Nonextensive Gross Pitaevskii Equation

Abstract

In this paper, we consider the generalization of Gross Pitaevskii equation for condensate of bosons with nonextensive statistics. First, we use the non-additive methods and formalism to obtain the well-known Schrödinger equation. Using a suitable Hamiltonian for condensate phase and minimizing the free energy of the system by non-additive formalism, we work out the nonextensive Gross Pitaevskii equation.

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

“…This approach aligns with experimental observations of anyons [22][23][24]. To our best knowledge, the topic of the GPE has been addressed in terms of a modified momentum operator only once [21].…”

“…They naturally introduce a modified uncertainty principle, which is associated with the quantum structure of space-time. Additionally, in [21], the authors examine the GPE within the framework of q-deformed or nonextensive statistics which is mathematically equivalent to equation (1). This approach aligns with experimental observations of anyons [22][23][24].…”

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

“…The same remark is valid for the repulsive case. It is noticeable, that there is no symmetric between the probability in the regions [0, 0.5] and [0.5, 1] for α ≠ 0, and to explain why, let us write the probability density for equations (32) in terms of η,…”

“…The study of the impact of EUP on BEC has been explored in [31], where the modified uncertainty principle with linear form has naturally reproduced by considering the effects originating from the Planck scale regime during the free expansion of a condensate. Moreover, in [32], the authors investigate the GPE within the framework of q-deformed or nonextensive statistics, which is mathematically equivalent to equation (2). This methodology is consistent with experimental observations of anyons [33][34][35].…”