不同物理过程中混合态的Loscherton振幅零点的普遍性及其意义
Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
摘要：
混合态密度矩阵的纯化状态的洛施图振幅示出有零时，系统经历准静态，淬火，或Uhlmann过程。当淬火过程的洛施密特振幅零点对应于伴随着发散的动力学自由能的动力学量子相变（DQPT）时，Uhlmann过程的洛施密特振幅零点对应于伴随着Uhlmann相的跳跃的拓扑相变（TQPT）。虽然密度矩阵在准静态过程中保持完整，但洛施图振幅可以具有与相变无关的零。我们提出的例子，两个级别和三个级别的系统表现出有限或无限温度DQPT和有限温度TQPT与Loschmidt振幅零点。此外，混合态的动力学相位或几何相位也可以从洛施图振幅中提取出来。这些相位可能变得量化或在洛施密特振幅零点处表现出不连续性。本文给出了一般二能级系统的纯态旋量表示，以便更深入地了解不同过程中纯态的变化。准静态过程，例如，被证明是导致旋转的旋量。
英文摘要：
The Loschmidt amplitude of the purified states of mixed-state density matrices is shown to have zeros when the system undergoes a quasistatic, quench, or Uhlmann process. While the Loschmidt-amplitude zero of a quench process corresponds to a dynamical quantum phase transition (DQPT) accompanied by the diverging dynamical free energy, the Loschmidt-amplitude zero of the Uhlmann process corresponds to a topological phase transition (TQPT) accompanied by a jump of the Uhlmann phase. Although the density matrix remains intact in a quasistatic process, the Loschmidt amplitude can have zeros not associated with a phase transition. We present examples of two-level and three-level systems exhibiting finite- or infinite- temperature DQPTs and finite-temperature TQPTs associated with the Loschmidt-amplitude zeros. Moreover, the dynamical phase or geometrical phase of mixed states can be extracted from the Loschmidt amplitude. Those phases may become quantized or exhibit discontinuity at the Loschmidt-amplitude zeros. A spinor representation of the purified states of a general two-level system is presented to offer more insights into the change of purification in different processes. The quasistatic process, for example, is shown to cause a rotation of the spinor.
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