Dynamics of Weyl wave-packets in a noisy environment

We study the effect of coupling to an environment a particle whose dynamics is governed by the Weyl equation. This model describes chiral quasi-particles in graphene in the presence of noise. Using an exact mapping of the Hamiltonian onto a conditional spin-boson model we study the dynamics of wave-packets, and how the phenomena of spin-separation and Zitterbewegung survive in the presence of noise. We studied three limits of the problem, for which exact results can be derived, namely noise with arbitrary spectrum coupled parallel to the direction of motion, and for arbitrary orientation the limits of low frequency and white noise.