多体量子系统中含时驱动的随机矩阵方法
Random-matrix approach to time-dependent forcing in many-body quantum systems
AI总结：
本文发展基于典型性和随机矩阵的非线性响应理论，解析推导快速与强短程驱动下多体量子系统的响应函数，并验证于有限时间淬火及破缺守恒律的含时驱动，数值验证预测并讨论适用范围。
摘要：
随时间改变其某些参数是将孤立多体量子系统驱动出平衡态的一种典型方式，也是构建量子计算机和模拟器的重要要素。在此，我们进一步发展了近期提出的基于典型性和随机矩阵方法的非线性响应理论，该理论适用于各种此类参数扰动系统，无论其处于平衡态还是非平衡态：我们针对快速驱动和强且能量上短程驱动这两种极限情况，推导了特征响应函数的解析近似。此外，我们为常见应用推导了推论和预测，包括有限时间淬火以及破坏底层未驱动系统守恒律的含时驱动。最后，我们通过数值示例验证了所有预测，并讨论了该理论的适用范围和局限性。
英文摘要：
Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a recently proposed nonlinear response theory which is based on typicality and random-matrix methods, and which is applicable to a wide variety of such parametrically perturbed systems in and out of equilibrium: We derive analytical approximations of the characteristic response function for the two limiting cases of fast driving and of strong and short-ranged-in-energy driving. Furthermore, we work out implications and predictions for common applications, including finite-time quenches and time-dependent forcing that breaks conservation laws of the underlying undriven system. Finally, we verify all predictions by numerical examples and discuss the theory's scope and limitations.
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