The dielectric response, epsilon'(omega) + i epsilon ''(omega), of amo
rphous and glassy systems at low temperatures has been explained with
considerable success by relaxation and resonant tunneling of independe
nt tunneling two level systems (TLS) in response to an AC electric fie
ld. However, recent measurements have shown an AC response to the appl
ication of large DC electric fields which does not appear explicable i
n terms of independent TLS, but instead may result from the formation
of a hole in the density of states of the TLS at zero effective local
electric field, similar to that postulated to exist in spin glasses. T
his paper reports new studies of this response at very low temperature
s which further support this interpretation, again suggesting that int
eractions are important in understanding the dynamics of such systems
at low temperatures.