q-deformed Bose statistics and the Gross-Pitaevskii equation

In continuation of our earlier work on the nonextensive form of the Gross-Pitaevskii equation (GPE) [M. Maleki, H. Mohammadzadeh and Z. Ebadi, Int. J. Geom. Methods Mod. Phys. 20 (2023) 2350216], we now delve into its q-deformed counterpart. GPE is a type of nonlinear partial differential equation that is specifically designed to describe the behavior of a group of particles with Bose-Einstein statistics, such as atoms in a superfluid or a Bose-Einstein condensate (BEC). In some systems, the standard Bose-Einstein or Fermi-Dirac statistics may not apply, and generalized statistics may be needed to describe the behavior of the particles. Therefore in this paper, we investigate the dynamics of a system with particle obeying q-deformed statistics described by the q-deformed GPE. First, we use the oscillator algebra and q-calculus to obtain the well-known Schrodinger equation. By selecting an appropriate Hamiltonian for the condensate phase and minimizing the free energy, we derive the q-deformed time-independent GPE.