Spectral rigidity of vehicular streams (random matrix theory approach)

Using a method originally developed for the random matrix theory, we derive an approximate mathematical formula for the number variance Delta(N)(L) describing the rigidity of particle ensembles with a power-law repulsion. The resulting relation is compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of the inverse temperature beta, which can be identified as a coefficient of the mental strain of the car drivers, is then discussed in detail with the relation to the traffic density rho and flow J.