Energy fluctuations in a biharmonically driven nonlinear system

We study the fluctuations of work done and dissipated heat of a Brownian particle in a symmetric double well system. The system is driven by two periodic input signals that rock the potential simultaneously. Confinement in one preferred well can be achieved by modulating the relative phase between the drives. We show that in the presence of pumping the stochastic resonance signal is enhanced when analysed in terms of the average work done on the system per cycle. This is in contrast with the case when pumping is achieved by applying an external static bias, which degrades resonance. We analyse the nature of work and heat fluctuations and show that the steady state fluctuation theorem holds in this system.     

Active versus passive scalar turbulence

Active and passive scalars transported by an incompressible two-dimensional conductive fluid are investigated. It is shown that a passive scalar displays a direct cascade towards the small scales while the active magnetic potential builds up large-scale structures in an inverse cascade process. Correlations between scalar input and particle trajectories are found to be responsible for those dramatic differences as well as for the behavior of dissipative anomalies.     

单势阱粒子溢流模型中热力学量的涨落效应

采用相空间积分方法严格导出了各态历经条件下单势阱粒子溢流模型中系统温度和阱内粒子数涨落的解析表达式,着重讨论了热力学量涨落与总粒子数和势阱体积之间的关系.研究表明,系统总粒子数越少以及势阱体积越小,热力学涨落越显著,并且热力学涨落与阱内粒子的溢出密切相关.粒子的溢出和系统负比热及热力学大幅涨落的发生存在一一对应的关系,这一对应关系的根源可以从表观能量逆均分来理解.     

光学双稳态的输出特性研究

研究了光学双稳系统在处理带噪声周期信号时的一种新的功能,并对输入任意周期小信号时的输出特性进行了研究。     

Directed transport of two interacting particles in a washboard potential

We study the conservative and deterministic dynamics of two nonlinearly interacting particles evolving in a one-dimensional spatially periodic washboard potential. A weak tilt of the washboard potential is applied biasing one direction for particle transport. However, the tilt vanishes asymptotically in the direction of bias. Moreover, the total energy content is not enough for both particles to be able to escape simultaneously from an initial potential well; to achieve transport the coupled particles need to interact cooperatively. For low coupling strength the two particles remain trapped inside the starting potential well permanently. For increased coupling strength there exists a regime in which one of the particles transfers the majority of its energy to the other one, as a consequence of which the latter escapes from the potential well and the bond between them breaks. Finally, for suitably large couplings, coordinated energy exchange between the particles allows them to achieve escapes — one particle followed by the other — from consecutive potential wells resulting in directed collective motion. The key mechanism of transport rectification is based on the asymptotically vanishing tilt causing a symmetry breaking of the non-chaotic fraction of the dynamics in the mixed phase space. That is, after a chaotic transient, only at one of the boundaries of the chaotic layer do resonance islands appear. The settling of trajectories in the ballistic channels associated with transporting islands provides long-range directed transport dynamics of the escaping dimer.     

Noise-free logic and Set-Reset latch operation in a triple-well potential system

We demonstrate additive driving force can induce logic and Set-Reset latch operation in a triple-well potential system and find the optimal parameter region with contour maps. The logic input signal plays the role of system bias. To be specific, the external driving force makes the system jump from high potential well to low potential well without jumping back, and thus can induce correct logic output. The problem that the optimal parameter region is too narrow can be solved in two ways: one is to increase the amplitude of the logic input signal, and the other is to introduce of logical vibration resonance. In addition, the logic input itself can be directly acted as the driving force to make the system in the correct potential well, that is, to achieve the correct logic and Set-Reset latch operation without other external driving force.     

Ladungsträgerdichte,Neutralgasdichte, elektrisches Potential und Elektronentemperatur in der zylindrischen Diffusionssäule unter Berücksichtigung des Elektronendruckes

The profiles of charged particle density, neutral gas density, charged particle generation and the electron temperature itself are calculated in the cylindrical positive column under diffusion conditions. The electron pressure is taken into account. The nonlinear differential equations for the charged particle density and the neutral gas density are solved by means of relatively well konverging power series. Inside the column the neutral gas partial pressure decreases with increasing electron partial pressure. Thereby, the profiles for charged particle density and electrical potential are flattened near the axis and fall more rapidly near the wall, and the electron temperature increases. The electron pressure increases with rising electric power input into the column. The necessary condition for the existence of a steady-state low pressure discharge with high current densities is investigated shortly.     

Information-theoretic stochastic resonance in noise-floor limited systems: the case for adding noise

We show that in systems whose output must compete with a noise source, stochastic resonance (maximization of output signal-noise separation as a nonmonotonic function of input noise strength) exists even when measured in terms of fundamental statistical measures and optimal detector performance. This is in contrast to the commonly considered scenario where, without the competing noise, the system (e.g., a driven, overdamped particle moving in a double well potential) is essentially invertible and optimal detector performance monotonically deteriorates with increasing input noise strength.     

On the feasibility of a neutron Hanbury Brown—Twiss experiment with gravitationally-induced phase shift

It is shown that a gravitational potential difference between the two components of a split fermion beam in a Mach—Zehnder type interferometer can influence the fermion second-order, one-point correlation function and hence the conditional probability of fermion arrivals at one output port. Manifestation of the effect requires use of two statistically-inequivalent input beams. The configuration is a particle analogue of the optical Hanbury Brown—Twiss experiments. Contrary to previous report of a signal-to-noise performance orders of magnitude higher than that characterising the cross-correlation of particle fluctuations in two beams, it is shown that both types of measurements are characterised by comparable signal-to-noise expressions. The implications for observation of neutron antibunching are discussed.     

Reservoir Computing with Delayed Input for Fast and Easy Optimisation

Reservoir computing is a machine learning method that solves tasks using the response of a dynamical system to a certain input. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task-dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.     

基于声压-振速测量的平面近场声全息实验研究

常规的近场声全息均是采用全息面声压或质点振速作为输入量求解,由于采用单一输入量无法分离来自全息面背向声波的干扰,因此要求所有声源均位于全息面的同一侧,即测量声场为自由声场,这种要求大大限制了近场声全息的实际应用.基于声压-速度测量的近场声全息以全息面上声压和质点振速同时作为输入量,通过建立和求解两侧声源在全息面上的声压和质点振速耦合关系,可以实现全息面两侧声波的分离,从而解决上述问题.文中在前期对声场分离技术研究的基础上,基于欧拉公式和有限差分近似,推导了新的基于声压-速度测量的平面近场声全息理论公式.随后通过实验检验了该方法在有背景源干扰情况下实现声场分离和重建的有效性.     

Fluctuations and dissipation in an elementary one-bit information Storage System

A bistable system, capabie of storing one bit of information, and exemplified by a particle in a dual-trough potential well, is modeled to determine the effects of a coupling between its information-bearing and the thermal degrees of freedom. Energy dissipation accompanying the change of the stored information is calculated in terms of parameters describing the potential well. The fluctuations cause spontaneous changes in the stored information, and the mean time for this error is also calculated in terms of the well parameters. The results can be used for determining the influence of the well parameters on the performance of the information storage system.     

一维势阱中被噪声驱动的粒子的逃逸问题

通过计算机数值模拟直接解朗之万方程，得到一维势阱中被高斯白噪声驱动的粒子的逃逸率，并与理论结果进行了对照。     

Light intensity and its fluctuations on a layered microsphere: Effects of shell thickness acting as a quantum well

The present study is an extension of the former research where a double-layer microsphere is irradiated by monochromatic unpolarized plane light. One can realize intensity fluctuations on the particle surface by the numerical boundary element method. The effect of the shell thickness is primarily investigated in the present study. A refractive index reflects its potential energy photons experience in a domain. The potential energies in the air, shell, and core are different from one another with the smallest in the shell. As the shell thickness reduces, the shell layer behaves like a quantum well after a critical thickness. The resultant light intensities on the particle surface show noise-like fluctuations depending on such parameters as the shell thickness, the light wavelength, the particle size, etc. Noticeable fluctuations appeared with the shell thicknesses less than around 5 nm. The thinner the shell, the stronger the intensity fluctuations, suggesting the more light absorbing ability. More efficient photon energy absorption observed with quantum well optoelectronic devices should be explained by stronger intensity fluctuations, not by higher intensities ensuing from photon confinement in quantum wells.     

Schwarzschild黑洞的Dirac粒子准束缚态

本文将Schwarzschild度规中的二分量Dirac方程(Brill-Wheeler方程)化为一个单分量的二阶方程,考查了方程的有效势,找出了自旋轨道耦合项。视界附近是一个势垒,当K²>3η²,势垒外侧出现势阱。Dirac粒子将在势阱中某些能级上共振,并穿越势垒被视界吸收。借WKB方法求得准束缚态的能谱,并计算了大|K|情形下的寿命。同样的处理方法还推广至Reissner-Nordstrom度规。 关键词：     

Origin of the ground-state energy of a particle in a potential well

In this paper, an apparently universal feature of the ground-state energy of a particle in a potential well is pointed out. Namely, by the example of an infinitely deep rectangular potential well, we clearly demonstrate that this energy, as well as the localization energy of a particle ensuing from the Heisenberg relation, is accumulated by the work of an external force against the particle pressure force on the well walls during compression of the particle substance and, correspondingly, its wave function ψ from unbounded free space to the finite volume of the well. This work is exactly equal to the particle ground-state energy.     

Diffusion and convection after escape from a potential well

The escape by diffusion of a particle from a potential well in one dimension is strongly influenced by the application of a field in the adjacent half-space. At long times the probability distribution becomes a uniformly moving and steadily broadening gaussian in this half-space. The mean time of escape from the well is given by a simple expression in terms of the mean first passage time and the coefficient of the long-time tail in the occupation probability of the well in the absence of the field. Transient effects in space and time are studied in explicit form for a parabolic potential well.     

基于Bloch球面搜索的量子粒子群优化算法

通过分析量子势阱粒子群优化算法的设计过程,提出一种基于Bloch球面搜索的量子粒子群优化算法.首先用基于Bloch球面描述的量子位描述粒子,用泡利矩阵建立旋转轴,用Delta势阱模型计算旋转角度,用量子位在Bloch球面上的绕轴旋转实现搜索.然后用Hadamard门实现粒子变异,以避免早熟收敛.这种旋转可使当前量子位沿着Bloch球面上的大圆逼近目标量子位,从而可加速优化进程.仿真结果表明,该算法的优化能力优于原算法.     

量子势阱粒子群优化算法的改进研究

为提高量子势阱粒子群优化算法的优化能力, 通过分析目前量子势阱粒子群优化算法的设计过程, 提出了改进的量子势阱粒子群优化算法. 首先, 分别基于Delta势阱、谐振子和方势阱 提出了改进的量子势阱粒子群优化算法, 并提出了基于统计量均值的控制参数设计方法. 然后, 在势阱中心的设计方面, 为强调全局最优粒子的指导作用, 提出了基于自身最优粒子加权平均和动态随机变量的两种设计策略. 实验结果表明, 三种势阱粒子群优化算法性能比较接近, 都优于原算法, 且Delta势阱模型略优于其他两种.     

Noise activated granular dynamics

We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized "phase" one encounters two different scenarios: For moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously.