Takahashi Kazutaka
Department of Physics Engineering, Faculty of Engineering, Mie University, Mie 514-8507, Japan.
Philos Trans A Math Phys Eng Sci. 2022 Dec 26;380(2239):20220301. doi: 10.1098/rsta.2022.0301. Epub 2022 Nov 7.
We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients. We discuss how the method allows us to mimic adiabatic dynamics and describe a relation to the counterdiabatic formalism. The equation for the dynamical invariant takes a familiar form and is often used in various fields of physics. We introduce examples of Lax pair, quantum brachistochrone and flow equation. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
我们对绝热捷径的动力学不变形式进行了深入浅出的介绍。对于具有待定系数的哈密顿量的给定算符形式，引入动力学不变量来设计系数。我们讨论了该方法如何使我们能够模拟绝热动力学，并描述了与反绝热形式的关系。动力学不变量的方程具有常见形式，并且在物理学的各个领域中经常使用。我们介绍了拉克斯对、量子最速降线和流方程的例子。本文是主题为“绝热捷径：理论、实验和跨学科视角”的一部分。
