AI 中文总结
研究玻色凝聚相实时动力学，开发玻色RPMD方法，该方法在特定极限下精确，能处理交换效应，通过在模型系统上的测试，首次实现用RPMD直接模拟大型玻色凝聚相有限温度实时动力学。
AI 中文摘要
我们提出了一种近似玻色凝聚相实时关联函数和量子输运系数的方法。由于严重的动力学符号问题，在路径积分表述中直接评估量子实时关联函数是不可能的。通过解析延拓来评估虚时关联函数并进行反演是不适定的。环聚合物分子动力学（RPMD）提供了一种替代方法，可对凝聚相的实时关联函数进行精确近似，但忽略了交换效应。在这项工作中，我们开发了一种玻色RPMD方法，它在谐波、短时间和高温极限下是精确的。一个关键的观察结果是，仅当相关可观测量在交换下对称时，玻色子的久保变换关联函数才是实的。我们在谐波和非谐波模型系统上对该方法进行了基准测试，然后用它直接获得了不同温度和动量转移下的Lieb-Liniger气体密度-密度实时关联函数。这项工作首次使得使用RPMD直接模拟大型玻色凝聚相的有限温度实时动力学成为可能。
英文摘要
We present a method for approximating real-time correlation functions and quantum transport coefficients of bosonic condensed phases. The direct evaluation of quantum real-time correlation functions in the path integral formulation is impossible due to a severe dynamical sign problem. Evaluating imaginary-time correlation functions and inverting them using analytic continuation is famously ill-posed. Ring polymer molecular dynamics (RPMD) provides an alternative approach resulting in accurate approximations for real-time correlation functions of condensed phases but neglects exchange effects. In this work, we develop a bosonic RPMD method, which is exact in the harmonic, short time, and high temperature limits. A critical enabling observation is that the Kubo-transformed correlation function for bosons is real only when the correlated observables are symmetric under exchange. We benchmark the method on harmonic and anharmonic model systems and then use it to directly obtain the Lieb-Liniger gas density-density real-time correlation functions at various temperatures and momentum transfers. This work enables the direct simulation of finite-temperature, real-time dynamics of large bosonic condensed phases using RPMD for the first time.
