arXiv quant-ph/06041502006-04-20quant-ph

具有复Action的玻姆力学：一种新的基于轨道的量子力学公式

Bohmian Mechanics with Complex Action: A New Trajectory-Based Formulation of Quantum Mechanics

Yair Goldfarb, Ilan Degani, David J. Tannor

DOI：: 10.1063/1.2798762

摘要：

近年来，人们对Bohmian力学作为数值工具的兴趣重新抬头，因为它的局部动力学，这表明了大型量子系统模拟的显着计算优势的可能性。然而，对玻姆公式的进一步研究表明，量子力学的非定域性并没有消失--它只是被扫到了量子力的地毯下。本文提出了一种新的玻姆力学公式，其中量子作用量S是复的。这导致了一个单一的方程，用于复S，最终是复x和p，但这种复杂化有一个回报--一个显着更高程度的局部化。新方法中的量子力在高斯波包动力学中为零，它对势垒隧穿过程的影响比经典力低几个数量级。我们证明了隧穿概率与精确的量子力学几乎完全一致，最低可达10^{-7}，这些概率是从严格定域的量子轨道计算出来的，这些轨道不与它们的邻居通信。新的公式可能对基础量子力学有重要的影响，从非定域性的解释到量子复杂性的度量。

英文摘要：

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared -- it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification -- a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wavepacket dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10^{-7} calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.

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