Multiple Quasiparticle Pairs in The BCS Model

Abstract

We study the case when in the system are present multiple quasiparticles in terms of the BCS model. Multiple quasiparticles are thermally or externally excited as a result of breaking apart of Cooper pairs form the BCS condensate. We consider the multiple pairs of quasiparticles in terms of the BCS Hamiltonian and the BCS ground state. Although there is no interaction between quasiparticle pairs in terms of the BCS Hamiltonian, yet we have shown that two and four quasiparticles can be paired and form a bound state. The bound state for a pair of quasiparticles exists as a result of the large quasiparticle density of states and the residual interaction between two quasiparticles which is described by the non-diagonal terms in the BCS Hamiltonian written in terms of quasiparticles. In the case of four quasiparticles the bound state exists only as a result of the Pauli principle and the large quasiparticle density of states. We have shown that in the BCS ground state quasiparticle pairs can form bound pairs similar to the Cooper’s pair of particles due to the nondiagonal terms in the BCS Hamiltonian. We show that a quartet of bound quasiparticles represents a composite boson, and the multiple quartets of bound quasiparticles can undergo the conventional Bose condensation of a boson gas. The temperature of the Bose condensation corresponds to the conventional temperature of Bose condensation for non-interacting bosons where each boson has quadruple mass of quasiparticles and the boson density is one-quarter of quasiparticle density.