We study an interacting spinless Bose-Einstein condensate to clarify theoretically whether the spectra of its quasiparticles (one-particle excitations) and collective modes (two-particle excitations) are identical, as concluded by Gavoret and Nozières [Ann. Phys. 28, 349 (1964)]. We derive analytic expressions for their first and second moments so as to extend the Bijl-Feynman formula for the peak of the collective-mode spectrum to its width (inverse lifetime) and also to the one-particle channel. The obtained formulas indicate that the width of the collective-mode spectrum manifestly vanishes in the long-wavelength limit, whereas that of the quasiparticle spectrum apparently remains finite. We also evaluate the peaks and widths of the two spectra numerically for a model interaction potential in terms of the Jastrow wave function optimized by a variational method. It is thereby found that the width of the quasiparticle spectrum increases towards a constant as the wavenumber decreases. This marked difference in the spectral widths implies that the two spectra are distinct. In particular, the lifetime of the quasiparticles remains finite even in the long-wavelength limit.

No abstract

No abstract

We study the lifetime of single-particle excitations in a dilute homogeneous Bose-Einstein condensate at zero temperature based on a self-consistent perturbation expansion of satisfying Goldstone's theorem and conservation laws simultaneously. It is shown that every excitation for each momentum p should have a finite lifetime proportional to the inverse a −1 of the s-wave scattering length a, instead of a −2 for the normal state, due to a new class of Feynman diagrams for the self-energy that emerges upon condensation. We calculate the lifetime as a function of |p| approximately.The interaction between particles yields a finite decay rate in every single-particle excitation of many-particle systems. It is caused by collisions between particles that are describable as second-and higher-order processes of the perturbation expansion in terms of the interaction.

We consider the Bose-Einstein transition of homogeneous weakly interacting spin-0 particles based on the normal-state Φ-derivable approximation. Self-consistent calculations of Green's function and the chemical potential with several approximate Φ's are performed numerically as a function of temperature near Tc, which exhibit qualitatively different results. The ladder approximation apparently shows a continuous transition with the prefactor c = 2.94 for the transition-temperature shift ∆Tc/T 0 c = can 1/3 given in terms of the scattering length a and density n. In contrast, the second-order, particle-hole, and fluctuation-exchange approximations yield a first-order transition. The fact that some standard Φ's predict a first-order transition challenges us to clarify whether or not the transition is really continuous.