Long-term Correlations and 1/f^alpha Noise in the Steady States of Multi-Species Resistor Networks

We introduce a multi-species network model which describes the resistance fluctuations of a resistor in a non-equilibrium stationary state. More precisely, a thin resistor characterized by a 1/f^alpha resistance noise is described as a two-dimensional network made by different species of elementary resistors. The resistor species are distinguished by their resistances and by their energies associated with thermally activated processes of breaking and recovery. Depending on the external conditions, stationary states of the network can arise as a result of the competition between these processes. The properties of the network are studied as a function of the temperature by Monte Carlo simulations carried out in the temperature range 300 \div 800 K. At low temperatures, the resistance fluctuations display long-term correlations expressed by a power-law behavior of the auto-correlation function and by a value approx 1 of the alpha-exponent of the spectral density. On the contrary, at high temperatures the resistance fluctuations exhibit a finite and progressively smaller correlation time associated with a non-exponential decay of correlations and with a value of the alpha-exponent smaller than one. This temperature dependence of the alpha coefficient reproduces qualitatively well the experimental findings.