论文标题
开放量子系统的对称性：耗散量子混乱的分类
Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
论文作者
论文摘要
我们在开放量子系统中发展了对称性理论。使用操作员态映射，我们表征了liouvillian超级操作器的对称性，以通过双hilbert空间中的操作员的对称性进行开放的量子动力学，并应用非赫米蒂亚运算符的38倍内对称分类。我们发现，由于相应的封闭量子系统中的对称性与构建Liouvillian超级操作员固有的对称性之间的相互作用，我们发现了丰富的对称分类。作为开放量子骨体系统的说明性示例，我们研究了耗散量子自旋模型的对称类别。对于开放的量子费米子系统，我们开发了$ \ mathbb {z} _4 $在双Hilbert空间中的费米昂均等对称性和反对对称性的分类，这与$ \ Mathbb {Z} _8在封闭量子系统中的分类形成了鲜明对比。我们还开发了开放量子费米子多体系统的对称分类 - lindblad主方程描述的sachdev-ye-kitaev（SYK）模型的耗散概括。我们建立了Syk Lindbladians的周期性表格，并阐明了与Syk Hamiltonians的差异。此外，从广泛的数值计算中，我们研究了其复杂的传热统计数据，并证明了通过对称性富集的耗散量子混乱。
We develop a theory of symmetry in open quantum systems. Using the operator-state mapping, we characterize symmetry of Liouvillian superoperators for the open quantum dynamics by symmetry of operators in the double Hilbert space and apply the 38-fold internal-symmetry classification of non-Hermitian operators. We find rich symmetry classification due to the interplay between symmetry in the corresponding closed quantum systems and symmetry inherent in the construction of the Liouvillian superoperators. As an illustrative example of open quantum bosonic systems, we study symmetry classes of dissipative quantum spin models. For open quantum fermionic systems, we develop the $\mathbb{Z}_4$ classification of fermion parity symmetry and antiunitary symmetry in the double Hilbert space, which contrasts with the $\mathbb{Z}_8$ classification in closed quantum systems. We also develop the symmetry classification of open quantum fermionic many-body systems -- a dissipative generalization of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation. We establish the periodic tables of the SYK Lindbladians and elucidate the difference from the SYK Hamiltonians. Furthermore, from extensive numerical calculations, we study its complex-spectral statistics and demonstrate dissipative quantum chaos enriched by symmetry.
