Quantum phase coherence in non-Markovian and reaction-diffusive transport

We study quantum phase coherence and weak localization (WL) in disordered metals with restricted back-scattering and phenomenologically formulate a large class of unconventional transport mechanisms as modified diffusion processes not captured by the Boltzmann picture. Inspired by conductivity measurements in ferromagnetic films and semiconductors where anomalous power law corrections have been observed, we constrain memory dependent, self avoidance effects onto the quantum enhanced back-scattered trajectories, drastically altering the effect of weak localization in two dimensions (2D). Scale dependent corrections to the conductivity fail to localize the electrons in $d \ge 2$ for sufficiently weak disorder. Additionally, we analyze quantum transport in reaction-diffusion systems governed by the Fisher's equation and observe asymptotically similar delocalization in 2D. Such unconventional transport might be relevant to certain non-Fermi liquid or strongly correlated phases in 2D within the negative compressibility regime.