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首页> 外文期刊>Physical Review, A >Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations
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Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations

机译：用于热辅助隧道和量子蒙特卡罗模拟的缩放分析和算子

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We develop an instantonic calculus to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path-integral quantum Monte Carlo (QMC).We show analytically that the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single-site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the “spiky” barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins N while a purely classical over-the-barrier activation rate scales exponentially with N.
机译：我们开发了一种直升机计算，从而导出了完全连接量子旋转模型中的亚稳态的热辅助隧道衰减速率的分析表达。隧道衰减问题可以映射到经典随机动态场的克拉姆斯转义问题。通过路径积分量子蒙特卡罗（QMC）有效地模拟该动态场。我们分析地显示了具有热辅助量子隧道速率的旋转次数和QMC过程的逃生率的指数缩放相同。我们将这种效果与主导式即时隧道路径的存在相关。用于单站点磁化矢量的非线性动力学平均场理论方程描述了算法轨迹，我们精确地解决了。最后，当旋转隧道和QMC速率尺度随着旋转数量的数量时，我们派生了“尖峰”屏障形状的缩放关系，而纯粹的经典过屏障激活速率与N呈指数级别。

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