Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent

TL;DR

This paper introduces a logarithmic wave equation model for Bose liquids that exhibits self-sustainability, formation of finite-sized droplets, and diverse excitation spectra, offering a new perspective beyond the traditional Gross-Pitaevskii approach.

Contribution

It presents a novel logarithmic nonlinear model for Bose liquids that captures self-sustained droplets and emergent spatial extent, unlike the standard Gross-Pitaevskii equation.

Findings

Logarithmic Bose liquid forms Gaussian droplets without external traps.

Quasi-particle modes have finite size due to many-body correlations.

Excitation spectra vary with density, showing different relativistic behaviors.

Abstract

The Gross-Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose-Einstein condensates (BEC). However, in many physical situations, such as higher densities, this approximation unlikely suffices hence one might need models which would account for long-range correlations and multi-body 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 self-sustainability property: while the free GP condensate tends to spill all over the available volume the logarithmic one tends to form a Gaussian-type droplet - even in the absence of an external trapping potential. The quasi-particle modes of the logarithmic BEC are shown to acquire a finite size despite the bare particles being assumed point-like, i.e., the spatial extent emerges here as a result of quantum many-body 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.