The quantum–classical crossover of the escape rate is studied in a nanomagnetic Josephson $$\varphi _0$$ φ 0 junction within the framework of the spin-coherent-state path integral method. The nonlinear perturbation approach is employed to obtain the crossover boundary separating the first- and the second-order crossovers. The region for the first-order crossover is greatly suppressed by the bias current applied to the junction as well as the external magnetic field. These features can be tested using existing experimental techniques.

中文翻译：

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嵌入约瑟夫森 $$\varphi _0$$ 结中的纳米自旋系统中的量子经典交叉

在自旋相干态路径积分方法的框架内，在纳米磁性约瑟夫森 $$\varphi _0$$ φ 0 结中研究逃逸率的量子-经典交叉。非线性微扰方法用于获得分隔一阶和二阶交叉的交叉边界。施加到结的偏置电流以及外部磁场极大地抑制了一阶交叉区域。这些功能可以使用现有的实验技术进行测试。