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Negative Compressability of Non-Equilibrium Non-Ideal Bose--Einstein Condensate

An ideal equilibrium Bose--Einstein condensate (BEC) is usually considered in the grand canonical ($μV T$) ensemble, which implies the presence of the chemical equilibrium with the environment. However, in most experimental scenarios, the total amount of particles in BEC is determined either by the initial conditions or by the balance between dissipation and pumping. As a result, BEC may possess the thermal equilibrium but almost never the chemical equilibrium. In addition, many experimentally achievable BECs are non-ideal due to interaction between particles. In the recent work [10.1103/PhysRevLett.128.065301], it has been shown that invariant subspaces in the system Hilbert space appear in non-equilibrium BEC in the fast thermalization limit. In each of these subspaces, Gibbs distribution is established with a certain number of particles that makes it possible to investigate properties of non-ideal non-equilibrium BEC independently in each invariant subspace. In this work, we analyze the BEC stability due to change in dispersion curve caused by non-ideal interactions in BEC. Generally, non-ideal interactions lead to the redshift or blueshift of the dispertion curve and to the change in the effective mass of the particles. We show that the redshift of the dispersion curve can lead to the negative compressibility of BEC, whereas the change in the effective mass always makes BEC more stable. We find the explicit condition for the particle density in BEC, at which the negative compressibility appears.