In the present chapter, we shall apply the theory developed in the previous chapter to study ultra-cold quantum liquid droplets qualitatively described in Sects. 2.2 and 5.9. We have mentioned that, in a two-component Bose system, a stable Bose phase-quantum droplet may arise due to the balance between attractive intercomponent \((g_{ab}<0)\) and repulsive intracomponent \((g_{aa}\equiv g_a>0, g_{bb}\equiv g_b>0 )\) interactions. Below we quantitatively discuss this point, showing that such a picture will take place when the attractive mean-field term \({\mathcal {E}}_{MFA} \sim \rho ^2\) is compensated by the repulsive LHY energy term \({\mathcal {E}}_{LHY}\sim \rho ^{5/2}\) . In other words, the resulting effective interaction \({\mathcal {E}}_{tot}\sim {\tilde{\alpha }} \rho ^2+{\tilde{\beta }} \rho ^{5/2}\) with \({\tilde{\alpha }}<0\) and \({\tilde{\beta }}>0\) will give rise to a self-bound solution: so-called quantum liquid droplet.

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Quantum Liquid Droplets in Two-Component Bose Mixtures

  • Abdulla Rakhimov,
  • Shukhrat Mardonov

摘要

In the present chapter, we shall apply the theory developed in the previous chapter to study ultra-cold quantum liquid droplets qualitatively described in Sects. 2.2 and 5.9. We have mentioned that, in a two-component Bose system, a stable Bose phase-quantum droplet may arise due to the balance between attractive intercomponent \((g_{ab}<0)\) and repulsive intracomponent \((g_{aa}\equiv g_a>0, g_{bb}\equiv g_b>0 )\) interactions. Below we quantitatively discuss this point, showing that such a picture will take place when the attractive mean-field term \({\mathcal {E}}_{MFA} \sim \rho ^2\) is compensated by the repulsive LHY energy term \({\mathcal {E}}_{LHY}\sim \rho ^{5/2}\) . In other words, the resulting effective interaction \({\mathcal {E}}_{tot}\sim {\tilde{\alpha }} \rho ^2+{\tilde{\beta }} \rho ^{5/2}\) with \({\tilde{\alpha }}<0\) and \({\tilde{\beta }}>0\) will give rise to a self-bound solution: so-called quantum liquid droplet.