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An ideal equilibrium Bose--Einstein condensate (BEC) is usually considered inthe grand canonical ($\mu V T$) ensemble, which implies the presence of thechemical equilibrium with the environment. However, in most experimentalscenarios, the total amount of particles in BEC is determined either by theinitial conditions or by the balance between dissipation and pumping. As aresult, BEC may possess the thermal equilibrium but almost never the chemicalequilibrium. In addition, many experimentally achievable BECs are non-ideal dueto interaction between particles. In the recent work[10.1103/PhysRevLett.128.065301], it has been shown that invariant subspaces inthe system Hilbert space appear in non-equilibrium BEC in the fastthermalization limit. In each of these subspaces, Gibbs distribution isestablished with a certain number of particles that makes it possible toinvestigate properties of non-ideal non-equilibrium BEC independently in eachinvariant subspace. In this work, we analyze the BEC stability due to change indispersion curve caused by non-ideal interactions in BEC. Generally, non-idealinteractions lead to the redshift or blueshift of the dispertion curve and tothe change in the effective mass of the particles. We show that the redshift ofthe dispersion curve can lead to the negative compressibility of BEC, whereasthe change in the effective mass always makes BEC more stable. We find theexplicit condition for the particle density in BEC, at which the negativecompressibility appears.

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