Dynamical zero modes and boundary dependence in dynamical quantum phase transitions
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理北京国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Boundary conditions are usually expected to cause only finite-size corrections to bulk quantities, but this expectation can fail for dynamical quantum phase transitions. In this work, we show that such boundary dependence is encoded in dynamical zero modes (DZMs) of the Loschmidt matrix, which are defined as singular vectors whose singular values vanish in the thermodynamic limit. Using the Su-Schrieffer-Heeger (SSH), extended SSH, and Kitaev models as examples, we find that the time interval where the Loschmidt rate functions (LRFs) under periodic and open boundary conditions differ coincides with the emergence of DZMs in the open-boundary Loschmidt matrix. These modes carry the boundary-dependent contribution: removing them from the open-boundary LRF recovers the periodic-boundary result. We further show that these DZMs lead to finite-precision numerical instability, since their finite-size singular values decay exponentially with system size and eventually become unresolved in fixed-precision arithmetic. A reliable small-size branch before this loss of precision can be used to estimate the LRF in the thermodynamic limit by linear extrapolation. Our results identify DZMs as both a diagnostic of boundary-dependent LRFs and the origin of the associated numerical instability.
Dynamical Casimir effect for a massless scalar field between two concentric spherical shells with mixed boundary condictions
本文分析了两个同心球壳间无质量标量场的Casimir动力学效应，并在此基础上给出了场混合边界条件。因此，我们补充了以前的结果[Phys. Rev. A \textbf{78}，032521（2008）]，其中考虑了相同的问题，但在这种情况下，该领域提交的Dirichlet边界条件，在两个移动球壳。对于任意的球壳径向运动规律，推导出平均生成粒子数的一般表达式。然后将该表达式应用于壳体的谐振，并分析了所产生的粒子数，并与Dirichlet-Dirichlet边界条件下的结果进行了比较。
Characterizing dynamical behaviors in topological open systems with boundary dissipations
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems
将厄米算符的自伴扩张理论应用于Koopman von Neumann经典力学，发现了一组最一般的概率分布，其熵由哈密顿演化守恒。一个新的动力学阶段与这样的建设确定。通过选择不属于这一类的分布，我们产生明确的例子，自由粒子和谐波系统在有界相空间中的熵是不守恒的。虽然这些非守恒态在经典上是被禁止的，但它们可以被解释为量子系统隧穿势垒边界的状态。在这种情况下，允许的边界条件是经典系统和量子系统之间的唯一区别。我们证明了隧穿量子系统的边界条件成为经典极限下熵守恒的判据。这些发现突出了边界效应如何彻底改变系统的性质。
Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
