2010/06/30 by Nicola Cufaro Petroni · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Law #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Schrödinger equation #Sign (mathematics) #Unitary state #Variable (mathematics) #Wave packet #cond-mat.stat-mech #math.PR #msc:60G51 #msc:81P20 #quant-ph
paper · pdf · doi:10.1088/1751-8113/44/16/165305
published as J. Phys. A 44 (2011) 165305 · 41 pages, 13 figures; paper substantially shortened, while keeping intact examples and results; changed format from "report" to "article"; eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old numbers) from text to Appendices C, D (new names); introduced connection between Relativistic q.m. laws and Generalized Hyperbolic laws
arxiv created 2010/08/24 · openalex publication_date 2011/03/28 · arxiv updated 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the time-dependent solutions of the pseudo-differential Lévy–Schrödinger wave equation in the free case, and compare them with the associated Lévy processes. We list the principal laws used to describe the time evolutions of both the Lévy process densities and the Lévy–Schrödinger wave packets. To have self-adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible Lévy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the Lévy–Schrödinger wave packets, and in particular of the multimodality arising in their evolutions: a feature at variance with the typical diffusive unimodality of both the corresponding Lévy process densities and usual Schrödinger wavefunctions.