Quantitative analysis of the stochastic approach to quantum tunneling
Quantitative analysis of the stochastic approach to quantum tunneling
复制标题
量子隧道随机方法的定量分析
DOI：
10.1103/physrevd.102.076003
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发表时间：
2020
影响因子：
5
通讯作者：
Shah, Neil
中科院分区：
文献类型：
--
作者：
Hertzberg, Mark P.;Rompineve, Fabrizio;Shah, Neil
最近，人们对场论中计算量子隧道的替代方法越来越感兴趣。特别令人感兴趣的是一种随机方法，它涉及(I)从自由理论的高斯近似到Wigner分布的采样，以获得场和动量共轭的随机初始条件，然后(Ii)在经典的场运动方程下演化，这导致随机气泡的形成。以前的工作表明，这种随机方法的隧穿速率的对数与通常的瞬子近似之间是参数一致的。然而，最近的工作[J.Braden，Phys.莱特牧师。123,031601(2019)PRLTAO0031-900710.1103/PhysRevLett.123.031601]声称这些方法之间有很好的一致性。这里我们表明，这种方法实际上并不是精确匹配的；随机方法往往会过度预测瞬子隧穿速率。为了量化这一点，我们将初始随机波动中的标准偏差参数化为，其中是高斯分布的实际标准偏差，是一个模糊因子；是物理值。我们数值实现了随机方法来获得一系列位势在维度中的气泡形成率，发现总是需要比单位小一点才能压制相对于瞬子速率大得多的随机速率；例如，在Bradenet等人的势中，人们需要。我们发现，当从其他Wigner分布和单粒子量子力学中采样时，即使初始量子系统是在精确的高斯态下制备的，预测中的不匹配也会发生。如果我们的目标是在两种方法之间取得一致，我们的结果表明，如果能够开发出一种处方来指定波动的最佳模糊因子，那么随机方法将是有用的。
Recently there has been increasing interest in alternate methods to compute quantum tunneling in field theory. Of particular interest is a stochastic approach which involves (i) sampling from the free theory Gaussian approximation to the Wigner distribution in order to obtain stochastic initial conditions for the field and momentum conjugate and then (ii) evolving under the classical field equations of motion, which leads to random bubble formation. Previous work showed parametric agreement between the logarithm of the tunneling rate in this stochastic approach and the usual instanton approximation. However, recent work [J. Braden , Phys. Rev. Lett. 123, 031601 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.031601] claimed excellent agreement between these methods. Here we show that this approach does not in fact match precisely; the stochastic method tends to overpredict the instanton tunneling rate. To quantify this, we parameterize the standard deviations in the initial stochastic fluctuations by, whereis the actual standard deviation of the Gaussian distribution andis a fudge factor;is the physical value. We numerically implement the stochastic approach to obtain the bubble formation rate for a range of potentials indimensions, finding thatalways needs to be somewhat smaller than unity to suppress the otherwise much larger stochastic rates toward the instanton rates; for example, in the potential of Bradenet al., one needs. We find that a mismatch in predictions also occurs when sampling from other Wigner distributions and in single-particle quantum mechanics even when the initial quantum system is prepared in an exact Gaussian state. If the goal is to obtain agreement between the two methods, our results show that the stochastic approach would be useful if a prescription to specify optimal fudge factors for fluctuations can be developed.
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