We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters and dissipative mechanisms modeled by a Lindblad master equation, with either local or global spin operators acting as dissipative operators. Analogously to what happens at continuous quantum transitions, we observe a regime where the system develops a nontrivial dynamic scaling behavior, which is realized when the dissipation parameter $u$ (globally controlling the decay rate of the dissipation within the Lindblad framework) scales as the energy difference $\mathrm{\Delta }$ of the lowest levels of the Hamiltonian, i.e., $u\sim \mathrm{\Delta }$. However, unlike continuous quantum transitions where $\mathrm{\Delta }$ is power-law suppressed, at first-order quantum transitions $\mathrm{\Delta }$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).

中文翻译：

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一阶量子跃迁的耗散动力学

我们研究了耗散对多体系统在量子跃迁处的量子动力学的影响，特别是考虑了一阶跃迁的影响。在范式一维量子伊辛模型中研究了此问题。我们分析了由哈密顿参数的淬灭和由Lindblad主方程建模的耗散机制引起的失衡动力学，其中局部或全局自旋算子充当耗散算子。类似于在连续量子跃迁中发生的情况，我们观察到一种状态，系统在该状态下发展出非平凡的动态缩放行为，这是在耗散参数实现时实现的$ü$ （在Lindblad框架内全局控制耗散的衰减率）随能量差而缩放 $\mathrm{\Delta }$ 哈密​​顿量最低的水平，即 $ü〜\mathrm{\Delta }$。但是，与连续量子跃迁不同的是，$\mathrm{\Delta }$ 在一阶量子跃迁处被幂律抑制 $\mathrm{\Delta }$ 随着系统尺寸的增加，指数被抑制（假设边界条件不适合任何特定相位）。