Variational Quantum Algorithms for the Steady States of Open Quantum Systems

The solutions of the problems related to open quantum systems have attracted considerable interest.We propose a variational quantum algorithm to find the steady state of open quantum systems.In this algorithm,we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation,which can be efficiently evaluated with quantum circuits.We then optimize the parameters of the quantum circuit to find the steady state.Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels.The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%.This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems.     

Correlated noises in an absorptive optical bistable model

We study the steady state properties of an absorptive optical bistable model in the presence of correlated noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution and the average value of the transmitted light have been investigated. We have found that fluctuations of the input light amplitude improve the transmitted light and an optimized value exists for the fluctuations of the population difference at which the transmitted light takes its maximum value. The correlation between the two noises reduce the transmitted light and the noises in the model can induce a phase transition.     

Steady state and relaxation spectrum of the Oslo rice-pile model

We show that the one-dimensional Oslo rice-pile model is a special case of the abelian distributed processors model. The exact steady state of the model is determined. We show that the time evolution operator for the system satisfies the equation where n=L(L+1)/2 for a pile with L sites. This implies that has only one eigenvalue 1 corresponding to the steady state, and all other eigenvalues are exactly zero. Also, all connected time-dependent correlation functions in the steady state of the pile are exactly zero for time difference greater than n. Generalization to other abelian critical height models where the critical thresholds are randomly reset after each toppling is briefly discussed.     

Fluctuation of Parameters in Tumor Cell Growth Model

We study the steady state properties of a logistic growth model in the presence of Gaussian white noise.Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution functionand its extrema have been investigated. It is found that the fluctuation of the tumor birth rate reduces the populationof the cells while the fluctuation of predation rate can prevent the population of tumor cells from going into extinction.Noise in the system can induce the phase transition.     

Fluctuation of Parameters in Tumor Cell Growth Model

We study the steady state properties of a logistic growth model in the presence of Gaussian white noise.Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution function and its extrema have been investigated. It is found that the fluctuation of the tumor birth rate reduces the population of the cells while the fluctuation of predation rate can prevent the population of tumor ceils from going into extinction.Noise in the system can induce the phase transition.     

Statistical mechanical theory of the nonlinear steady state

By making use of perturbation techniques, we develop a theory of the non-linear steady state. We find that the linear term of a mechanical equation such as the Langevin equation is not responsible for the nonlinear terms of its expectation values at the nonequilibrium state arbitrarily far from the thermal equilibrium. The nonlinear steady state is formulated in the two cases where the microscopic conservation law exists and where it does not exist. The expressions for the expectation values of the physical quantities at the steady state are obtained as the functions of other physical quantities which are regarded as the parameters of the steady state. The stability and the instability of the steady state are discussed. A difference in the character of the instability of the steady state from that of the stationary state is discussed. It is noted that the first expansion coefficient should not exhibit an anomaly for instabilities of the steady state. The relation between the mechanical forces appearing in our approach and the corresponding thermal forces is discussed. The variational principle which is valid for the open system is developed.     

双包层掺染料聚合物光纤放大器的增益性能分析

双包层聚合物光纤放大器可以减小染料的热漂白,使用速率方程的方法,给出了一个能够全面描述双包层掺染料聚合物光纤放大器增益性能的模型,模型既考虑了染料三重态能级对速率方程的影响,又考虑了双包层结构对泵浦光的影响,可以在稳态的情况下计算放大器的各种增益性能指标.     

Nonequilibrium phase transitions in chemical reactions

The far from equilibrium steady states of a simple nonlinear chemical system are analyzed. A standard macroscopic analysis shows that the nonlinearity introduces an instability which causes a transition analogous to a thermodynamic second-order phase transition. Fluctuations are introduced into this model through a stochastic master equation approach. The solution of this master equation in the steady state reveals that the system goes into a more ordered state above the transition point. An analogy is drawn with the nonequilibrium phase transition occurring in the laser at threshold.Supported by a New Zealand U.G.C. Postgraduate Scholarship.     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.     

Adaptive computation of articulatory parameters from the speech signal

An unconstrained optimization technique is used to find the values of parameters, of a combination of an articulatory and a vocal tract model, that minimize the difference between model spectra and natural speech spectra. The articulatory model is anatomically realistic and the vocal tract model is a "lossy" Webster equation for which a method of solution is given. For English vowels in the steady state, anatomically reasonable articulatory configurations whose corresponding spectra match those of human speech to within 2 dB have been computed in fewer than ten iterations. Results are also given which demonstrate a limited ability of the system to track the articulatory dynamics of voiced speech.     

Effect of coagulation of nodes in an evolving complex network

We propose a new type of stochastic network evolution model based on annihilation, creation, and coagulation of nodes, together with the preferential attachment rule. The system reaches a unique quasistatistically steady state in which the distribution of links follows a power law, lifetime of nodes follows an exponential distribution, and the mean number of links grows exponentially with time. The master equation of the model is solved analytically by applying Smoluchowski's coagulation equation for aerosols. The results indicate that coagulation of nodes in complex networks and mean field analysis of aerosols are similar in both the growth dynamics with irreversible processes and in the steady state statistics. We confirm that the basic properties of the model are consistent with the empirical results of a business transaction network having about 1×10(6) firms.     

弥散补偿飞秒激光量子理论研究

本文根据我们新建的激光器模型,导出了非线性成形飞秒光脉冲的量子理论锁模方程。在薛定谔表象中,用含时哈特利近似方法求得了脉冲电场及光子数分布的形式解。最后讨论了量子锁模方程过渡到经典情形下稳态时的脉冲能量、脉宽及啁啾参量与飞秒激光器运转参量间的关系,得到了理论与实验一致的结果。     

Directed Motion of a Molecular Motor Based Qn the Four－State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps between arbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probability distribution as a function of the time and position for any initial distribution with all the transients included. Next, the transient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecular motor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kinetic behaviors of a molecular motor under external load F.     

随机基因选择模型中的延迟效应

研究了噪声驱动的基因选择模型中的延迟效应. 据小延迟方法和随机等价法则得到相应的延迟Fokker-Planck方程, 给出稳态概率分布函数的近似表达式. 分析了在噪声驱动下, 延迟时间对系统稳态性质的影响. 结果表明: 延迟时间可以诱导系统从单稳态向双稳态转化, 发生相变; 在基因选择过程中, 延迟时间有利于从基因群体中选择出某一单倍体基因. 数值模拟结果与理论预测基本符合.     

Computer simulation of passive mode-locking of dye lasers with consideration of coherent light-matter interaction

A numerical model of passive mode-locking of dye lasers is presented, which allows the calculation of the steady state pulse parameters without any limitation to pulse energy and duration. The solutions are compared with previous analytical results based on a rate equation treatment (i.e. without considering the phase memory). The pulse evolution and the influence of cavity dumping on the steady state are discussed.     

Photovoltaic spatial soliton pairs in two-photon photorefractive materials

We report the existence of incoherently coupled bright-bright steady state photovoltaic soliton pairs in two-photon photorefractive material under open circuit conditions. Based on WKBJ method and paraxial ray approximation, we have obtained coupled equations describing dynamical evolution of spatial soliton pairs. In the steady state regime, the present analysis leads to the identification of existence equation of bright-bright solitons, which captures a plethora of soliton pairs. We have undertaken linear stability analysis which shows that these solitons are stable.     

Diffusion models of dechannelling of energetic H+-ions in single crystals

The Fokker-Planck equations is shown to be a good expression to describe the dechannelling of energetic H⁺-ions in single crystals. The relation between the Fokker-Planck equation, the ordinary diffusion equation and the steady state model is discussed.     

Mode selection in nearly-self-sustained explosive crystallization

We study a model of a driven thermally activated, exothermic process, in the context of explosive crystallization of a thin amorphous film. In the limit in which self-sustained crystallization at a speed close to the laser scan speed is almost possible, the model reduces to a single autonomous second-order differential equation for the amorphous-crystalline interface position. The steady state of this equation represents a straight-line interface advancing into the amorphous region at a speed equal to the laser scan speed. As a control parameter is increased, this steady state of the model becomes linearly unstable, undergoing a Hopf bifurcation which gives rise to oscillations of the interface velocity. For parameter ranges in which the interface remains a straight line, the amplitude, period, and form of these oscillations is calculated as a function of the control parameter. A similar equation, valid when the interface does not necessarily remain straight but may take on a long-wavelength shape, is also derived; it is harder to analyze.     

Ensemble mechanics for the random-forced Navier-Stokes flow

It is shown that the so-called statistical theory of turbulence, which can be exactly incorporated by the Hopf functional equation, is imperfect in that it fails to ensure the irreversible approach to a unique ultimate steady state of turbulence (for a steady boundary condition) expected from observation; and that this imperfection is removed if a stochastic random-force term is added into the Navier-Stokes equation. The ensemble mechanics for the random-forced Navier-Stokes flow is formulated by taking into account the natural random force, which has usually been neglected in the Navier-Stokes equation.     

光学双稳性的强迫振动模型

本文提出一个新的光学双稳性模型.基于平均场近似,慢变振幅近似和绝热近似的思想,把光学双稳系统看成一个“黑箱”,类比非线性振动理论,指出不同的光学双稳过程(包括不同的工作物质和不同的腔(F-P腔或环腔)),能用一个恰当的强迫振动方程统一地描述.方程中所包含的都是可测量的宏观参量,使得可能直接用实验拟合,与理论结果进行定量对照.用振动理论的方法,把方程演变成自治方程组,从而方便地得到光学双稳性稳态和动态解的一般形式.并用若干已报道的具体例子验证了这个模型的普适性.