一个自束缚的物质波玻色子-费米子量子球
A self-bound matter-wave boson-fermion quantum ball
摘要：
我们证明了在存在吸引玻色子-费米子相互作用和小的排斥三玻色子相互作用的情况下，产生自束缚稳定的三维物质波球形玻色子-费米子量子球的可能性。三玻色子的相互作用可以是吸引的或排斥的，而费米子被认为是在一个完全配对的超流态在Barnes-Cooper-Schreifer（准非相互作用弱耦合）限制。我们还包括李-黄-杨（LHY）修正的排斥玻色子相互作用项。三玻色子排斥相互作用和LHY修正可以联合或单独作用来阻止整体坍缩。本研究是基于一个平均场模型，玻色子是受一个Gross-Pitaevskii（GP）拉格朗日功能和完全配对的费米子描述的伽利略不变的密度泛函拉格朗日。玻色子-费米子相互作用被视为平均场Hartree相互作用，与GP方程中的相互作用项非常相似。本文用玻色子-费米子$^7$ Li- $^6$ Li系统的平均场模型的变分和数值解来说明这一研究。
英文摘要：
We demonstrate the possibility of creating a self-bound stable three-dimensional matter-wave spherical boson-fermion quantum ball in the presence of an attractive boson-fermion interaction and a small repulsive three-boson interaction. The three-boson interaction could be attractive or repulsive whereas the fermions are taken to be in a fully-paired super-fluid state in the Bardeen- Cooper-Schreifer ( quasi-noninteracting weak-coupling) limit. We also include the Lee-Huang-Yang (LHY) correction to a repulsive bosonic interaction term. The repulsive three-boson interaction and the LHY correction can stop a global collapse while acting jointly or separately. The present study is based on a mean-field model, where the bosons are subject to a Gross-Pitaevskii (GP) Lagrangian functional and the fully-paired fermions are described by a Galilean-invariant density functional Lagrangian. The boson-fermion interaction is taken to be the mean-field Hartree interaction, quite similar to the interaction term in the GP equation. The study is illustrated by a variational and a numerical solution of the mean-field model for the boson-fermion $^7$Li- $^6$Li system.
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