Current noise frequency distribution

If the distribution function of electrons in the cavity f(e,t) were not allowed to fluctuate, the contacts would be independent generators of current noise whose zero-frequency energy-resolved cumulants ((/ R))e could be obtained from a quantum-mechanical formula... 

The results obtained during the Couette flow of aqueous solutions of polyethylene oxide and other water-soluble polymers appear especially promising since they showed an appreciable increase in the current noise level with shear rate. The current noise level depended also on the viscosity (molecular weight) of the solution. A slight increase of thermal noise was recorded also. The pseudoplasticity exponent n in the Ostwald-de Waele power law formula and the exponent a in the l/f -frequency distribution of the current noise were interrelated. This relation appeared to be generally valid. 

Current noise is the noise component exceeding the thermal noise level. In systems relevant to the present context, i.e., carbon-black-filled polymers, carbon resistors, solutions etc., it normally has a frequency distribution of the form l// , where a = 1-3. The intensity of the noise thus falls rapidly with increasing frequency. The current noise level usually greatly exceeds that of the thermal noise. 

The frequency distribution of the current noise was of the l// -type and was independent of temperature that is to say, it was the same inside and outside the Tg or Tm region, respectively. This constancy is illustrated in Figure 4 for the Tg region of PS. The spectrum for thermal noise was white in all the measurements carried out. The sample resistance values calculated from the observed noise spectra agreed with the resistance values obtained with the conventional resistance bridge irrespective of the temperature or time scale of the experiment. 

If the voltage is high enough, the noise of isolated contacts can be considered as white at frequencies at which the distribution function / fluctuates. This allows us to consider the contacts as independent generators of white noise, whose intensity is determined by the instantaneous distribution function of electrons in the cavity. Based on this time-scale separation, we perform a recursive expansion of higher cumulants of current in terms of its lower cumulants. In the low-frequency limit, the expressions for the third and fourth cumulants coincide with those obtained by quantum-mechanical methods for arbitrary ratio of conductances Gl/Gr and transparencies Pl,r [9]. Very recently, the same recursive relations were obtained as a saddle-point expansion of a stochastic path integral [10]. 

Combining these two properties, it is easily seen that STSA transforms the original broad band noise into a signal composed of short-lived tones with randomly distributed frequencies. Moreover, with a standard suppression rule (one that depends only on the relative signal level as measured in the current short-time frame) this phenomenon can only be eliminated by a crude overestimation of the noise level. Using the result of Eq. 4.20 in the case where Q= 1, it is easily shown that the overestimation needed to make the probability of appearance of musical noise negligible (below 0.1%) is about 9 dB [Cappe, 1991],... 

A model membrane system that also shows reproducible and clear 1/f behavior was described by Bezrukov and Brutyan (76). Fluctuations of current through lipid bilayers with one-sided application of three different polyene antibiotics of very close chemical structure (i.e., amphotericin B, nystatin, and mycoheptin) were studied. For one-sided application these antibiotics form channels that are weakly bound to the membrane as compared with the channels of the two-sided action. All three compounds produced pronounced noise component with spectral distribution of 1/f type (Figure 8). It was found that the noise intensity scales as the ratio of single channel conductances for amphotericin B, nystatin, and mycoheptin namely, hA hN hM = 10 5 1. For mycoheptin the spectrum is described by the function 1/f0-86 over the whole frequency range used. With two-sided application of these antibiotics, channels are more stable and strongly bound to the bilayer. In this case, significantly lower noise intensities were found the spectrum for amphotericin B was described by a single Lorentzian spectrum of relatively small amplitude (63). 

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