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A comparison of generalized hybrid Monte Carlo methods with and without momentum flip

机译：带有和不带有动量翻转的广义混合蒙特卡罗方法的比较

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摘要

The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC. (C) 2008 Elsevier Inc. All rights reserved.
机译：广义混合蒙特卡罗（GHMC）方法将Metropolis校正的恒定能量模拟与粒子动量中的部分随机刷新步骤结合在一起。标准的详细平衡条件要求在拒绝分子动力学建议步骤时抵消动量。暗示是排斥时的轨迹反转，这在将GHMC解释为恒温分子动力学时是不希望的。我们表明，修改后的详细平衡条件可用于实施GHMC，而无需动量翻转。相同的修改可以应用于广义阴影混合蒙特卡罗（GSHMC）方法。数值结果表明，具有动量翻转的GHMC / GSHMC实现在采样效率方面表现出良好的行为，即传统的具有动量翻转的GHMC / GSHMC实现具有较高的接受率和更快的蒙特卡洛样本去相关性的优势。 GHMC的差异更为明显。我们还数值研究了GHMC方法作为Langevin型恒温器的行为。我们发现，不存在动量翻转的GHMC方法在自相关函数方面对潜在的随机分子动力学的干扰较小，因此它优于具有动量翻转的GHMC方法。同样的发现适用于GSHMC。 （C）2008 Elsevier Inc.保留所有权利。

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