  Relativistic Brownian motion can be inexpensively demonstrated on a graphene
chip. The interplay of stochastic and relativistic dynamics, governing the
transport of charge carrier in graphene, induces noise-controlled effects such
as (i) a stochastic effective mass, detectable as a suppression of the particle
mobility with increasing the temperature; (ii) a transverse ratchet effect,
measurable as a net current orthogonal to an ac drive on an asymmetric
substrate, and (iii) a chaotic stochastic resonance. Such properties can be of
practical applications in the emerging graphene technology.
