标题： 耗散动力学中的渐近异常稳态 显示英文标题

标题： Asymptotic Exceptional Steady States in Dissipative Dynamics

摘要： 李纳德方程生成元中的光谱退化通常作为例外点出现，此时相应的非厄米算子变得不可对角化。 稳态，即李纳德算符的零模，被视为这一规则的一个基本例外，因为一个不可能定理排除了那里的不可对角化退化。 在这里，我们通过耗散态制备的背景，展示了系统如何在热力学极限下渐近接近禁止的例外稳态情形。 基于从编码在量子主方程中的NP难满足问题到对称保护拓扑相的耗散制备的各种案例研究，我们揭示了当前问题的计算复杂性与向例外稳态的有限尺寸标度之间的密切关系，分别举例说明了指数和多项式标度。 将林德布拉德主方程中量子跃迁的强度$W$作为一个参数来处理，我们表明在物理值$W=1$处的例外稳态可以被理解为标志动力不稳定性开始的临界点。 显示英文摘要

摘要： Spectral degeneracies in Liouvillian generators of dissipative dynamics generically occur as exceptional points, where the corresponding non-Hermitian operator becomes non-diagonalizable. Steady states, i.e. zero-modes of Liouvillians, are considered a fundamental exception to this rule since a no-go theorem excludes non-diagonalizable degeneracies there. Here, we demonstrate in the context of dissipative state preparation how a system may asymptotically approach the forbidden scenario of an exceptional steady state in the thermodynamic limit. Building on case studies ranging from NP-complete satisfiability problems encoded in a quantum master equation to the dissipative preparation of a symmetry protected topological phase, we reveal the close relation between the computational complexity of the problem at hand, and the finite size scaling towards the exceptional steady state, exemplifying both exponential and polynomial scaling. Treating the strength $W$ of quantum jumps in the Lindblad master equation as a parameter, we show that exceptional steady states at the physical value $W=1$ may be understood as a critical point hallmarking the onset of dynamical instability.