科研之友
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摘要
Manifestations of space fractional quantum mechanics (SFQM), as it was formulated by Laskin [Phys. Rev. E 62, 3135 (2000)], are deemed to offer a better physical interpretation of Levy flight statistics on a quantum mechanical level. We start with the SFQM Schrodinger equation characterized by a Levy flight index alpha is an element of (1,2), perform a Wigner transform, and draw the limit (h) over bar /E tau -> 0 (i.e., let the observed energy scale E go to infinity in comparison to the quantization given by (h) over bar/tau). In order to obtain classical transport equations two possible substitutions for the terms vertical bar p vertical bar alpha and vertical bar p'vertical bar alpha which appear in von Neumann's equation are presented. It is demonstrated that they conform to the criteria for a successful Wigner transform. Their benefits and caveats are discussed in detail. We find, that, indeed, SFQM manifests itself in an anomalous kinetic term of the free particle's motion and, assuming an external potential diagonal in momentum space for the sake of simplicity, in corresponding anomalous terms in the resulting drift current. All our results reduce to the classical forms in the limit alpha = 2.
- 出版日期2011-12-15
