Quantum-coherent transport of a heavy particle in a fermionic bath

In this review, a detailed discussion of the behaviour of a heavy particle interacting with a Fermi sea is given. Particular emphasis is put on the is sue of how strong correlations influence coherence and transport of the par ticle. First, we investigate the question of whether the heavy particle is a well defined qausiparticle at low temperatures. While in one dimension (D = 1) and at a van Hove singularity in D = 2 the coherence of the particle is destroyed, the quasiparticle weight is finite in higher dimensions. The most important transport quantity is the diffusion constant or mobility of the heavy particle. We are able to describe both the well known high-temper ature properties and the cross-over to the lowest temperatures in a unified approximation scheme based on a self-consistent evaluation of an effective action. Two strong-correlation effects of independent origin are discussed . The first arises if the scattering of the fermions from the heavy particl e is nearly resonant, that is, if one of the scattering phase shifts delta is close to pi/2. In this regime an anomalous exponent is observed in the t emperature dependence of the mobility mu(T). In D = 3, for instance, the mo bility is proportional to T-3/2 rather than to T-2 The second effect is a g iant mass renormalization in the case of a large particle. In this situatio n, the low-temperature effective mass M* increases up to an exponentially l arge value, M* proportional to exp[c(r/lambda(F))(3)], where r is the effec tive radius of the particle, lambda(F) the Fermi wavelength and c a non-uni versal constant of order one.