Linear response and fluctuation theorems for nonstationary stochastic processes

Linear response theory is developed for nonstationary Markov processes. A generalized fluctuation theorem is derived which relates the response function to a correlation of fluctuations of the unperturbed nonstationary process. It is shown that it reduces to an ordinary fluctuation theorem relating the response function to the two-point correlation between fluctuations of state variables in the case of a Gaussian distribution function. The results are illustrated by explicit calculation for the class of nonstationary linear Fokker-Planck processes.Supported by Schweizerischer Nationalfonds.     

Periodic renewal processes: application to periodically driven FitzHugh-Nagumo system

Stimulation with periodic force is a standard method to study response properties of a system. Here we examine a special type of systems which generate a sequence of events with uncorrelated time intervals. We review analytical tools to calculate the gain and the signal-to-noise ratio for such systems when perturbed by sinusoidal signal and then apply these tools to the stochastic FitzHugh-Nagumo model.     

Plasmonic response of gold film to potential perturbation

Gold film (～50 nm) serves as the working electrode to allow the electrochemical process to be monitored using surface plasmon resonance (SPR) technology. The extracted precise value of time resolved SPR signal perturbed by the non-faradic potential was investigated to study the response time of gold film under potential application. A qualitative model of the reflection and transmission spectra of gold film working as the electrochemical interface is presented. The correlation between three parameters, including thickness of gold film, incident angle and wavelength of beam, were analyzed to generate an optimized configuration for gold film to detect potential. These results emphasis the efficiency of SPR technique used as a diagnostic tool for the electrochemical process.     

Dynamical response to perturbation of critical Boolean networks

Boolean networks can be used as simple but general models for complex self-organizing systems. The freedom to choose different rules and structures of interactions makes this model applicable to a wide variety of complex phenomena. It is known that the damage dynamics in annealed Boolean systems should fall in the same universality class of the directed percolation model. In this work we present results about the behavior of this model at and near the critically ordered condition for both the annealed and the quenched versions of the model. Our study concentrates on the way the system responds to a small perturbation. We show that the characteristic correlation time, i.e., the time in which any memory of this perturbation is lost, diverges as one moves towards criticality. Exactly at the critical point, we observe that the time for returning to the natural state after the perturbation follows a power-law distribution. This indicates that most perturbations are quickly restored, while few events may have a global effect on the system, suggesting a mechanism that assures at the same time robustness and adaptability. The critical exponents obtained are in agreement with the values expected for the universality class of mean-field directed percolation both in the annealed and in the quenched Boolean network model. This gives further evidence that annealed Boolean networks may in certain conditions provide a good model for understanding the behavior of regulatory systems. Our results may give insight into the way real self-organizing systems respond to external stimuli, and why critically ordered systems are often observed in Nature.     

Residence time statistics for N renewal processes

We present a study of residence time statistics for N renewal processes with a long tailed distribution of the waiting time. Such processes describe many nonequilibrium systems ranging from the intensity of N blinking quantum dots to the residence time of N Brownian particles. With numerical simulations and exact calculations, we show sharp transitions for a critical number of degrees of freedom N. In contrast to the expectation, the fluctuations in the limit of N→∞ are nontrivial. We briefly discuss how our approach can be used to detect nonergodic kinetics from the measurements of many blinking chromophores, without the need to reach the single molecule limit.     

Chiral perturbation theory for anomalous processes

A general expression containing all the divergences in Chiral Perturbation Theory at one loop for anomalous processes has been calculated. The nonrenormalization of some amplitudes (Adler-Bardeen theorem) is observed. The different types of corrections are identified. The contributions from vector meson exchange are determined for all anomalous processes. Explicit cancellation of divergences is shown for π⁰, η and η′ decays to γγ^*. The dependence on the γ^* mass squared is predicted to be essentially the same for all the three processes. It proceeds mainly through the VMD estimate of the finite parts of the next order Lagrangian and compares reasonably well with the available experimental data.     

Lattice response of quantum solids to an impulsive local perturbation

The lattice response of solid para-H2 to an impulsive electronic excitation was studied using femtosecond pump-probe spectroscopy. The evolution of an electronic bubble in the crystal, created upon excitation of the A(3ssigma) Rydberg state of an NO impurity, was followed in real time, with a resolution of 100 fs. The experimental results, interpreted in connection with molecular dynamics simulations with quantum corrections, indicate the presence of three stages in the dynamics: a sub-100 fs "adiabatic" phase, a 0.5-1 ps phase, corresponding to the interaction of the first with the next shells driven by the bubble expansion, and a 5 ps phase, corresponding to a slow rearrangement of the environment surrounding the impurity. These findings indicate that the lattice response in solid para-H2 resembles that of a liquid.     

基于环境扰动的线性匹配场处理方法

匹配场处理面临的挑战主要是拷贝场失配。常规线性匹配场处理方法虽然对失配较宽容,但旁瓣较高,定位正确率依赖于失配的程度,且很容易受到强干扰的影响而失效。自适应匹配场处理可以获得较高的定位精度和旁瓣抑制性能,但环境参数失配、距离/深度空间欠采样、基阵及环境的波动所造成的误差等因素,均会导致其性能严重下降。环境扰动约束可提高自适应匹配场处理器的稳健性,基于这种思想,提出了基于环境扰动的线性匹配场处理方法,它不仅在环境失配的条件下比常规线性方法的定位正确率更高,而且在阵列采样数据存在幅度与相位随机误差的条件下,比自适应匹配场方法的稳健性更强.针对环境失配条件下的强干扰问题,还提出了一种线性匹配场干扰抑制算法,可有效地抑制水面干扰。典型浅海环境下的数值仿真和实测数据分析验证了方法的有效性.     

A singular perturbation approach to first passage times for Markov jump processes

We introduce singular perturbation methods for constructing asymptotic approximations to the mean first passage time for Markov jump processes. Our methods are applied directly to the integrai equation for the mean first passage time and do not involve the use of diffusion approximations. An absorbing interval condition is used to properly account for the possible jumps of the process over the boundary which leads to a Wiener-Hopf problem in the neighborhood of the boundary. A model of unimolecular dissociation is considered to illustrate our methods.     

A cross-language study of compensation in response to real-time formant perturbation

Past studies have shown that when formants are perturbed in real time, speakers spontaneously compensate for the perturbation by changing their formant frequencies in the opposite direction to the perturbation. Further, the pattern of these results suggests that the processing of auditory feedback error operates at a purely acoustic level. This hypothesis was tested by comparing the response of three language groups to real-time formant perturbations, (1) native English speakers producing an English vowel /ε/, (2) native Japanese speakers producing a Japanese vowel (/e([inverted perpendicular])/), and (3) native Japanese speakers learning English, producing /ε/. All three groups showed similar production patterns when F1 was decreased; however, when F1 was increased, the Japanese groups did not compensate as much as the native English speakers. Due to this asymmetry, the hypothesis that the compensatory production for formant perturbation operates at a purely acoustic level was rejected. Rather, some level of phonological processing influences the feedback processing behavior.     

Dynamic response of an irreversible reaction system to a pulsed perturbation

The dynamic response of the ZGB surface reaction lattice gas model, for the catalyzed reaction , is studied by means of Monte-Carlo simulations in the neighborhood of its second order irreversible phase transition (IPT). It is found that shortly after driving a stationary configuration into the absorbing state, the relaxation of the system can be well described by a stretched exponential behavior. The dependence of the relaxation characteristic time and the induced changes on the coverage of the reactants, on both, the intensity and the period of the pulsed perturbation, are systematically investigated. The obtained insights can straightforwardly be extended to a wide variety of irreversible systems exhibiting second order IPT's, such as directed percolation, forest fire models, the contact process, branching annihilating walkers, catalyzed reactions, etc. Received 6 July 1998     

Linear response of tripartite entanglement to infinitesimal noise

Recent experimental progress in prolonging the coherence time of a quantum system prompts us to explore the behavior of quantum entanglement at the beginning of the decoherence process. The response of the entanglement under an infinitesimal noise can serve as a signature of the robustness of entangled states. A crucial problem of this topic in multipartite systems is to compute the degree of entanglement in a mixed state. We find a family of global noise in three-qubit systems, which is composed of four W states. Under its influence, the linear response of the tripartite entanglement of a symmetrical three-qubit pure state is studied. A lower bound of the linear response is found to depend completely on the initial tripartite and bipartite entanglement. This result shows that the decay of tripartite entanglement is hastened by the bipartite one.     

Analysis of nonexponential capacitance relaxation signals

The kinetics of charge transfer by deep energy levels of the semiconductor gap, describing nonexponential shape of capacitance relaxation signals, is suggested. A method of analysis of these signals, possessing higher accuracy and resolution in comparison with the conventional methods based on the relaxation-time approximation, is developed.     

Linear response equilibrium

A new periodic pulse sequence employing weak excitation is presented. This type of sequence drives the system into a steady-state with periodic time evolution from which the data can be reconstructed to a spectrum. It is demonstrated that the frequency response of such a sequence can be analyzed using perturbation methods and linear system analysis. A mathematical framework is proposed allowing the frequency response to be tailored by weighting a periodic flip function. The weak excitation level used implies very low specific absorption rates while generating a highly frequency selective signal in the order of 1/T2 with signal strengths comparable to those obtainable with conventional large flip angle balanced steady-state free precession techniques. The concept is illustrated with phantom experiments and in vivo feasibility of water fat separation is shown on human knee images.     

Linear perturbation amplification in self-similar ablation flows of inertial confinement fusion

Exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction are proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Both the similarity solutions and their linear perturbations are numerically computed with a dynamical multidomain Chebyshev pseudospectral method. Herewith the first analysis of laser-imprinting based on a dynamic solution is presented, showing that maximum perturbation amplification occurs for a laser-intensity modulation of zero transverse wave number, with growth dominated by the mean flow stretching.     

Dissipative evolution of quantum statistical ensembles and nonlinear response to a time-periodic perturbation

We present a detailed discussion of the evolution of a statistical ensemble of quantum mechanical systems coupled weakly to a bath. The Hilbert space of the full system is given by the tensor product between the Hilbert spaces associated with the bath and the bathed system. The statistical states of the ensemble are described in terms of density matrices. Supposing the bath to be held at some - not necessarily thermal - statistical equilibrium and tracing over the bath degrees of freedom, we obtain reduced density matrices defining the statistical states of the bathed system. The master equations describing the evolution of these reduced density matrices are derived under the most general conditions. On time scales that are large with respect to the bath correlation time and with respect to the reciprocal transition frequencies of the bathed system, the resulting evolution of the reduced density matrix of the bathed system is of Markovian type. The detailed balance relations valid for a thermal equilibrium of the bath are derived and the conditions for the validity of the fluctuation-dissipation theorem are given. Based on the general approach, we investigate the non-linear response of the bathed subsystem to a time-periodic perturbation. Summing the perturbation series we obtain the coherences and the populations for arbitrary strengths of the perturbation.Received: 26 November 2003, Published online: 30 January 2004PACS: 05.30.-d Quantum statistical mechanics - 33.35. + r Electron resonance and relaxation - 33.25. + k Nuclear resonance and relaxation