Internal noise

Kapral R and Wu X-G Internal noise, osoillations, ehaos and ehemieal waves Chemical M/aves and Patterns eds R Kapral and K Showalter (Dordreoht Kluwer) eh 18, pp 609-34... 

In threshold measuring situations small signals are presented and at times when the internal noise is low, the total impact of the noise plus signal may be lower than that of the strongest noise alone. In such a case the subject may say no to a presentation containing the signal (a miss) and yes to a presentation in which only the strong noise was present (a false alarm). 

Internal or intrinsic noise is caused by the fact that the system itself consists of discrete particles it is inherent in the very mechanism by which the system evolves, as described in III.2. All our examples concerning chemical reactions, emission and absorption of light, growth of populations, etc., were of this type. Internal noise cannot be switched off and it is therefore impossible to identify A(y) as the evolution equation for the system in isolation. One usually identifies it... 

Conclusion. For internal noise one cannot just postulate a nonlinear Langevin equation or a Fokker-Planck equation and then hope to determine its coefficients from macroscopic data. ) The more fundamental approach of the next chapter is indispensable. ... 

Although we have found that for internal noise the Ito-Stratonovich dilemma is undecidable for lack of a precise A(t) there are cases in which the Ito equation seems the more appropriate option. As an example we take the decay process defined in IV.6 the M-equation is (V.1.7) and the average obeys the radioactive decay law (V.1.9). As the jumps are relatively small one may hope to describe the process by means of a Langevin equation. Following the Langevin approach we guess... 

Internal noise is described by a master equation. When this equation cannot be solved exactly it is necessary to have a systematic approximation method - rather than the naive Fokker-Planck and Langevin approximations. Such a method will now be developed in the form of a power series expansion in a parameter Q. In lowest order it reproduces the macroscopic equation and thereby demonstrates how a deterministic equation emerges from the stochastic description. 

In the present section we are concerned with genuine internal noise. We consider a closed, isolated many-body system, whose evolution is given by a Schrodinger equation. Remember that in the classical case in III.2 we gave a macroscopic description in terms of a reduced set of macroscopic variables, which obey an autonomous set of differential equations. These equations are approximate and deviations appear in the form of fluctuations, which are a vestige of the large number of eliminated microscopic variables. Our task is to carry out this program in the framework of quantum mechanics. 

For detection of the small number of scattered photons, modern photomultiplier tubes having low internal noise and high gain are used. The amplification method employed is generally direct-current amplification. 

Figure 3. Signal-to-noise-ratio (SNR) in the optical experiment for a signal at frequency fl = 3.9 Hz as a function of the internal noise intensity [115]. Inset the corresponding signal amplification.

In non-deterministic regime, in electrical and electronic systems (communications), we can have internal noise which is inherent in the system and external noise which is the disturbance caused by external factors. It may be noted that the study of effect of noise on oscillatory behaviour is of relevance in neuro-sciences and information processing [20-22]. It has been pointed out that in linear systems, noise plays a destructive role, whereas in non-linear systems, the noise can play a constructive role in some cases. 

To make a practical photodetector, it is not sufficient to study and evaluate the interaction of radiation with materials giving rise to a photoeffect. As with all types of sensors, internal noise limits the ability to detect a very small signal in the detector output. Thus accompanying the study of photoeffects in materials is one of noise in materials. Since the effects of greatest utility are those in which the signal is manifested as a change in the electrical properties of the material. Section 2.2 presents a description of electrical noise in photosensitive materials. 

The other sources are radiation noise and noise internal to the detector. It is the objective of optimum detector design to reduce the internal noise of the... 

In the absence of electrical bias, the absolute minimum internal noise exists, termed Johnson noise, Nyquist noise or thermal noise. This form of noise arises from the random motion of the current carriers within any resistive material and is always associated with a dissipative mechanism. The Johnson noise power is dependent only upon the temperature of the material and the measurement bandwidth, although the noise voltage and current depend upon the value of the resistance. 

There have been several recent bolometer designs which have succeeded in making the internal noise sources very small. Thus Drew and Sievers [3.39] have shown that with an element cooled to about 0.5 K in a He cryostat the NEP associated with the temperature and Johnson noise is about 10" " while Draine and Sievers [3.40] have shown that using He dilution cooling to 0.1 K this NEP falls to 3 x 10 WHz However this very low value could probably only be exploited in an experiment conducted entirely at cryogenic temperatures, and would certainly require a cryogenically operated low noise amplifier. 

In the devises for the measurement, a usual system is schematically illustrated in Fig. 2.8. In principle, amplifiers shall be set up as close as possible to AE sensors. The internal noise of the amplifier shall be inherently low and less than 20 pV as the peak voltage converted as input voltage. The amplifier shall be robust enough against the environmental conditions and be protected properly. The frequency range, which are usually controlled by filters, shall be determined prior to the measurement, taking into account the performance of AE sensors and the amplifiers. 

Now we outline another method based upon a stochastic differential equation model of a certain internal noise of unspecified origin in a reaction not coming from the reaction itself. A possible way of doing this is to consider the stochastic differential equation... 

---