Infrared behavior and spectral function of a Bose superfluid at zero temperature
- Laboratoire de Physique Theorique de la Matiere Condensee, CNRS UMR 7600, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France) and Laboratoire de Physique des Solides, CNRS UMR 8502, Universite Paris-Sud, 91405 Orsay (France)
In a Bose superfluid, the coupling between transverse (phase) and longitudinal fluctuations leads to a divergence of the longitudinal correlation function, which is responsible for the occurrence of infrared divergences in the perturbation theory and the breakdown of the Bogoliubov approximation. We report a nonperturbative renormalization-group calculation of the one-particle Green's function of an interacting boson system at zero temperature. We find two regimes separated by a characteristic momentum scale k{sub G} ('Ginzburg' scale). While the Bogoliubov approximation is valid at large momenta and energies,|p|,|{omega}|/c>>k{sub G} (with c as the velocity of the Bogoliubov sound mode), in the infrared (hydrodynamic) regime,|p|,|{omega}|/c<<k{sub G}, the normal and anomalous self-energies exhibit singularities reflecting the divergence of the longitudinal correlation function. In particular, we find that the anomalous self-energy agrees with the Bogoliubov result {sigma}{sub an}(p,{omega}){approx_equal}const at high energies and behaves as {sigma}{sub an}(p,{omega}){approx}(c{sup 2}p{sup 2}-{omega}{sup 2}){sup (d-3)/2} in the infrared regime (with d as the space dimension), in agreement with the Nepomnyashchii identity {sigma}{sub an}(0,0)=0 and the predictions of Popov's hydrodynamic theory. We argue that the hydrodynamic limit of the one-particle Green's function is fully determined by the knowledge of the exponent 3-d characterizing the divergence of the longitudinal susceptibility and the Ward identities associated to gauge and Galilean invariances. The infrared singularity of {sigma}{sub an}(p,{omega}) leads to a continuum of excitations (coexisting with the sound mode) which shows up in the one-particle spectral function.
- OSTI ID:
- 21316464
- Journal Information:
- Physical Review. A, Vol. 80, Issue 4; Other Information: DOI: 10.1103/PhysRevA.80.043627; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
CORRELATION FUNCTIONS
EXCITATION
FLUCTUATIONS
GREEN FUNCTION
INFRARED DIVERGENCES
INTERACTING BOSON MODEL
PARTICLES
PERTURBATION THEORY
RENORMALIZATION
SELF-ENERGY
SINGULARITY
SOUND WAVES
SPECTRAL FUNCTIONS
SUPERFLUIDITY
WARD IDENTITY