We study the interaction-induced quantum correction δσ_αβ to the conductivity tensor of electrons in two dimensions for arbitrary Tτ (where T is the temperature and τ the transport scattering time), magnetic field, and type of disorder. A general theory is developed, allowing us to express δσ_αβ in terms of classical propagators (``ballistic diffusons''). The formalism is used to calculate the interaction contribution to the longitudinal and the Hall resistivities in a transverse magnetic field in the whole range of temperature from the diffusive (Tτ1) to the ballistic (Tτ1) regime, both in smooth disorder and in the presence of short-range scatterers. Further, we apply the formalism to anisotropic systems and demonstrate that the interaction induces quantum oscillations in the resistivity of lateral superlattices.
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Gornyi et al. (2004) studied this question.