Are Quasiparticles and Phonons Identical in Bose--Einstein Condensates?

TL;DR

This paper investigates whether quasiparticles and collective modes in a Bose-Einstein condensate have identical spectra, finding that their spectral widths differ significantly and they are fundamentally distinct, especially in the long-wavelength limit.

Contribution

The study provides analytic expressions extending the Bijl-Feynman formula to include spectral widths and demonstrates that quasiparticles and collective modes are not identical in spectral properties.

Findings

Collective-mode spectrum width vanishes at long wavelengths.

Quasiparticle spectrum width remains finite at long wavelengths.

Quasiparticles have a finite lifetime even as wavelength increases.

Abstract

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 Nozi\`eres [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.