{"paper":{"title":"Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Carl M. Bender, Dorje C. Brody","submitted_at":"2008-08-13T12:51:58Z","abstract_excerpt":"Consider the set of all Hamiltonians whose largest and smallest energy eigenvalues, E_max and E_min, differ by a fixed energy \\omega. Given two quantum states, an initial state |\\psi_I> and a final state |\\psi_F>, there exist many Hamiltonians H belonging to this set under which |\\psi_I> evolves in time into |\\psi_F>. Which Hamiltonian transforms the initial state to the final state in the least possible time \\tau? For Hermitian Hamiltonians, $\\tau$ has a nonzero lower bound. However, among complex non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, \\tau can be made "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1823","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"}