We report on BeppoSAX and Chandra observations of three Hard X-Ray Transients in quiescence containing fast spinning (P<5 s) neutron stars: A 0538-66, 4U 0115+63 and V 0332+53. These observations allowed us to study these transients at the faintest flux levels thus far. Spectra are remarkably different from the ones obtained at luminosities a factor >10 higher, testifying that the quiescent emission mechanism is different. Pulsations were not detected in any of the sources, indicating that accretion of matter down to the neutron star surface has ceased. We conclude that the quiescent emission of the three X-ray transients likely originates from accretion onto the magnetospheric boundary in the propeller regime and/or from deep crustal heating resulting from pycnonuclear reactions during the outbursts.

Accepted for publication on ApJ (5 pages and 2 figures)