{"paper":{"title":"Nonlinear QM as a fractal Brownian motion with complex diffusion constant","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Boris Rodriguez, Carlos Castro, Jorge Mahecha","submitted_at":"2002-02-05T03:09:45Z","abstract_excerpt":"A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the free particle case. The hydro-dynamical model analog yields another (new) nonlinear QM wave equation with physically meaningful soliton solutions. One remarkable feature of this nonlinear Schroedinger equation based on a fractal Brownian motion model, over all the other nonlinear QM models, is that the quantum-mechanical energy functional coincides with the fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0202026","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}