Anomalous paths in quantum mechanical path-integrals

作者：Grimsmo Arne L; Klauder John R; Skagerstam Bo Sture K^*

来源：Physics Letters B, 2013, 727(1-3): 330-335.

DOI：10.1016/j.physletb.2013.10.044

We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the naive continuum limit but which, nevertheless, induce non-trivial effects due to quantum fluctuations. These effects are seen to modify the geometry of the paths contributing to the path-integral describing the time evolution of the particle, which we investigate through numerical simulations. In particular, we demonstrate the existence of a modified lattice action resulting in paths with any fractal dimension, d(f), between one and two. We argue that d(f) = 2 is a critical value, and we exhibit a type of lattice modification where the fluctuations in the position of the particle becomes independent of the time step, in which case the paths are interpreted as superdiffusive Levy flights. We also consider the jaggedness of the paths, and show that this gives an independent classification of lattice theories.

• 出版日期2013-11
• 单位中国科学院理论物理研究所