We present the phase diagram of the mean-field driven-dissipative Bose-Hubbard dimer model. For a dimer with repulsive on-site interactions ($U>0$) and coherent driving we prove that $\mathbb{Z}_2$-symmetry breaking, via pitchfork bifurcations with sizable extensions of the asymmetric solutions, require a negative tunneling parameter ($J<0$). In addition, we show that the model exhibits deterministic dissipative chaos. The chaotic attractor emerges from a Shilnikov mechanism of a periodic orbit born in a Hopf bifurcation and, depending on its symmetry properties, it is either localized or not.

中文翻译：

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驱动耗散 Bose-Hubbard 二聚体：相图和混沌

我们展示了平均场驱动耗散 Bose-Hubbard 二聚体模型的相图。对于具有排斥性现场相互作用（$U>0$）和相干驱动的二聚体，我们证明 $\mathbb{Z}_2$-对称破坏，通过具有相当大非对称解扩展的干草叉分叉，需要负隧道参数($J<0$)。此外，我们表明该模型表现出确定性耗散混沌。混沌吸引子产生于 Hopf 分岔中周期性轨道的 Shilnikov 机制，根据其对称性，它要么是局部的，要么不是局部的。