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二维玻姆系统中的不稳定点、遍历性与玻恩定则

Unstable Points, Ergodicity and Born's Rule in 2d Bohmian Systems.

作者信息

Tzemos Athanasios C, Contopoulos George

机构信息

Research Center for Astronomy and Applied Mathematics of the Academy of Athens, Soranou Efessiou 4, GR-11527 Athens, Greece.

出版信息

Entropy (Basel). 2023 Jul 20;25(7):1089. doi: 10.3390/e25071089.

DOI:10.3390/e25071089
PMID:37510036
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10379029/
Abstract

We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of the moving nodal points, in cases with 1, 2 and multiple nodal points. Then, we find the contributions of the ordered and chaotic trajectories in the Born distribution, and when the latter is accessible by an initial particle distribution which does not satisfy Born's rule.

摘要

我们研究了由两个非相互作用的谐振子组成的二维系统在玻姆流中不稳定点的作用。特别地，我们研究了在惯性参考系以及移动节点参考系中的不稳定点，包括具有1个、2个和多个节点的情况。然后，我们在玻恩分布中找到了有序和混沌轨迹的贡献，以及当初始粒子分布不满足玻恩规则时后者是否可及的情况。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/64b4c591ba5e/entropy-25-01089-g017.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/b22b94ecfc26/entropy-25-01089-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/df0170ddca6b/entropy-25-01089-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/234951bef97b/entropy-25-01089-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/4601068ea849/entropy-25-01089-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/aed9c62fbb11/entropy-25-01089-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/00fe66702cf4/entropy-25-01089-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/8fa3b20d5c54/entropy-25-01089-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/00e602c2b84f/entropy-25-01089-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/da76fa9913d6/entropy-25-01089-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/e616c3136b88/entropy-25-01089-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/145d71853988/entropy-25-01089-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/de25c40b8c31/entropy-25-01089-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/c9b6ee514e73/entropy-25-01089-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/a943cc5f7926/entropy-25-01089-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/ed0f73645ffd/entropy-25-01089-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/59c933c11fab/entropy-25-01089-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/64b4c591ba5e/entropy-25-01089-g017.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/b22b94ecfc26/entropy-25-01089-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/df0170ddca6b/entropy-25-01089-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/234951bef97b/entropy-25-01089-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/4601068ea849/entropy-25-01089-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/aed9c62fbb11/entropy-25-01089-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/00fe66702cf4/entropy-25-01089-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/8fa3b20d5c54/entropy-25-01089-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/00e602c2b84f/entropy-25-01089-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/da76fa9913d6/entropy-25-01089-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/e616c3136b88/entropy-25-01089-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/145d71853988/entropy-25-01089-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/de25c40b8c31/entropy-25-01089-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/c9b6ee514e73/entropy-25-01089-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/a943cc5f7926/entropy-25-01089-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/ed0f73645ffd/entropy-25-01089-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/59c933c11fab/entropy-25-01089-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9d50/10379029/64b4c591ba5e/entropy-25-01089-g017.jpg

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本文引用的文献

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2
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Phys Rev E. 2020 Oct;102(4-1):042205. doi: 10.1103/PhysRevE.102.042205.
3
Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory.三维量子涡旋附近混沌的起源：一种广义的玻姆理论。
Phys Rev E. 2018 Apr;97(4-1):042201. doi: 10.1103/PhysRevE.97.042201.
4
Origin of chaos near critical points of quantum flow.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Mar;79(3 Pt 2):036203. doi: 10.1103/PhysRevE.79.036203. Epub 2009 Mar 16.