ABSTRACT
Analyzing disorder effects in three‐dimensional Landau Fermi liquids in Chapter 8, we showed that the quasiparticle relaxation rate 1 1/τ ee ∼ |ɛ|3/2, is larger than in the clean Fermi liquid in which 1/τ ee ∼ ɛ 2. The calculation of the relaxation rate was based on application of the Fermi Golden Rule, which is relevant where the final states in a scattering process can be regarded as a continuum. Coulomb interaction provides the means by which a particle scatters into another particle state together with a particle‐hole pair. Physically, the enhancement of the decay rate in the disordered case arises from reduction of some of the phase space constraints related to momentum conservation, which in the clean Fermi liquid lead to the ɛ 2 dependence. We pose the following question in this chapter: what happens to the electron relaxation rate in a disordered metal when its volume is progressively decreased? The point is that in a finite volume, the energy levels become discrete and one needs to exercise care while using the Fermi Golden Rule, or for that matter, even understanding the meaning of quasiparticle relaxation.
