Anomalous Paths in Quantum Mechanical Path-Integrals
Journal article, Peer reviewed
Published version
Permanent lenke
http://hdl.handle.net/11250/2624781Utgivelsesdato
2013Metadata
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- Institutt for fysikk [2790]
- Publikasjoner fra CRIStin - NTNU [39811]
Sammendrag
We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the naïve continuum limit but which, nevertheless, induce nontrivial 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 Lévy flights. We also consider the jaggedness of the paths, and show that this gives an independent classification of lattice theories