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arXiv 0901.1768hep-thgr-qchep-phquant-ph
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广义不确定原理的唯象意义

Phenomenological Implications of the Generalized Uncertainty Principle

Saurya Das, Elias C. Vagenas

摘要:

各种量子引力理论认为,在普朗克尺度附近,海森堡不确定原理应该被所谓的广义不确定原理(GUP)所取代。我们证明了GUP在任何量子力学哈密顿量中都会产生两个附加项,分别与βp^4和β^2 p^6成比例,其中β \sim 1/(M_{Pl} c)^2是GUP参数。这些项在普朗克能量或普朗克能量以上变得重要。仅考虑其中的第一个,并将其作为一个扰动,我们表明,GUP影响的兰姆位移,朗道能级,反射和透射系数的电位阶跃和势垒,以及在扫描隧道显微镜(STM)的电流。虽然这些太小,目前无法测量,但我们推测未来提取可测量预测的可能性。

英文摘要:

Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to βp^4 and β^2 p^6 respectively, where β\sim 1/(M_{Pl}c)^2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these, and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a Scanning Tunnel Microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.

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