Due to the central limit theorem, Gaussian fluctuations are expected for most systems in thermodynamic equilibrium. All correlation functions of order greater than two of Gaussian random processes can be expressed in terms of first- and second-order correlation functions; therefore non-Gaussianity is quantified by the deviation of high-order statistics (i.e. order greater than two) from the expectation for Gaussian noise.
Non-Gaussian noise is often associated with the presence of correlations between microscopic fluctuations. One important example of this behavior occurs in the vicinity of a second-order phase transition, where the divergence of the correlation length mandates that fluctuations be non-Gaussian. Large non-Gaussian fluctuations are also present in steady-state driven systems with non-linear response functions. Careful study of the high-order statistics of fluctuations can give insight into the microscopic properties of complex systems.
Recent work has both resolved and raised important questions concerning the high-order statistics of 1/f resistance noise. The metal-insulator transition in percolation resistor networks is a canonical example of a second-order phase transition; hence, the resistance fluctuations as a function of variations in network topology are strongly non-Gaussian. Resistance noise in conductors near the percolation threshold has previously been envisioned as a fundamentally different situation in which one has Gaussian noise from a fixed-topology resistor network where each discrete element has statistically-independent fluctuations.
However, Prof. Seidler and coworkers at NEC Research Institute demonstrated that this sharp distinction between the dynamic- and static-configuration treatments is not appropriate for many materials. Local resistivity fluctuations result in a sampling of some subset of the phase space of configurations of the resistor network. When these fluctuations are not small the dynamical redistribution of current in the sample leads to long-range non-linear statistical couplings between the contributions to the total sample noise power from otherwise statistically-independent fluctuators. This results in non-Gaussian noise. Although the divergence of the noise power in conductors near the percolation threshold has been studied by several groups, no systematic study of the high-order statistics exists. This group will pursue this experiment using both thin-film and composite systems. In the long term, this work will evolve into investigations of the high-order statistics of impedance noise on both sides of the metal-insulator transition. Applications of impedance fluctuation spectroscopy for characterization of the microstructure of composite conducting materials and polycrystalline ferroelectric films will also be pursued.
Shown below is the power spectrum for a home-made carbon resistor (R ~ 3 kOhms) at a dc current of 1.1 mA and with the power supply disconnected. The horizontal dashed line indicates the Johnson noise level for this sample. The deviations from this level for the measurement with I = 0 have three main causes: 1) the 5 kHz cut-off from the antialiasing filter, 2) narrow-band contamination (mostly at harmonics of 60 Hz), and 3) amplifier noise at low frequencies due to imperfect impedance matching. The measurement with I = 1.1 mA shows the expected behavior (~1/f1.0) over the frequency range 5 Hz < f < 5 kHz. The low-frequency cut-off is from RC limitations of the preamplifier inputs, and the high-frequency cut-off is again from the anti-aliasing filter.
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