We study quantum phase coherence and weak localization (WL) in disorderedmetals with restricted back-scattering and phenomenologically formulate a largeclass of unconventional transport mechanisms as modified diffusion processesnot captured by the Boltzmann picture. Inspired by conductivity measurements inferromagnetic films and semiconductors where anomalous power law correctionshave been observed, we constrain memory dependent, self avoidance effects ontothe quantum enhanced back-scattered trajectories, drastically altering theeffect of weak localization in two dimensions (2D). Scale dependent correctionsto the conductivity fail to localize the electrons in $d \ge 2$ forsufficiently weak disorder. Additionally, we analyze quantum transport inreaction-diffusion systems governed by the Fisher's equation and observeasymptotically similar delocalization in 2D. Such unconventional transportmight be relevant to certain non-Fermi liquid or strongly correlated phases in2D within the negative compressibility regime.
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