One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

Abstract

In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose-Einstein condensate (BEC) described by the deformed one-dimensional Gross-Pitaevskii equation (GPE). Analytical solutions were derived for null potential, while, we used variational and numerical methods for harmonic oscillator potential. Subsequently, we analyzed the probability density, position, and momentum uncertainties as functions of the deformation parameter α

Study of Bose–Einstein condensate in the presence of the extended uncertainty principle: infinite potential well

“…This methodology is consistent with experimental observations of anyons [33][34][35]. In our previous study, we addressed the deformed one-dimensional GPE in the absence of an external potential and under the presence of a harmonic potential [36]. In this work, we will investigate the effect of EUP and nonlinearity on the probability density, energy eigenvalues, position, and momentum uncertainties of BEC confined in a box, for attractive and repulsive interactions, in other words, we will see how BEC interacts with curved space-time.…”