A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current.Within such an approach, counting charge without breaking the circuit is possible. As an application, we derive the counting statistics in a single channel conductor at finite temperature and bias. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant bias and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics. Another application considered is the noise due to short current pulses that involve few electrons.We find the time-dependence of the driving potential that produces coherent noise-minimizing current pulses, and display analogies of such current states with quantum-mechanical coherent states.

In this study we analyzed backscattering mechanism using a non-Gaussian correlation function, called exponential-like, for rough surface. The corresponding surface spectrum properties were investigated. It contains an excessive amount of high frequency spectral components. But unlike exponential one, it has rms slopes and allows to obtain the desired rms slopes. New insight into the physical implications of mechanism behind the backscattering behavior was obtained using the advanced integral equation model (AIEM). It 106 Chen et al.is known that backscattering at large incident angles is proportional to the presence of small scale roughness or the high-frequency spectral components of the surface spectrum. Similarly, the peaking at near normal incidence is proportional to the large scale roughness or the low frequency spectral components of the surface spectrum. However, by increasing frequency while keeping the small roughness scale, scattering cannot approach the geometric optics at large angles of incidence where small roughness scales dominate scattering. There is condition where VV tends to HH returns without approaching the geometric optics limit. This is where we increase the surface rms slope. In fact, the presence of roughness scales, small or comparable to the incident wavelength, implies that the geometric optics condition is not satisfied. When there is a significant amount of backscattering in the large incident angle region, it indicates presence of high frequency spectral components in the surface spectrum. To demonstrate the applicability of the proposed correlation function, comparison of backscattering coefficients between model predictions and insitu measurements was made. Well match was obtained in terms of level and angular trend.