In this work we develop the theory of the Loschmidt echo and dynamical phase transitions in non-interacting strongly disordered Fermi systems after a quench. In finite systems the Loschmidt echo displays zeros in the complex time plane that depend on the random potential realization. Remarkably, the zeros coalesce to form a 2D manifold in the thermodynamic limit, atypical for 1D systems, crossing the real axis at a sharply-defined critical time. We show that this dynamical phase transition can be understood as a transition in the distribution function of the smallest eigenvalue of the Loschmidt matrix, and develop a finite-size scaling theory. Contrary to expectations, the notion of dynamical phase transitions in disordered systems becomes decoupled from the equilibrium Anderson localization transition. Our results highlight the striking qualitative differences of quench dynamics in disordered and non-disordered many-fermion systems.

中文翻译：

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无序费米系统中的洛施密特回波和动态量子相变理论

在这项工作中，我们发展了失超后非相互作用的强无序费米系统中的洛施密特回波和动态相变理论。在有限系统中，Loschmidt 回波在复杂的时间平面中显示零点，这取决于随机势的实现。值得注意的是，零点在热力学极限中合并形成二维流形，这对于一维系统来说是非典型的，在明确定义的临界时间穿过实轴。我们表明，这种动态相变可以理解为洛施密特矩阵最小特征值分布函数的转变，并发展了有限尺寸标度理论。与预期相反，无序系统中动态相变的概念与平衡安德森定位转变脱钩。