We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator, which in turn give access to closed-form analytical expressions for the time evolution of the density operator and observables. Our approach is valid for large systems but takes into account leading-order finite-size corrections to the infinite-system result. As an application, we show that the dissipative Lipkin-Meshkov-Glick model equilibrates by passing through a continuum of thermal states with damped oscillations superimposed, until finally reaching an equilibrium state with a temperature that in general differs from the bath temperature. We discuss limitations of our analytic techniques by comparing to exact numerical results.

中文翻译：

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具有马尔可夫耗散的Lipkin-Meshkov-Glick模型的Bosonic表示

我们研究了存在马尔可夫耗散的Lipkin-Meshkov-Glick模型的动力学，重点是后期动力学和热平衡方法。利用相应Lindblad主方程的矢量化玻色子表示形式，我们使用弱耗散极限中的简并扰动理论来解析获得Liouvillian超级算子的特征值和特征向量，从而可以得到闭合形式的解析表达式密度算子和可观测物的时间演化。我们的方法对于大型系统是有效的，但是考虑了对无限系统结果的前导有限大小校正。作为应用，我们表明，耗散的Lipkin-Meshkov-Glick模型通过连续的热态与阻尼振荡的叠加来达到平衡，直到最终达到一个通常与浴温不同的温度的平衡态。通过与精确的数值结果进行比较，我们讨论了分析技术的局限性。