论文标题

Susy Saddle主导的晚期动态通过更高点OTOC

Late time dynamics in SUSY saddle-dominated scrambling through higher-point OTOC

论文作者

Das, Rathindra Nath, Dutta, Sourav, Maji, Archana

论文摘要

在本文中,我们研究了超对称量子机械系统中的争夺动力学。此类超对称系统的本征态表示使我们能够使用两个同等形式主义(即$ 2N $ - 点的超级订单相关器(OTOC))的明确形式。 “张量形式主义”和“伴侣汉密尔顿形式主义”。我们通过分析计算超对称1D谐波振荡器的$ 2N $ - 点OTOC,发现结果与1D波索尼克谐波振荡器系统的OTOC完全一致。与通常的4点OTOC相比,更高点的OTOC是更敏感的争夺量度。为了证明这一功能,我们考虑了一个超对称的六振荡器,玻色子伴侣系统在该相位空间中具有不稳定的鞍座,而在费米子对应物中不存在。对于这样的系统,我们表明,由于超对称性约束,玻色粒,费米子和超对称的OTOC表现出相似的动力学。最后,我们说明了在鞍形的争夺和非谐波振荡器系统中,高点OTOC的后期振荡行为,并提出它是表现出快速早期打击的非核糖系统中延迟动态的探测。

In this article, we study the scrambling dynamics in supersymmetric quantum mechanical systems. The eigenstate representation of such supersymmetric systems allows us to present an explicit form of the $2N$-point out-of-time-order correlator (OTOC) using two equivalent formalisms viz. "Tensor Product formalism" and "Partner Hamiltonian formalism". We analytically compute the $2N$-point OTOC for the supersymmetric 1D harmonic oscillator and find that the result is in exact agreement with that of the OTOC of the 1D bosonic harmonic oscillator system. The higher-point OTOC is a more sensitive measure of scrambling than the usual 4-point OTOC. To demonstrate this feature, we consider a supersymmetric sextic 1D oscillator for which the bosonic partner system has an unstable saddle in the phase space, which is absent in the fermionic counterpart. For such a system we show that the bosonic, the fermionic as well as the supersymmetric OTOC exhibit similar dynamics due to supersymmetry constraints. Finally, we illustrate the late-time oscillatory behaviour of higher-point OTOC for saddle-dominated scrambling and anharmonic oscillator systems and propose it to be a probe of late-time dynamics in non-chaotic systems that exhibit fast early-time scrambling.

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