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arXiv 2007.02150quant-phmath-phmath.MP
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基于参数振荡器的淬火协议效应

Effects of quenching protocols based on parametric oscillators

Mariagiovanna Gianfreda, Giulio Landolfi

备注：
Revised version for the manuscript initially entitled: Classical and quantum analysis of the parametric oscillator with Morse-like time-dependent frequency. Overall presentation has been improved: some figures have been removed, the section with the most mathematical material now appears as Appendix, more applications of parametric oscillator systems have been mentioned in the Introduction
发表信息：
Chin. J. Phys., vol .74, December 2021, Pages 328-349 (https://www.sciencedirect.com/science/article/pii/S0577907321001702)
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AI总结：

本研究探讨参数振荡器在淬火协议下的量子行为，通过解析准正态模振幅，并分析不确定性原理与统计特性，揭示系统演化特征。

摘要：

我们考虑理解由参数振荡器描述的量子系统所展现的基本特征的问题，这些振荡器的时间相关频率参数 $\omega(t)$ 在演化过程中连续变化，以实现不同类型的淬火协议。为此，我们关注 $\omega(t)^2$ 表现为莫尔斯势的情况，直至在 $(t,\omega^2)$ 平面上可能的符号反转和平移。我们推导了准正态模的时间相关振幅的闭式解，这是描述经典和量子参数振荡器的最基本动力学对象，并强调了其在不同驱动细节所导致的独特情况下的显著特征。此后，我们通过关注位置-动量海森堡不确定性原理以及数态上二阶相关函数所隐含的统计方面，对量子态的演化方式提供了见解。

英文摘要：

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter $ω(t)$ varies continuously during evolution so to realise quenching protocols of different types. To this scope we focus on the case where $ω(t)^2$ behaves like a Morse potential, up to possible sign reversion and translations in the $(t,ω^2)$ plane. We derive closed form solution for the time-dependent amplitude of quasi-normal modes, which is the very fundamental dynamical object entering the description of both classical and quantum parametric oscillators, and highlight its significant characteristics for distinctive cases arising based on the driving specifics. After doing so, we provide an insight on the way quantum states evolve by paying attention on the position-momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states.

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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