Model of r space Boson-Fermion mixture and its relevance to high-T-c cuprates

Motivated by a correlation between experimentally measured in-plane resistivity R and nuclear spin-lattice relaxation time T-1 for Cu nuclei in an underdoped high-T-c cuprate, a model is set up and solved for the equilibrium between (e) Fermion monomers and (2e) composite r space Bosons. Quantum statistics is fully included and of special interest for the R-T-1 correlation are the numbers of Fermion monomers in equilibrium with these composite Bosons for T > T-c. The model is shown to give the gist of the explanation of a pronounced minimum in a plot of the product RT1 vs T for the underdoped cuprate. Some contact is also made with transverse plasmon measurements, which are related to the composite Boson density in the condensate below T-c. Refinements of the simple model used here will eventually need to treat the finite lifetime of the composite Bosons and the screening of the charged particles, especially in the normal state. These can be expected to reduce the temperature range over which, in the normal state, the composite Boson number density is an appreciable fraction of the Fermion monomer density.