How Do Quasi-Particles Exist?

Philippe Nozières, David Pines

The density fluctuation excitation spectrum is continuous, since all particle transitions allowed by the Pauli principle will contribute. This chapter shows that the quasi-particle, as a bare particle moving together with the surrounding distortion brought about by particle interactions. The importance, or indeed the existence, of the mechanism, depends on the quasi-particle energies and the phase space available for the decay process. Higher order collision processes can also limit the lifetime of a quasi-particle. In contrast to the single quasi-particle excitations, the multi-particle excitations will be spread over a continuous range of energies, as one allows the momentum of any single quasi-particle component to vary. For an arbitrary particle interaction, there is no a priori region of momenta for which quasi-particles exist as well-defined elementary excitations of the system. In contrast to the single quasi-particle excitations, the multi-particle excitations will be spread over a continuous range of energies, as one allows the momentum of any single quasi-particle component to vary.

Heide Narnhofer, Manfred Requardt, Walter E Thirring

M. Kato, Kazumi Maki

Making use of the Bogoliubov-de Gennes equation, we study the quasi-particle spectrum and the vortex core structure of a single vortex in quasi 2D s-wave superconductors for small pFξ0, where pF is the Fermi momentum and ξ0=vF/Δ0 is the coherence length (ħ=1). During our numerical calculation, the particle number is conserved for each pFξ0. In particular, we find that there are only 1 or 2 bound states for pFξ0=1. Also, for pFξ0=1, the Kramer-Pesch effect ceases to exist at around T/Tc≃0.3.

Dmitry Yarotsky

We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that the presence of isolated eigenvalues in the spectrum of the decoupled model leads to the existence of quasi-particles in the perturbed model. Also, a scattering theory for asymptotically free many-particle states is developed.

Frederick Reif