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arXiv 1707.01490quant-phcond-mat.stat-mech
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利用流场研究绝热性的捷径

Shortcuts to adiabaticity using flow fields

Ayoti Patra, Christopher Jarzynski

摘要:

$\textit{shortcut to adiabaticity}$是一种以任意速度产生绝热演化的方法。捷径已经开发了量子,经典和(最近)随机动力学。捷径可能涉及$\textit{counterdiabatic}$哈密尔顿算子,使系统始终遵循绝热演化,或者它可能利用$\textit{fast-forward}$势,使系统在过程结束时返回绝热路径。我们开发了一个通用的框架,用于构建快捷方式绝热从$\textit{flow fields}$描述所需的绝热演化。我们的方法包括量子,经典和随机动力学,并提供了令人惊讶的紧凑的表达式为counterdiabatic哈密顿和快进潜力。我们说明了我们的方法与模型系统的数值模拟,我们比较我们的捷径与以前获得的结果。我们还考虑了我们的量子和经典捷径之间的半经典联系。我们的方法,像以前的作者开发的快进的方法,是容易受到奇点时,应用到量子系统的激发态,我们提出了一个简单,直观的标准来确定这些奇点是否会出现,对于一个给定的激发态。

英文摘要:

A $\textit{shortcut to adiabaticity}$ is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a $\textit{counterdiabatic}$ Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a $\textit{fast-forward}$ potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from $\textit{flow fields}$ that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both counterdiabatic Hamiltonians and fast-forward potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the fast-forward approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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