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arXiv · 0901.4631

Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory

N. Dupuis
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Abstract

Using a non-perturbative renormalization-group technique, we compute the momentum and frequency dependence of the anomalous self-energy and the one-particle spectral function of two-dimensional interacting bosons at zero temperature. Below a characteristic momentum scale $k_G$, where the Bogoliubov approximation breaks down, the anomalous self-energy develops a square root singularity and the Goldstone mode of the superfluid phase (Bogoliubov sound mode) coexists with a continuum of excitations, in agreement with the predictions of Popov's hydrodynamic theory. Thus our results provide a unified picture of superfluidity in interacting boson systems and connect Bogoliubov's theory (valid for momenta larger than $k_G$) to Popov's hydrodynamic approach.

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N. Dupuis. 2009-05-22. Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory. https://doi.org/10.1103/physrevlett.102.190401

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