Stability and metastability of trapless Bose-Einstein condensates and quantum liquids

TL;DR

This paper investigates the stability of trapless Bose-Einstein condensates across various models and dimensions, revealing that logarithmic models are stable while polynomial models are metastable and prone to delocalization.

Contribution

It provides a comprehensive stability analysis of trapless BECs using variational and Vakhitov-Kolokolov methods across different wave equations and dimensions.

Findings

Logarithmic BECs are essentially stable regardless of dimension.

Polynomial BECs are metastable and can delocalize spontaneously.

Stability depends on the type of wave equation describing the condensate.

Abstract

Various kinds of Bose-Einstein condensates are considered, which evolve without any geometric constraints or external trap potentials including gravitational. For studies of their collective oscillations and stability, including the metastability and macroscopic tunneling phenomena, both the variational approach and the Vakhitov-Kolokolov criterion are employed, calculations are done for condensates of an arbitrary spatial dimension. It is determined that that the trapless condensate described by the logarithmic wave equation is essentially stable, regardless of its dimensionality, while the trapless condensates described by wave equations of a polynomial type with respect to the wavefunction, such as the Gross-Pitaevskii (cubic), cubic-quintic, and so on, are at best metastable. This means that trapless "polynomial" condensates are unstable against spontaneous delocalization caused by fluctuations of their width, density and energy, leading to a finite lifetime.