External noise

The lifetime resolution is the smallest variation in lifetime that can be detected. If external noise sources are ignored, the lifetime resolution depends essentially on the photon-economy of the system. For instance, if a 2 ns lifetime is measured with a 4 gate TG single-photon counting FLIM (F = 1.3) and 1000 photons, variations of about 80 ps can be resolved. However, for reasons discussed earlier, in biological samples these values could be higher. 

Here again, in the low-noise case of scintillation noise, the absorbance noise is again independent of the reference signal level, and is now independent of the sample characteristics, as well, and depends only on the magnitude of the external noise source. 

The stability of scarred states to external noise and other environmental disturbances was the next natural issue that was raised and partially addressed earlier (L. Sirko, et.al., 1993 R. Scharf, et.al., 1994). The main conclusion was that scarred states are quite robust to reasonable levels of noise. This question took on added relevance with the coming of age of mesoscopic systems where, be it spontaneous emission in atom optics or leads or scattering and other forms of dissipation in heterostructures, the open nature of the system must be accounted for. These new experiments also provided non-ideal realizations of simple theoretical paradigms such as stadium billiards and the kicked rotor, with additional issues that had to be accounted for in the theory. 

Decrease stimulation by reducing external noise and exposure to others and placing patient in a quiet isolated room with low lighting... 

In the experiment, the transmission intensities for the excited and the dark sample are determined by the number of x-ray photons (/t) recorded on the detector behind the sample, and we typically accumulate for several pump-probe shots. In the absence of external noise sources the accuracy of such a measurement is governed by the shot noise distribution, which is given by Poisson statistics of the transmitted pulse intensity. Indeed, we have demonstrated that we can suppress the majority of electronic noise in experiment, which validates this rather idealistic treatment [13,14]. Applying the error propagation formula to eq. (1) then delivers the experimental noise of the measurement, and we can thus calculate the signal-to-noise ratio S/N as a function of the input parameters. Most important is hereby the sample concentration nsam at the chosen sample thickness d. Via the occasionally very different absorption cross sections in the optical (pump) and the x-ray (probe) domains it will determine the fraction of excited state species as a function of laser fluence. 

External noise denotes fluctuations created in an otherwise deterministic system by the application of a random force, whose stochastic properties are supposed to be known. Examples are a noise generator inserted into an electric circuit, a random signal fed into a transmission line, the growth of a species under influence of the weather, random loading of a bridge, and most other stochastic problems that occur in engineering. In all these cases clearly (4.5) holds if one inserts for A(y) the deterministic equation of motion for the isolated system, while L(t) is approximately but never completely white. Thus for external noise the Stratonovich result (4.8) and (4.9) applies, in which A(y) represents the dynamics of the system with the noise turned off. 

A stochastic differential equation is a differential equation whose coefficients are random numbers or random functions of the independent variable (or variables). Just as in normal differential equations, the coefficients are supposed to be given, independently of the solution that has to be found. Hence stochastic differential equations are the appropriate tool for describing systems with external noise (see IX.5). 

Unfortunately it is not going to be easy to test experimentally or even to simulate on the computer. The reason is the extreme sensitivity of states of high n to external perturbations. In the laboratory, stray electrical fields, which cannot be completely avoided (or black-body radiation) will cause ionization of these states. Even on the computer, numerical roundoff errors will act as external noise. 

The Fourier spectra of concentrations and of the reaction rate are quite similar. The difference is that the strong concentration decay suppresses the Fourier amplitudes at high frequencies. For the concentration motion the change in time of the K (t) acts as an external noise from which the concentration motion selects the main frequencies. 

In this problem, in ad tion to discussed in Section IV, we have another time scale, Let us assume that our experimental apparatus only allows us to observe long-time regions corresponding to r yr/, where is the mechanical time scale introduced in provision (i) of Section V.A. In consequence, the dynamics induced by the interplay of inertia and external noise belongs to the short-time region. In such a limit T,y - Ty, both and v play the role of fast-relaxing variable while x is our variable of interest. By applying our AEP, we then recover the corrections to the diffusional approximation due to the non-white external noise. 

Kawakubo et al. studied the behavior of a self-exdted oscillator under the influence of an extomal noise. Th found that the self-osdUations are suppressed by the external noise with a threshold behavior reminiscent of the phase transitions of a ferroelectric sample. 

This equation produces a divergence when the external noise is so intense as to get the condition... 

This type of problem has recently become of great interest in the field of physics, being directly related to basic problems such as noise-induced phase transitions and the dependence of the relaxation time of the variable of interest on the intensity of external noise terms. As in Chapter X, the reduced equation of motion itself can be assumed to be rehable only when this relaxation time decreases with increasing noise intensity. Further problems of interest are whether or not the threshold of a noise-induced phase transition is characterized by a slowing dowrf " and what is the analytical form of the long-time decay. ... 

The constant D in this description constitutes the intensity of the external noise. 

---