标题： 压缩、混沌与热化在周期驱动量子系统中的表现：玻色子再加热的情况 显示英文标题

标题： Squeezing, Chaos and Thermalization in Periodically Driven Quantum Systems: The Case of Bosonic Preheating

摘要： 挤压和混沌现象最近在暴胀的背景下被研究。 我们在暴胀后的再加热阶段应用这个形式化方法。 在此阶段，暴胀场经历准周期振荡，这作为量子涨落或粒子产生的共振增长的驱动力。 此外，已知涨落的量子态演化为压缩态。 在本次提交中，我们通过计算相空间变量的时空序关联函数（OTOC），并建立李雅普诺夫指数、弗洛凯指数和压缩参数之间的关系，来探讨共振增长、压缩和混沌之间的潜在联系。 在我们的研究中，我们考虑观测上有利的$\alpha$-吸引子 E 模型的暴胀场，该模型与玻色场耦合。 在产生之后，由暴胀场产生的玻色涨落/粒子系统被认为会热化，并且这被认为与系统在扰动下的混沌性质有有趣的联系。 %通过使用这个我们计算了温度${\bar T}_{\rm MSS}$的近似下限。 我们假设系统热化温度$({\bar T}_{\rm SS})$与量子压缩之间存在关系，进一步表明该关系与众所周知的以${\bar T}_{\rm RJ}$表示的温度的瑞利-金斯公式一致，即${\bar T}_{\rm SS} \simeq {\bar T}_{\rm RJ}$。 最后，我们表明系统的温度符合 Maldacena-Shenker-Stanford（MSS）提出的混沌系统的温度下限。 显示英文摘要

摘要： The phenomena of Squeezing and chaos have recently been studied in the context of inflation. We apply this formalism in the post-inflationary preheating phase. During this phase, inflaton field undergoes quasi-periodic oscillation, which acts as a driving force for the resonant growth of quantum fluctuation or particle production. Furthermore, the quantum state of the fluctuations is known to have evolved into a squeezed state. In this submission, we explore the underlying connection between the resonant growth, squeezing, and chaos by computing the Out of Time Order Correlator (OTOC) of phase space variables and establishing a relation among the Lyapunov, Floquet exponents, and squeezing parameters. For our study, we consider observationally favored $\alpha$-attractor E-model of inflaton which is coupled with the bosonic field. After the production, the system of produced bosonic fluctuations/particles from the inflaton is supposed to thermalize, and that is believed to have an intriguing connection to the nature of chaos of the system under perturbation. %By using this we calculated approximate lower bound of temperature ${\bar T}_{\rm MSS}$. We conjecture a relation between the thermalization temperature $({\bar T}_{\rm SS})$ of the system and quantum squeezing, which is further shown to be consistent with the well-known Rayleigh-Jeans formula for the temperature symbolized as ${\bar T}_{\rm RJ}$, and that is ${\bar T}_{\rm SS} \simeq {\bar T}_{\rm RJ}$. Finally, we show that the system temperature is in accord with the well-known lower bound on the temperature of a chaotic system proposed by Maldacena-Shenker-Stanford (MSS).