MULTI-TIME CORRELATIONS IN OPEN QUANTUM SYSTEMS

研究开放量子系统(OQS)的动力学和可能的量子力学替代方案，如崩塌模型(CM)，是技术和基础发展的基础。通常，动力学研究的重点是系统可观测的单时间期望值。然而，单时间期望值只提供了支撑动力学的部分描述，因此，需要考虑多时间关联函数(MTCF)以获得更完整的图像。本项目的目标是通过开发一种新的方法框架来评估OQS动力学，该方法能够处理从标准环境退相干到奇异CM的各种情况。该目标将通过三个步骤实现：1)引入一种新的非微扰技术来计算OQS与玻色浴相互作用的MTCF，即使在强耦合区域和任何浴的温度下也是如此。这项技术将基于用有限数量的阻尼谐振子描述的替代浴缸来取代原始浴槽，从而使其更容易模拟。有限网络的设计将确保系统的MTCF与使用原始BART计算的MTCF相同。2)CM中MTCF的计算。到目前为止，在CM中MTCF的所有计算都依赖于量子回归定理，该定理在强假设下是有效的。我们将首次在不假设量子回归定理的有效性的情况下，对CM中的MTCF进行研究。与单个时间期望值相比，初步分析表明，CM中的MTCF可能与OQS中的MTCF有质的不同，从而为测试CM动力学与OQS动力学提供了新的见解。3)将结果应用于感兴趣的特定设置，其中与实验小组合作，通过非线性光谱学对晶体石英中的振动模式进行测量

The study of the dynamics of Open Quantum Systems (OQS) and possible alternatives to quantum mechanics such as collapse models (CM) is fundamental for technological and foundational developments.Typically, the dynamics is studied focusing on single-time expectation values of observables of the system. However, single-time expectation values provide only a partial description of the underpinning dynamics hence, multi-time correlation functions (MTCF) need to be considered for a more complete picture.The goal of this project is to provide new insights into OQS dynamics by developing a new methodological framework for the assessment of MTCF that are able to tackle situations ranging from standard environmental decoherence all the way down to exotic CM.The goal will be achieved in 3 steps:1) Introduction of a new non-perturbative technique for computing MTCF in OQS interacting with bosonic baths even in the strong coupling regime and for any temperature of the baths. The technique will be based on replacing the original bath with a surrogate bath described by a finite number of damped harmonic oscillators, making it easier to simulate. The finite network will be engineered to guarantee that the MTCF of the system are the same as those computed using the original bath.2) Computation of MTCF in CM. Hitherto, all computations of MTCF in CM relies on the quantum regression theorem, which is valid under strong assumptions. We will perform for the first time a study of MTCF in CM without assuming the validity of the quantum regression theorem. In contrast to single time expectation values, preliminary analyses suggest that MTCF in CM may differ qualitatively from those in OQS, thus providing new insight in testing CM dynamics against OQS dynamics.3) Application of the results to a specific setup of interest, where measurements of the vibrational modes in a crystalline quartz are performed via non-linear spectroscopy, in collaboration with an experimental group