dorsal/arxiv
View SchemaBohmian Mechanics with Complex Action: A New Trajectory-Based Formulation of Quantum Mechanics
| Authors | Yair Goldfarb, Ilan Degani, David J. Tannor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604150 |
| URL | https://arxiv.org/abs/quant-ph/0604150 |
| DOI | 10.1063/1.2798762 |
Abstract
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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"abstract": "In recent years there has been a resurgence of interest in Bohmian mechanics\nas a numerical tool because of its local dynamics, which suggest the\npossibility of significant computational advantages for the simulation of large\nquantum systems. However, closer inspection of the Bohmian formulation reveals\nthat the nonlocality of quantum mechanics has not disappeared -- it has simply\nbeen swept under the rug into the quantum force. In this paper we present a new\nformulation of Bohmian mechanics in which the quantum action, S, is taken to be\ncomplex. This leads to a single equation for complex S, and ultimately complex\nx and p but there is a reward for this complexification -- a significantly\nhigher degree of localization. The quantum force in the new approach vanishes\nfor Gaussian wavepacket dynamics, and its effect on barrier tunneling processes\nis orders of magnitude lower than that of the classical force. We demonstrate\ntunneling probabilities that are in virtually perfect agreement with the exact\nquantum mechanics down to 10^{-7} calculated from strictly localized quantum\ntrajectories that do not communicate with their neighbors. The new formulation\nmay have significant implications for fundamental quantum mechanics, ranging\nfrom the interpretation of non-locality to measures of quantum complexity.",
"arxiv_id": "quant-ph/0604150",
"authors": [
"Yair Goldfarb",
"Ilan Degani",
"David J. Tannor"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2798762",
"title": "Bohmian Mechanics with Complex Action: A New Trajectory-Based Formulation of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0604150"
},
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