Kondo polarons

A few days ago I had what I thought was a good idea: to look at the behavior of moving magnetic impurities, and see if they interpolate somehow between the Kondo effect and the polaron as you tune the mass of the impurity down from infinity. (There are some obvious ways to realize the interpolation experimentally using cold Fermi gases.) I was disappointed to find that someone else got there first, and tantalizingly recently (May 2008); Lamacraft's result is, however, really interesting, and would've been beyond my powers to derive:

Kondo Polarons in a One-Dimensional Fermi Gas
Austen Lamacraft
PRL 101, 225301 (2008)

Abstract: We consider the motion of a spin-1/2 impurity in a one-dimensional gas of spin-1/2 fermions. For antiferromagnetic interaction between the impurity and the fermions, the low temperature behavior of the system is governed by the two-channel Kondo effect, leading to the impurity becoming completely opaque to the spin excitations of the gas. As well as the known spectral signatures of the two-channel Kondo effect, we find that the low temperature mobility of the resulting `Kondo polaron' takes the universal form $\mu\to \frac{3\hbar v_F^2}{2\pi k_B^2T^2}$, in sharp contrast to the spinless case where $\mu\propto T^{-4}$.

The really interesting thing here is that the case of the mobile impurity differs drastically from that of the fixed (infinite-mass) impurity because certain processes that are permitted with an infinite-mass impurity are forbidden, because of the impossibility of simultaneously conserving energy and momentum, in a finite-mass impurity. One consequence of this is that, whereas the infinite-mass impurity couples to a single scattering channel (even combinations of left- and right-moving traveling waves) the finite-mass impurity couples independently to the left- and right-moving channels. This means that the 1D Kondo problem with recoil is not the one-channel Kondo problem but the far more exotic two-channel Kondo problem.