Nonlinear time-independent and time-dependent propagation of light in direct-gap semiconductors with paired excitons bound into biexcitons

We study a new class of nonlinear cooperative phenomena that occur when light propagates in direct-gap semiconductors. The nonlinearity here is due to a process, first discussed by A. L. Ivanov, L. V. Keldysh, and V. V. Panashchenko, in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. For the geometry of a ring cavity, we derive a system of nonlinear differential equations describing the dynamical evolution of coherent excitons, photons, and biexcitons. For the time-independent case we arrive at the equation of state of optical bistability theory, and this equation is found to differ considerably from the equations of state in the two-level atom model and in the exciton region of the spectrum. We examine the stability of the steady states and determine the switchover times between the optical bistability branches. We also show that in the unstable sections of the equation of state, nonlinear periodic and chaotic self-pulsations may arise, with limit cycles and strange attractors being created in the phase space of the system. The scenario for the transition to the dynamical chaos mode is found. A computer experiment is used to study the dynamic optical bistability. Finally, we discuss the possibility of detecting these phenomena in experiments. Zh. éksp. Teor. Fiz. 112, 1778–1790 (November 1997)     

Light-induced bistability in spin transition solids leading to thermal and optical hysteresis

We investigate the behaviour of photo-excitable, bistable systems, under permanent light irradiation, in presence of relaxation towards the non-excited state. Cooperativity causes bistability of the steady state, leading to light-induced thermal and optical hysteresis (LITH and LIOH). The light-induced instability is expected to induce demixtion, i.e. the coexistence of domains of the two stable steady states. Such effects are evidenced by magnetic and reflectivity measurements on the spin-crossover solid solution: , with x= 0.3, 0.5, 0.85. Experimental data are in quantitative agreement with a simple macroscopic model which includes a non-linear relaxation term in the master equation. Received: 5 June 1997 / Accepted: 17 July 1998     

Quantum Statistics of Multimode Optical Bistability with Trilinear interaction

An externally driven light mode in a ring cavity may show multistable behaviour if linear losses and dispersive nonlinear coupling compete with each other. The paper considers the trilinear (sum frequency) system with two externally driven modes which shows bistability simultaneously in these two modes. It is described in a fully quantum manner. The master equation and the Fokker-Planck equation for the Glanmber-Sudarshan quasi-probalbility are deduced with appropriate consideration of fluctuations. A closed steady solution of the Fokker-Planck equation is given for one mode only under strong restrictive assumptions.     

Opto-electronic bistable devices in real-time optical information processing

An opto-electronic bistable device using a twisted nematic liquid crystal cell is described. The optical bistability characteristics of this device are used in a new liquid crystal light valve with bistability in cellular array structure. Experimental studies demonstrate the applications of such opto-electronic bistable devices in real-time optical information processing such as intensity limiting for contrast improvement and noise elimination, edge enhancement for pattern recognition, linear and nonlinear optical filtering (in spatial and spectral domains).     

Stable spatially localized solutions and holes in optical bistability

We investigate the spatial behavior of the electric field for optical bistability in the good cavity limit. We show that stable spatially localized solutions exist in one and two dimensions. In addition we find that stable one-dimensional hole solutions also arise in this driven non-equilibrium system with dissipation and dispersion thus demonstrating that stable holes are not restricted to dispersive systems, but can emerge in strongly dissipative systems as well. A critical comparison with the properties of stable localized solutions in other driven dissipative systems is also included.     

Bistability in cell signaling: How to make continuous processes discontinuous,and reversible processes irreversible

Xenopus oocyte maturation is an example of an all-or-none, irreversible cell fate induction process. In response to a submaximal concentration of the steroid hormone progesterone, a given oocyte may either mature or not mature, but it can exist in intermediate states only transiently. Moreover, once an oocyte has matured, it will remain arrested in the mature state even after the progesterone is removed. It has been hypothesized that the all-or-none character of oocyte maturation, and some aspects of the irreversibility of maturation, arise out of the bistability of the signal transduction system that triggers maturation. The bistability, in turn, is hypothesized to arise from the way the signal transducers are organized into a signaling circuit that includes positive feedback (which makes it so that the system cannot rest in intermediate states) and ultrasensitivity (which filters small stimuli out of the feedback loop, allowing the system to have a stable off-state). Here we review two simple graphical methods that are commonly used to analyze bistable systems, discuss the experimental evidence for bistability in oocyte maturation, and suggest that bistability may be a common means of producing all-or-none responses and a type of biochemical memory. (c) 2001 American Institute of Physics.     

Spatial solitary waves and patterns in type II second-harmonic generation

The existence of Turing patterns and of spatial solitary waves that arise from a polarization instability of the fundamental field is predicted in type II second-harmonic generation in a quadratically nonlinear optical cavity. The analogy between these dissipative structures and those studied in absorptive optical bistability is pointed out.     

Emergent phenomena in manganites under spatial confinement

It is becoming increasingly clear that the exotic properties displayed by correlated electronic materials such as high Tc superconductivity in cuprates,colossal magnetoresistance(CMR) in manganites,and heavy-fermion compounds are intimately related to the coexistence of competing nearly degenerate states which couple simultaneously active degrees of freedom-charge,lattice,orbital,and spin states.The striking phenomena associated with these materials are due in a large part to spatial electronic inhomogeneities,or electronic phase separation(EPS).In many of these hard materials,the functionality is a result of the soft electronic component that leads to self-organization.In this paper,we review our recent work on a novel spatial confinement technique that has led to some fascinating new discoveries about the role of EPS in manganites.Using lithographic techniques to confine manganite thin films to length scales of the EPS domains that reside within them,it is possible to simultaneously probe EPS domains with different electronic states.This method allows for a much more complete view of the phases residing in a material and gives vital information on phase formation,movement,and fluctuation.Pushing this trend to its limit,we propose to control the formation process of the EPS using external local fields,which include magnetic exchange field,strain field,and electric field.We term the ability to pattern EPS "electronic nanofabrication." This method allows us to control the global physical properties of the system at a very fundamental level,and greatly enhances the potential for realizing true oxide electronics.     

离子晶格非简谐振动引起的光学非线性与增强吸收型光双稳

处理了光场（电磁场）与离子晶体的非简谐性振动之间的相互作用问题。导出了用简正坐标即声子模式所表达的非线性晶格动力学和非线性宏观极化。在旋转波近似下，得到在入射光驱动下光子－声子耦合体系的总的相干性哈密顿算符。通过相应的静态方程证明该耦合系统会出现增强吸收型光学双稳性，这也就证明了光场与各种玻色子型固体元激发，如光频支声子和半导体中激子的非线性耦合可以作为增强吸收型光双稳的机制。     

Two optical bistability domains in composites of metal nanoparticles with nonlinear dielectric core

It is shown that the local field in metal spherical particles with a dielectric core in an external varying electric field has two maxima at two different frequencies. The second maximum becomes more important with an increment in the metal fraction. Due to the nonlinear dielectric function of the core, the composite of these inclusions may have two optically induced bistability domains at different frequencies. At rather high metal fraction, two bistability domains merge and form one entire bistability domain. The parameters of these domains are studied numerically. The paper focuses on the second bistability domain, which has not been discussed in the literature so far. This domain exists in a comparatively narrow frequency range and its onset fields are lower than those of the first bistability domain. The lowest bistability onset fields are obtained in the entire domain. This peculiarity of the optical induced bistability in the metal composite with small dielectric cores can be attractive for possible applications.     

Spatial bistability: a source of complex dynamics. From spatiotemporal reaction-diffusion patterns to chemomechanical structures

We show experimentally and theoretically that reaction systems characterized by a slow induction period followed by a fast evolution to equilibrium can readily generate "spatial bistability" when operated in thin gel reactors diffusively fed from one side. This phenomenon which corresponds to the coexistence of two different stable steady states, not breaking the symmetry of the boundary conditions, can be at the origin of diverse reaction-diffusion instabilities. Using different chemical reactions, we show how stationary pulses, labyrinthine patterns or spatiotemporal oscillations can be generated. Beyond simple reaction-diffusion instabilities, we also demonstrate that the cross coupling of spatial bistability with the size responsiveness of a chemosensitive gel can give rise to autonomous spatiotemporal shape patterns, referred to as chemomechanical structures.     

The C-number treatment for one-photon absorptive optical bistability in Fabry-Perot cavity

The problem of optical bistability in a standing wave cavity in the steady state leads to a pair of coupled, nonlinear, ordinary differential equations for the forward and backward waves. Here an approach different from the truncation of hierarchy and spatial average is applied to obtain this pair of equations. The results are compared with those obtained from the other approaches.     

具有非线性缺陷的光子晶体的局域模

采用传输矩阵的方法，严格导出一维具有克尔非线性缺陷的光子晶体的局域模频率方程。局域模频率依赖于局域光强。取负克尔系数时，随着局域光强的增加，局域模频率从下带边出现，在带隙间上升，最后消失在上带边。在给定人射光频率下，随着人射光强的变化，系统呈现出双稳态。这种光学稳态性质则由局域模频率的移动引起的。     

Multiscaling of lattice curvature on friction surfaces of metallic materials as a basis of their wear mechanism

A comprehensive structural study has been performed to explore deformation and wear debris formation on friction surfaces of metallic materials. A hierarchy of structural scales of plastic deformation and failure during wear has been established. The nanoscale plays the major role in the hierarchical self-organization of multiscale debris formation processes. On this scale, bifurcational interstitial states arise in zones of local lattice curvature, with plastic distortion and motion of nonequilibrium point defects which determine the nonlinear dynamics of structure formation and wear of surface layers. Nonequilibrium vacancies on lattice sites form microporosity through the coalescence mechanism under plastic distortion. The microporosity is a precursor of meso- and macroscale plastic shearing that defines wear debris formation.     

Fokker-Planck equation approach to fluctuations about nonequilibrium steady states

We examine the properties of steady states in systems which interact at the boundary with a nonequilibrium environment. The examination is based on a nonlinear Fokker-Planck equation, the structure of which is determined by the fact that it also governs the time evolution of the equilibrium fluctuations of the system. The nonlinearities in the Fokker-Planck equation may have two origins: thermodynamic nonlinearities which arise if the thermodynamic potential is not a bilinear function of the state variables, and nonlinear mode coupling which arises if the transport coefficients depend on the state. While these nonlinearities have only a small effect on the equilibrium fluctuations of a system away from critical points, they are shown to be important for the determination of fluctuations about nonequilibrium steady states. In particular the state dependence of the transport coefficients may lead to deviations from local equilibrium and to a breakdown of detail balance. An explicit formula for the time correlations of fluctuations about the nonequilibrium steady state is obtained. The formula leads to long-range correlations in fluids in the presence of a temperature gradient. The result is compared with earlier approaches to the same problem. Finally, we study the linear response to external forces and obtain a generalization of the fluctuation-dissipation formula relating the response functions with the nonequilibrium correlation functions.     

Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping

We report a theoretical study of a quantum optical model consisting of an array of strongly nonlinear cavities incoherently pumped by an ensemble of population-inverted two-level atoms. Projective methods are used to eliminate the atomic dynamics and write a generalized master equation for the photonic degrees of freedom only, where the frequency-dependence of gain introduces non-Markovian features. In the simplest single cavity configuration, this pumping scheme gives novel optical bistability effects and allows for the selective generation of Fock states with a well-defined photon number. For many cavities in a weakly non-Markovian limit, the non-equilibrium steady state recovers a Grand-Canonical statistical ensemble at a temperature determined by the effective atomic linewidth. For a two-cavity system in the strongly nonlinear regime, signatures of a Mott state with one photon per cavity are found.     

反应扩散模型在图灵斑图中的应用及数值模拟

反应扩散方程模型常被用于描述生物学中斑图的形成.从反应扩散模型出发,理论推导得到GiererMeinhardt模型的斑图形成机理,解释了非线性常微分方程系统的稳定常数平衡态在加入扩散项后会发生失稳并产生图灵斑图的过程.通过计算该模型,得到图灵斑图产生的参数条件.数值方法中采用一类有效的高精度数值格式,即在空间离散条件下采用Chebyshev谱配置方法,在时间离散条件下采用紧致隐积分因子方法.该方法结合了谱方法和紧致隐积分因子方法的优点,具有精度高、稳定性好、存储量小等优点.数值模拟表明,在其他条件一定的情况下,系统控制参数κ取不同值对于斑图的产生具有重要的影响,数值结果验证了理论结果.     

Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System

We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.     

Domain formation due to Ostwald ripening in bistable systems far from equilibrium

We develop growth rates ford-dimensional domains in bistable reaction-diffusion systems. The growth of the domain is restrained by an inhibitory nonlocal interaction and leads to stable stationary inhomogeneous states as known from many applications in nonequilibrium systems. The mathematical analysis is quite similar to problems of Ostwald ripening in van-der-Waals gases though the physical mechanism is different. We show that the nonlocal interaction leads to a competition between several domains. Finally our approach is applied to optical bistability, thermokinetic systems and to nonlinear semiconductors.     

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton's method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton's method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton's method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space.