In the present work we study possible time dependent effects in Axion Dark Matter searches employing resonant cavities. We find that the width of the resonance, which depends on the axion mean square velocity in the local frame, will show an annual variation due to the motion of the Earth around the sun (modulation). Furthermore, if the experiments become directional, employing suitable resonant cavities, one expects large asymmetries in the observed widths relative to the suns direction of motion. Due to the rotation of the Earth around its axis, these asymmetries will manifest themselves as a diurnal variation in the observed width.
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