Elementary excitations in quantum hydrodynamics for an ideal fluid

Anindya Biswas, I. Rama Rao

Tsubota Makoto, Kasamatsu Makoto

Abstract Chapter 2 describes the basic knowledge of Bose-condensed systems in order to study the quantum hydrodynamics for both the superfluid helium and the atomic-gas BECs in the following sections. Starting from the field theoretical formulation, we will first give a self-contained explanation of the derivation of the most fundamental GP equation for weakly interacting Bose gases at zero temperature. We will also highlight the theoretical treatment for incorporating the concept of elementary excitations to describe low-energy excitations of Bose systems, the definition of normal and superfluid components, and eventually the celebrated model of two-fluid hydrodynamics. Finally, the microscopic structure and dynamics of topological excitations obtained from the GP equation are discussed by exemplifying solitons, vortex lines, and vortex rings.

M. Saarela

Ulf Leonhardt, T. Kiss, Patrik Öhberg

Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the non-condensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to a sonic white hole and find that the spectrum of unstable modes is intrinsically discrete.

Moise Bonilla–Licea, Dieter Schuch

Fabio Franchini