{"paper":{"title":"Measuring the Hausdorff Dimension of Quantum Mechanical Paths","license":"","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-lat","authors_text":"B. Plache, H. Kroger, K.J.M. Moriarty, S. Lantagne","submitted_at":"1995-01-17T04:06:44Z","abstract_excerpt":"We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$.  We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \\propto \\int dt \\mid \\vec{v} \\mid^{\\alpha}$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\\frac{\\alpha }{\\alpha - 1}$ if $\\alpha > 2$ and $d_{H}=2$ if $\\alpha \\leq 2$. We discuss the relevance of fractal pathes in solid state physics and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/9501018","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"}