Fano factor

The diagonal elements Faa of the matrix Fag have the meaning of the Fano factors for the shot noise in a-th connector and may vary between 2/3 and... 

S pa ix — x2F/2, F being the Fano factor that describes the suppression of shot noise in comparison with the Poisson value [1],... 

This can be understood by a comparison with the classical calculation of Ref. [17] for a wire connected to normal reservoirs. Eq. (14) coincide with the Fano factor given there when the substitution e —> 2e, Gjj —> Go/2 and rn —> r= r%/(2 — rn)2 are performed. This is consistent with the expectation that phase coherence becomes irrelevant at high energy (see also the discussion in Ref. [18]). 

Fig. 1. (a) Conductance as a function of the gate voltage for 2D and ID configurations at T = 4.2 K. Insets (i) Cross-section of the transistor structure, (ii) Enlarged G (Vg) near the pinch-off. (b) Fano factor for different samples with a schematic representation of hopping paths in each case. Small crosses show dominant hops. The solid line shows the (L/Lc) 1 dependence and dotted lines are guides to the eye. 

We have measured the cross-correlated spectrum 5/ (Isd) [3]. In order to find the Fano factor we used the following fit Si (Iad) = F2elsd coth 2k T ) —... 

In A-1D sample the ID channel is only formed at Vg < —1.3 V, Fig. la. In the range of Vg from —1.32 to —1.63 V, F increases from 0.07 to 0.15 which corresponds to N 1/F = 7. With further increasing negative gate voltage (Vg < —1.65 V) the Fano factor in Fig. lb rapidly increases to 0.8. In this case, as the distribution of the resistances of these hops is exponentially broad, only a single hop dominates the whole conductance of the ID channel, so that the Fano factor is close to 1. 

For sample B the measurements of shot noise in the range of Vg from —1.36 V to —1.31 V have shown an increase of F from 0.6 to 0.8, Fig. lb (sample B). This large value of the Fano factor compared with F 0.2 expected for 2D hopping implies that hopping in this sample occurs through the ID split and is dominated by one or two hard hops. 

In such a modulation regime, the corresponding Fano factor can be written... 

By measuring the differential conductance as a function of Vg and Vs,i we have shown that the increase of shot noise occurs exactly in the region of Vg-Vsd where two interacting impurities carry the current in a correlated way, region 2 in Fig. 3a. In Fig. 3a at small Vsd a cross-like feature is clearly seen near point R2 - the exact positions of the maxima of the conductance peaks of this line are indicated by circles. With increasing Vsd, however, a new parallel line Rl appears at Vg ps —1.694 V and Vsj 1 mV. This happens when the line R2 enters the central area of cross M - the maxima of the conductance peaks of the new line are shown by triangles. In Fig. 3b current noise and the Fano factor are presented as functions of Vsa for different Vg. One can see that the modulation of the current occurs in region (2) of the central area of cross M, between lines Rl and R2. 

A convenient approximation in many applications is to assume that a region of interest with a RDOp p is in contact with a medium at thermal equilibrium. The system and medium are chosen so that the latter can be assumed to remain at equilibrium at all times, with a density operator yeq. In this case it is possible to search for solutions of the equations starting from a factorized density operator for the whole system, r = p 69 A/,q, in a procedure also called a Fano-factorization. [6] This however is not acceptable when the total system is subject to excitations which induce transitions among states of the medium. An example is a molecule adsorbed on a metal surface, excited by visible light which first creates electronic excitations in the substrate. In this case the active medium is described by a DOp evolving in time, and some of the common developments in the literature must be generalized. 

By assuming a value of 0.1 for the Fano factor, the following formula gives the germanium detector resolution at LN temperature ... 

E is the energy of characteristic X-ray line and Fisa constant called the Fano factor, which has a value of 0.12 for Si(Li). electronic noise factor, plays an important role in the resolution. Reduction of the electronic noise will improve the resolution of the EDS detector. Thus, the Si(Li) diode and the preamplifier are mounted in a cylindrical column (the cryostat) so that they can operate at the temperature of liquid nitrogen (-196°C) in order to reduce the electrical noise and increase the signal-to-noise ratio. 

Figure 11 The Fano factor as function of amplitude A of the dot oscillation. The static dot (A = 0) has the resonance transparency T = 1 and is characterized by zero noise. The Fano-factor grows fast until the A reaches the threshold value of Athr 7-1...

Fano factor as a function of shuttling amplitude and illustrates that the better the transparency the lower the noise, as it should be for a quiet electronic sea. 

Photocount noise of the observed statistics can simply be described by the (quantum) Fano factor [19]... 

In the classical trajectory approach, the Fano factor is defined to be... 

Analysis of a typical evolution of the Fano factors F 2, such as presented in Fig. la, leads to the conclusion that after initial short-time (gt < 1) relaxations in both modes, a strongly super-Poissonian (F 2 ) This behavior occurs for the majority of initial coherent states ai) and cq) except a certain set of initial... 

Figure 1. Fano factors of the fundamental, Ff, and the second-harmonic mode, / V. in the long-time interaction for initial coherent states with real amplitudes (a) ai = 6,0C2 — 1, and (b) ai — 6,0C2 = 3. Case a is a typical example of super-Poissonian behavior in both modes outside the no-energy-transfer regime. In case b, the harmonic mode exhibits stable sub-Poissonian statistics with F — 0.83. It is a charactersitc example of the sub-Poissonian behavior within the no-energy-transfer regime along the line ai = 2 ct21-...

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