Sim Karin, Defenu Nicolò, Molignini Paolo, Chitra R
Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland.
Cavendish Laboratory, University of Cambridge, 19 J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
Phys Rev Lett. 2023 Oct 13;131(15):156501. doi: 10.1103/PhysRevLett.131.156501.
Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly solvable non-Hermitian system, hosting both PT-symmetric and PT-broken modes subject to a linear quench. Employing a fully consistent framework, in which the Hilbert space is endowed with a nontrivial dynamical metric, we analyze the dynamics of the generated defects. In contrast to Hermitian systems, our study reveals that PT-broken time evolution leads to defect freezing and hence the violation of adiabaticity. This physics necessitates the so-called metric framework, as it is missed by the oft used approach of normalizing quantities by the time-dependent norm of the state. Our results are relevant for a wide class of experimental systems.
量子哈密顿量中的非厄米性会导致非幺正时间演化以及可能的复能量本征值，这可能会产生丰富的现象学，而厄米系统则没有与之对应的情况。在这项工作中，我们研究了一个精确可解的非厄米系统的动力学，该系统同时包含PT对称和PT破缺模式，并受到线性猝灭的影响。我们采用一个完全一致的框架，其中希尔伯特空间被赋予了一个非平凡的动力学度量，来分析所产生缺陷的动力学。与厄米系统不同，我们的研究表明，PT破缺的时间演化会导致缺陷冻结，从而违反绝热性。这种物理现象需要所谓的度量框架，因为常用的通过状态的含时范数对量进行归一化的方法会忽略这一点。我们的结果与广泛的一类实验系统相关。
