AI 中文总结
研究广义LMG模型与热环境耦合的耗散动力学，先利用线性Lindblad主方程推导磁化方程并得到规范平衡相图，后扩展到非线性方程，发现跳跃保留参数可调控相图，建立了动力学与稳态行为联系，为工程非平衡相提供机制。
AI 中文摘要
我们研究了与热环境耦合的广义Lipkin-Meshkov-Glick（LMG）模型的耗散动力学。在这个广义模型中，除了传统的二次相互作用，还考虑了自旋-1/2之间全对全耦合且在横向场存在下演化的四次相互作用。利用具有热平衡跳跃过程的通常线性Lindblad主方程，我们推导了磁化演化方程，并证明相应的稳态解再现了模型的规范平衡相图。然后我们将分析扩展到一个非线性Lindblad方程，该方程根据跳跃保留参数纳入了不完美量子跳跃过程。在此，显著的是，系统弛豫到一个真正的非平衡稳态，其性质与线性情况下获得的性质有质的不同。跳跃保留参数提供了可调旋钮，可移动相边界，甚至相对于线性情况改变相变的性质。我们的精确结果建立了耗散弛豫动力学与稳态行为之间的直接联系，同时将受控量子跳跃保留确定为在长程相互作用开放量子系统中工程非平衡相的一种机制。
英文摘要
We investigate the dissipative dynamics of a generalized Lipkin-Meshkov-Glick (LMG) model coupled to a thermal environment. In this generalized model, in addition to the conventional quadratic interaction, one considers quartic interactions between spin-$1/2$'s coupled all-to-all and evolving in presence of a transverse field. Employing the usual linear Lindblad master equation with thermally-balanced jump processes, we derive magnetisation evolution equations, and demonstrate that the corresponding stationary solution reproduces the canonical equilibrium phase diagram of the model. We then extend our analysis to a nonlinear Lindblad equation that incorporates imperfect quantum-jump processes in terms of jump-retention parameters. Here, remarkably, the system relaxes to a genuine nonequilibrium stationary state whose properties differ qualitatively from those obtained in the linear case. The jump-retention parameters provide tunable knobs that shift the phase boundaries and even modify the nature of the phase transitions with respect to the linear case. Our exact results establish a direct connection between dissipative relaxation dynamics and stationary-state behavior, while identifying controlled quantum-jump retention as a mechanism for engineering nonequilibrium phases in long-range interacting open quantum systems.
Comments13 Pages, 4 figures
