids, whose molecules interactvia hard-disc and square-well potential. It is found that the quantum effect increases with the increase of density and decrease of temperature.     

The study on a stochastic system with non-Gaussian noise and Gaussian colored noise

In this paper, a stochastic system with correlation between non-Gaussian noise and Gaussian colored noise is investigated. We carry out the functional methods to derive the approximate Fokker-Planck equation, and the expressions of stationary probability density function and mean first-passage time are presented. Also we explore the effects of correlation between non-Gaussian and Gaussian noise for the mean first-passage time.     

Time behavior of the correlation functions in a simple dissipative quantum model

The force and velocity correlation functions for a particle interacting with a bath are calculated within a model allowing for finite memory effects. The relevance of a Brownian picture is delineated in view of the respective behavior of these functions and appears fully inadequate below some cross-over temperature; then, the interplay between quantum and thermal fluctuations yields some long time tails on the same time scale for both correlation functions. The real space transient diffusion coefficient is found to exceed its asymptotic Einstein value for most times in that regime. The limiting case of an infinitely short memory time is also investigated and is seen to produce weak divergences on a time scale which is small as compared to the other characteristic times.     

From the eden model to the kinetic growth walk: A generalized growth model with a finite lifetime of growth sites

We propose a new class of cluster growth models where growth sites have a finite lifetime , which contains as special cases the Eden model ( = ) and the kinetic growth walk ( = 1). For finite but large values the growth process can be characterized by a crossover timet _X; for times belowt _X an Eden-type cluster is formed, while for times abovet _X the growth process belongs to the universality class of the self-avoiding random walk. The crossover time increases monotonically with . We develop a scaling theory for the time evolution of the mean end-to-end distance between the seed and the last-added site, and for the average number of growth sites by which the kinetics of the growth process can be characterized. We test this scaling theory by extensive Monte Carlo simulations. We also extend our results to inhomogeneous media (percolation systems).