  In this work we discuss the dynamical response of heavy quantum impurities
immersed in a Fermi gas at zero and at finite temperature. Studying both the
frequency and the time domain allows one to identify interaction regimes that
are characterized by distinct many-body dynamics. From this theoretical study a
picture emerges in which impurity dynamics is universal on essentially all time
scales, and where the high-frequency few-body response is related to the
long-time dynamics of the Anderson orthogonality catastrophe by Tan relations.
Our theoretical description relies on different and complementary approaches:
functional determinants give an exact numerical solution for time- and
frequency-resolved responses, bosonization provides analytical expressions at
low temperatures, and the theory of Toeplitz determinants allows one to
analytically predict response up to high temperatures. Using these approaches
we predict the thermal decoherence rate and prove that within the considered
model the fastest rate of long-time decoherence is given by $\gamma=\pi
k_BT/4$. We show that Feshbach resonances in cold atomic systems give access to
new interaction regimes where quantum effects prevail even in the thermal
regime of many-body dynamics. The key signature of this phenomenon is a
crossover between exponential decay rates of the real-time Ramsey signal. It is
shown that the physics of the orthogonality catastrophe is experimentally
observable up to temperatures $T/T_F\lesssim 0.2$ where it leaves its
fingerprint in a power-law temperature dependence of thermal spectral weight
and we review how this phenomenon is related to the physics of heavy ions in
liquid $^3$He and the formation of Fermi polarons. The presented results are in
excellent agreement with recent experiments on LiK mixtures, and we predict
several phenomena that can be tested using currently available experimental
technology.
