Abstract
We propose that memory effects in the conductivity of metallic systems can be produced by the same two-level systems that are responsible for the $1/f$ noise. Memory effects are extremely long-lived responses of the conductivity to changes in external parameters such as density or magnetic field. Using quantum transport theory, we derive a universal relationship between the memory effect and the $1/f$ noise. Finally, we propose a magnetic memory effect, where the magnetoresistance is sensitive to the history of the applied magnetic field.
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