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arXiv quant-ph/0412050quant-phphysics.atom-ph
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量子分形的玻姆方法

A Bohmian approach to quantum fractals

A. S. Sanz

摘要:

量子分形是一种波函数,其实部和虚部处处连续,但无处可微。这种可微性的缺乏被用来作为一个论点,否认玻姆力学(和其他基于轨道的方法)在提供量子力学的完整解释方面的普遍有效性。在这里,这一论断是克服了一个正式的扩展Bohmian力学的基础上的限制方法。在这个新的配方中,粒子动力学总是令人满意地描述了一个定义良好的运动方程。特别是在量子分形制导的情况下,相应的轨迹也将是分形的。

英文摘要:

A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and other trajectory--based approaches) in providing a complete interpretation of quantum mechanics. Here, this assertion is overcome by means of a formal extension of Bohmian mechanics based on a limiting approach. Within this novel formulation, the particle dynamics is always satisfactorily described by a well defined equation of motion. In particular, in the case of guidance under quantum fractals, the corresponding trajectories will also be fractal.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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