We study the quantum open system evolution described by a Gorini–Kossakowski–Sudarshan–Lindblad generator with creation and annihilation operators arising in Fock representations of the $$\mathfrak {sl}_2$$ sl 2 Lie algebra. We show that any initial density matrix evolves to a fully supported density matrix and converges towards a unique equilibrium state. We show that the convergence is exponentially fast and we exactly compute the rate for a wide range of parameters. We also discuss the connection with the two-photon absorption and emission process.

中文翻译：

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二次开式量子谐振子

我们研究了由 Gorini-Kossakowski-Sudarshan-Lindblad 生成器描述的量子开放系统演化，该生成器在 $$\mathfrak {sl}_2$$ sl 2 Lie 代数的 Fock 表示中产生了创生和湮灭算符。我们表明，任何初始密度矩阵都会演化为完全支持的密度矩阵，并会收敛到一个独特的平衡状态。我们表明收敛速度呈指数级增长，并且我们精确地计算了各种参数的速率。我们还讨论了与双光子吸收和发射过程的联系。