实时动力学的蒙特卡罗研究
Monte Carlo study of real time dynamics
摘要：
涉及实时动力学的蒙特卡罗研究受到路径积分的高振荡阶段出现的符号问题的严重限制。在这封信中，我们提出了一种新的方法来计算实时量的晶格上使用Schwinger-Keldysh形式主义通过蒙特卡罗模拟。其关键思想是将路径积分域变形为一个复杂的流形，在该流形上相位振荡是温和的，符号问题是可管理的。我们使用前面介绍的“收缩算法”，以创建一个马尔可夫链在这个替代流形。我们通过分析量子力学非谐振子来证实我们的方法。我们的结果与哈密顿量对角化得到的精确结果一致。我们介绍的方法是通用的，原则上适用于量子场论，虽然很慢。我们讨论了一些可能的改进，应该加快算法。
英文摘要：
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
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