2014/05/28 by Tom Price, Austen Lamacraft · 1 citation
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Dimension (graph theory) #Mathematics #Phonon #Physics #Pure mathematics #Quantum #Quantum hydrodynamics #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #Theoretical physics #cond-mat.quant-gas
paper · pdf · doi:10.1103/physrevb.90.241415
published as Phys. Rev. B 90, 241415 (2014) · 5 pages, 1 figure
arxiv created 2014/05/28 · openalex publication_date 2014/12/19 · arxiv updated 2014/12/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that the resonant interactions between phonons in one dimension may be treated consistently within quantum hydrodynamics by the introduction of phonon dispersion. In this way the physics of a nonlinear Luttinger liquid may be described in terms of hydrodynamic (i.e., bosonized) variables without the introduction of impurities at the outset, and gives a complementary view on the mobile impurity model from the hydrodynamics. We focus on the calculation of the dynamic structure factor for a model with quadratic dispersion, which has the Benjamin-Ono equation of fluid dynamics as its equation of motion. We find singular behavior in the vicinity of upper and lower energetic thresholds corresponding to phonon and soliton branches of the classical theory, which may be benchmarked against known results for the Calogero-Sutherland model.