We consider the condensate of q-deformed bosons as a model of dark matter. Our observations demonstrate that for all q values, the system condenses below a q-dependent critical temperature
T
c
q
. The critical temperature interestingly tends to infinity when q → 0, so that the q-deformed boson gas is always in the condensed phase in this limit irrespective to the temperature. We argue that this has remarkable outcomes, e.g. on the entropy of the system, and also the fraction of the particles in the ground state. Especially, by direct evaluation of the entropy of the system we reveal that it tends to zero at this limit for all temperatures, and also the fraction of particles in the ground state becomes unity. These observations prove the consistency of the model, put it in the list of appropriate candidates for dark matter.
We introduce the deformed boson condensate and argue that its properties are consistent with the properties of the dark matter (DM). For every candidate of DM, the mass bounds evaluation is important. Therefore, the lower and upper bounds of mass are evaluated using the phase space density and observational data for q deformed Bose–Einstein condensate (q-BEC) model. We show that the upper bound of q-BEC and ordinary BEC model is the same, while for small values of q, the lower bound tends to zero which is in favor of the light DM particles.
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.
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