Telegraphic noise

Fig. 9.28. Current-voltage characteristics for a resonant tunneling multilayer exhibiting telegraphic noise. The insert shows the time dependence of the current at a voltage of 0.5 V (Arce and Ley 1989).

Hanggi and Riseborough carried out an exact calculation of the activation rates for the bistable flow of Eq. (38) for the case when the noise of the control parameter can be modeled by a telegraphic noise of vanishing mean. 

Figure 7. Sketch of possible realizations of a telegraphic noise, f (t), for differing correlation times T, Eq. (41). The solid curve is for Ti and the dashed curve for tj, where tj < T]. [Taken from P. Hhnggi and P. Riseborough, Phys. Rev., A27, 3329 (1983).]...

An important property of the telegraphic noise, Eq. (41), is the approach to a Gaussian wlute noise in the limit t - 0. With... 

Next we consider several noise sources. They are Gaussian sources if their support of values is due to a Gaussian distribution. Contrary the dichotomic telegraph process assumes two values, i.e. = A and 2 = A. We will always assume A = — A. 

For colored noise sources the derivation of evolution equations for the probability densities is more difficult. In a Markovian embedding, i.e. if the Ornstein-Uhlenbeck process is defined via white noise (cf. chapter 1.3.2) and v t) is part of the phase space one again gets a Fokker-Planck equation for the density P x,y, Similarly, one finds in case of the telegraph... 

The results for i p(r) obtained for different values of A, see Fig. 1.11, demonstrate that under a random telegraph signal the coherence of noise-induced excitation is enhanced by an optimal choice of the correlation time. Here, the optimal correlation time Topt decreases as the noise amplitude A increases. Further simulations not shown here, confirm that this phenomenon holds for a wide range of the bifurcation parameter o, covering almost the whole excitable regime. We emphasize that for not well separated time scales, noise-induced excitations are possible even if both cp-... 

Figure 4.5. A schematic representation of the spectral diffusion process modeled by two-state jump process (random telegraph noise). The fluctuating transition frequency is given by Aco(t) = vMt).

To extend the validity range of noise-induced phenomena for a wider range of correlation times the dichotomous Markov noise has been used. The dichotomus Markov noise, also known as the random telegraph signal has a quite simple structure, therefore the stationary probability density can be calculated for an arbitrary value of the correlation time, and for any value of the noise intensity. The state of the Markovian dichotomous noise /, consists of two levels A+, A only. The noise is characterised by the transition probability ... 

Let us now consider the case ii)b), i.e. the two-state noise case. This noise is also known as the random telegraph signal. It is characterized by the following, so-called. Master equation... 

Chang, S. et al. Tunnel conductance of Watson-Crick nucleoside-base pairs from telegraph noise. Nanotechnology 20,185102-185110 (2009). 

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