量子动力学关联：有效势解析延拓方法
Quantum dynamical correlations: Effective potential analytic continuation approach
摘要：
提出了一种新的量子动力学方法--有效势解析延拓法（EPAC），用于计算有限温度下的实时量子关联函数。该方法是基于有效作用形式主义，其中包括标准的有效电位。介绍了一维双势阱系统的EPAC的基本概念，并与质心分子动力学（CMD）和精确实时量子关联函数进行了比较。结果表明，无论是EPAC和CMD很好地再现准确的短时间行为，而在较长的时间，他们的结果偏离准确的。由于系综失相，CMD关联函数随时间迅速衰减。然而，EPAC关联函数可以再现量子双阱系统中固有的长时间振荡。通过对有效作用量的高阶导数展开，可以使EPAC关联函数向精确的关联函数逼近。
英文摘要：
We propose a new quantum dynamics method called the effective potential analytic continuation (EPAC) to calculate the real time quantum correlation functions at finite temperature. The method is based on the effective action formalism which includes the standard effective potential. The basic notions of the EPAC are presented for a one-dimensional double well system in comparison with the centroid molecular dynamics (CMD) and the exact real time quantum correlation function. It is shown that both the EPAC and the CMD well reproduce the exact short time behavior, while at longer time their results deviate from the exact one. The CMD correlation function damps rapidly with time because of ensemble dephasing. The EPAC correlation function, however, can reproduce the long time oscillation inherent in the quantum double well systems. It is also shown that the EPAC correlation function can be improved toward the exact correlation function by means of the higher order derivative expansion of the effective action.
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