Quantum Bose liquids with logarithmic nonlinearity: selfsustainability and emergence of spatial extent
Abstract
The GrossPitaevskii (GP) equation is a longwavelength approach widely used to describe the dilute BoseEinstein condensates (BEC). However, in many physical situations, such as higher densities, it is unlikely that this approximation suffices; hence, one might need models which would account for longrange correlations and multibody interactions. We show that the Bose liquid described by the logarithmic wave equation has a number of drastic differences from the GP one. It possesses the selfsustainability property: while the free GP condensate tends to spill all over the available volume, the logarithmic one tends to form a Gaussiantype droplet—even in the absence of an external trapping potential. The quasiparticle modes of the logarithmic BEC are shown to acquire a finite size despite the bare particles being assumed to be pointlike, i.e. the spatial extent emerges here as a result of quantum manybody correlations. Finally, we study the elementary excitations and demonstrate that the background density changes the topological structure of their momentum space which, in turn, affects their dispersion relations. Depending on the density, the latter can be of the massive relativistic, massless relativistic, tachyonic and quaternionic type.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 October 2011
 DOI:
 10.1088/09534075/44/19/195303
 arXiv:
 arXiv:1108.0847
 Bibcode:
 2011JPhB...44s5303A
 Keywords:

 Condensed Matter  Quantum Gases;
 Astrophysics  Solar and Stellar Astrophysics;
 High Energy Physics  Theory;
 Nuclear Theory;
 Quantum Physics
 EPrint:
 14 pages, 5 figures. Updates: v2: minor corrections (published version)