{"paper":{"title":"Finite temperature free fermions and the Kardar-Parisi-Zhang equation at finite time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.quant-gas","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"David S. Dean, Gregory Schehr, Pierre Le Doussal, Satya N. Majumdar","submitted_at":"2014-12-04T09:01:07Z","abstract_excerpt":"We consider the system of $N$ one-dimensional free fermions confined by a harmonic well $V(x) = m\\omega^2 {x^2}/{2}$ at finite inverse temperature $\\beta = 1/T$. The average density of fermions $\\rho_N(x,T)$ at position $x$ is derived. For $N \\gg 1$ and $\\beta \\sim {\\cal O}(1/N)$, $\\rho_N(x,T)$ is given by a scaling function interpolating between a Gaussian at high temperature, for $\\beta \\ll 1/N$, and the Wigner semi-circle law at low temperature, for $\\beta \\gg N^{-1}$. In the latter regime, we unveil a scaling limit, for $\\beta {\\hbar \\omega}= b N^{-1/3}$, where the fluctuations close to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1590","kind":"arxiv","version":3},"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"}