Probability Evolution and Mean First-Passage Time for Multidimensional Non-Markovian Processes

We investigate a multidimensional system described by a set of stochastic differential equations in which the multiplicative noise is assumed to be an O-U noise. With the help of the projection operator technique, we derive an integrodifferential equation for the probability density and an approximate equation for the mean first-passage time (MFPT).Under some approximation, we obtain an effective Fokker-Planck equation and apply the equation to the single mode laser problem. The concrete calculations of MFPT are made with an important example.     

Thin-Film Flow Influenced by Thermal Noise

We study the influence of thermal fluctuations on the dewetting dynamics of thin liquid films. Starting from the incompressible Navier-Stokes equations with thermal noise, we derive a fourth-order degenerate parabolic stochastic partial differential equation which includes a conservative, multiplicative noise term—the stochastic thin-film equation. Technically, we rely on a long-wave-approximation and Fokker–Planck-type arguments. We formulate a discretization method and give first numerical evidence for our conjecture that thermal fluctuations are capable of accelerating film rupture and that discrepancies with respect to time-scales between physical experiments and deterministic numerical simulations can be resolved by taking noise effects into account.     

The role of the reservoir correlations in the relaxation rates for different coupling models

A quantal system is assumed to interact with a thermal environment. The fully coupled (FC) and the rotating wave approximation (RWA) models are considered to derive a generalized master equation for the reduced density operator in terms of the spectral density of the correlation function of the thermal environment. The parameters of the irreversible motion are compared for different reservoir models. In particular, we examine the case of normal and odd heat baths and work out specific examples for both coupling mechanisms.     

The kinetic equation and the equation of momentum transfer for a plasma

An attempt is made to derive a simple form of the collision integral of the kinetic equation for a plasma, by using Rostoker’s equation which expresses the pair correlation function in terms of the distribution functions of the particles, and the conditional probability of one particle shielding the other. The conditional probability function is assumed to be given by its equilibrium value. By taking first order velocity-moment of the resulting kinetic equation, the equation of momentum transfer has been obtained.     

Real-Time Thermal Schwinger-Dyson Equation for Quark Self-energy in Landau Gauge

By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A(p2)p - B(p2), we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A(p2) = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.     

Chapman-Kolmogorov equation and path integrals for discrete chaos in presence of noise

We derive an equation of the Chapman-Kolmogorov type for discrete multi-dimensional mappings under the action of additive and multiplicative noise with arbitrary distribution function. The resulting equation is reduced to a Fredholm integral equation. By iteration of the Chapman-Kolmogorov equation as usual, a path integral solution is found. Specializing the distribution function of the noise to a Gaussian distribution and taking the Fourier transform contant can be made with the path integral formulation used by Shraiman, Wayne and Martin.     

Annular convective-radiative fins with a step change in thickness,and temperature-dependent thermal conductivity and heat transfer coefficient

This article investigates the thermal performance of convective-radiative annular fins with a step reduction in local cross section (SRC). The thermal conductivity of the fin’s material is assumed to be a linear function of temperature, and heat transfer coefficient is assumed to be a power-law function of surface temperature. Moreover, nonzero convection and radiation sink temperatures are included in the mathematical model of the energy equation. The well-known differential transformation method (DTM) is used to derive the analytical solution. An exact analytical solution for a special case is derived to prove the validity of the obtained results from the DTM. The model provided here is a more realistic representation of SRC annular fins in actual engineering practices. Effects of many parameters such as conduction-convection parameters, conduction-radiation parameter and sink temperature, and also some parameters which deal with step fins such as thickness parameter and dimensionless parameter describing the position of junction in the fin on the temperature distribution of both thin and thick sections of the fin are investigated. It is believed that the obtained results will facilitate the design and performance evaluation of SRC annular fins.     

A Semiclassical Theory of a Dissipative Henon—Heiles System

A semiclassical theory of a dissipative Henon—Heiles system is proposed. Based on -scaling of an equation for the evolution of the Wigner quasiprobability distribution function in the presence of dissipation and thermal diffusion, we derive a semiclassical equation for quantum fluctuations, governed by the dissipation and the curvature of the classical potential. We show how the initial quantum noise gets amplified by classical chaotic diffusion, which is expressible in terms of a correlation of stochastic fluctuations of the curvature of the potential due to classical chaos, and ultimately settles down to equilibrium under the influence of dissipation. We also establish that there exists a critical limit to the expansion of phase space. The limit is set by chaotic diffusion and dissipation. Our semiclassical analysis is corroborated by numerical simulation of a quantum operator master equation.     

受迫薛罗格双匣化学反应模型的随机共振

为了在理论上揭示高斯白噪声激励的薛罗格双匣化学反应模型对弱周期扰动的线性与非线性响应 ,分四态近似和两态近似两种情形 ,基于绝热近似与速率方程方法 ,解析导出线性的和非线性的敏感性以及信噪比的表达式 ,并与数值模拟结果进行比较 ,在一次谐波的意义上得到了解析结果与数值模拟结果的定量一致性 .理论上讲 ,该模型只能表现出奇次谐波的随机共振 ,但数值模拟结果也出现了二次谐波的随机共振 ,其原因可能归结为在数值模拟中有限频率的截断引入了误差 ,也可能归结为信号的高次谐波与背景噪声难以区分所致 .     

Renormalization of N = 1 supersymmetric Yang-Mills theories: (II). The radiative corrections

We give a general proof of ultraviolet renormalizability relying on the methods of BRS and find that no anomaly can occur if the gauge group is assumed to be semisimple. We derive the Callan-Symanzik equation.     

Quenched master fields

We derive an exact algebraic (master) equation for the euclidean master field of any large-N matrix theory, including quantum chromodynamics. The master equation is the quenched Langevin equation. The master field, a translationally covariant function of (uniform) random momenta and (gaussian) random noise, is easily constructed in perturbation theory.     

Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.     

纳米尺度金属-氧化物半导体场效应晶体管沟道热噪声模型

随着CMOS工艺的发展,热载流子效应对沟道热噪声的影响随着器件尺寸的降低而增大,传统热噪声模型未能准确表征沟道的热噪声.本文通过解能量平衡方程,得到电子温度表达式,并结合沟道漏电流表达式,建立了沟道热噪声模型.利用建立的电子温度表达式,该热噪声模型考虑了热载流子效应的影响,并且在计算热噪声的过程中考虑了电子温度对迁移率降低的影响以及温度梯度对热噪声的影响.通过分析与计算,结果显示,随着器件尺寸的减小,温度梯度对电子温度产生显著影响,使得热载流子效应的影响增大,热载流子效应对热噪声的增长作用超过了迁移率降低对热噪声的减小作用,最终导致热噪声增大.本文建立的沟道热噪声模型可应用于纳米尺寸金属-氧化物半导体场效应晶体管器件的噪声性能分析及建模.     

光泵三能级激光的全量子理论

本文采用Langevin量子理论处理光泵三能级激光体系。在激光场的光子数不太高时导出一个普适的激光场Van der Pol运动方程。它既包括了非相干和相干泵浦,又包括了强泵浦和弱泵浦情况。若对热库取平均,该方程将给出半经典理论的全部结果。本文的结果表明,激光增益来源于两个基本过程:两个光子过程和两步过程。当泵浦强度大于某阈值时,将出现动态斯塔克效应。激光线宽主要来源于热噪声、真空涨落、激光能级的自发辐射以及自发Raman散射。 关键词：     

A New Approach to Noise in Quantum Mechanics

Journal of Statistical Physics - The standard way of describing noise in a quantum system consists in attaching to the system a reservoir or bath, which is assumed to be in thermal equilibrium....     

Generalized Fokker-Planck equation: Derivation and exact solutions

We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise, and show that it reproduces all Fokker-Planck equations that are known for these noises. Exact analytical, time-dependent and stationary solutions of the generalized Fokker-Planck equation are derived and analyzed in detail for the cases of a linear, a quadratic, and a tailored potential.     

纳米尺度MOSFET过剩噪声的定性分析

最近实验表明纳米尺度MOSFET中的过剩噪声主要为散粒噪声,而此前研究认为MOSFET中不存在散粒噪声,短沟道MOSFET中的过剩噪声为热噪声. 本文基于器件电流模型分析散粒噪声取代热噪声成为过剩噪声主要成分的转变条件,根据该条件对纳米尺度MOSFET噪声特性的预测与文献报道的实验现象、模拟结果以及介观散粒噪声相关结论相符合. 关键词： 散粒噪声 过剩噪声 纳米尺度MOSFET     

Current-oscillator correlation and Fano factor spectrum of quantum shuttle with finite bias voltage and temperature

A general master equation is derived to describe an electromechanical single-dot transistor in the Coulomb blockade regime. In the equation, Fermi distribution functions in the two leads are taken into account, which allows one to study the system as a function of bias voltage and temperature of the leads. Furthermore, we treat the coherent interaction mechanism between electron tunneling events and the dynamics of excited vibrational modes. Stationary solutions of the equation are numerically calculated. We show that current through the oscillating island at low temperature appears to have step-like characteristics as a function of the bias voltage and the steps depend on the mean phonon number of the oscillator. At higher temperatures the current steps would disappear and this event is accompanied by the emergence of thermal noise of the charge transfer. When the system is mainly in the ground state, the zero frequency Fano factor of current manifests sub-Poissonian noise and when the system is partially driven into its excited states it exhibits super-Poissonian noise. The difference in the current noise would almost be removed for the situation in which the dissipation rate of the oscillator is much larger than the bare tunneling rates of electrons.     

Closed-form MSE and achievable rate for indirect learning DPD

The digital pre-distortion (DPD) signal processing is an effective way to mitigate the power amplifier (PA) nonlinearity effect. For communication systems containing DPD and PA, it is difficult to acquire performance metrics closed-forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption, etc. Consequently, the performance is evaluated through intensive simulation. In this paper, we show how one can exploit the results of our recent work to mathematically model the indirect learning architecture (ILA) DPD and efficiently derive important measures in communication systems, e.g. normalized mean square error (NMSE), achievable rate, and signal-to-noise plus distortion ratio (SNDR). The author would like to clarify that this work might be the first one to provide closed-form analysis for DPD systems. We think the provided framework/analysis will open the door to other researchers/engineers to plug their own assumptions and derive the performance metrics. The derived expressions of the performance metrics (NMSE, SNDR, and achievable rate) are validated through Monte Carlo simulations. We also derive a closed-form expression for the achievable rate bound for the transmit chain. Moreover, we analytically study the effect of the thermal noise and the quantization noise, in the analog-digital conversion (ADC) process, on the NMSE and achievable rate. The analytical expressions are validated through numerical simulations.