Do tunneling two-level defects dephase conduction electrons at millikelvin temperatures?
In plain words
Atomic defects that flip slowly between two positions, of the kind found in glasses, create fluctuating potentials that can scramble electron phases. Whether such defects are numerous and fast enough to produce the observed leveling-off of the phase-coherence time is not established.
Precise statement
Imry, Fukuyama and Schwab (Europhysics Letters 47, 608, 1999) proposed that two-level systems with a broad ($1/f$-type) distribution of relaxation rates give a nearly temperature-independent dephasing rate $1/\tau_{\phi}$ in disordered conductors. For a disordered metal film with independently measured fluctuator density and rate distribution (from $1/f$ resistance noise or low-$T$ acoustic data), compute $1/\tau_{\phi}(T)$ and decide whether it matches the measured saturated value with no free parameters.
What would settle it
Joint measurement of $1/f$ resistance noise, low-temperature internal friction or heat capacity, and weak-localization $\tau_{\phi}$ on the same films, compared with a two-level-system dephasing calculation that uses the measured fluctuator distribution.