2008/04/30 by Ali Mostafazadeh
Mathematics · Physics and Astronomy · #Classical mechanics #Hamiltonian (control theory) #Hermitian matrix #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Theoretical physics #Time evolution #Topological Materials and Phenomena #Unitary matrix #Unitary state #Universality (dynamical systems) #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1103/physreva.79.014101
published as Phys. Rev. A 79, 014101 (2009) · Published version
openalex publication_date 2009/01/06 · arxiv created 2009/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric (inner product) dependence of the lower bound on the travel time and the universality (metric independence) of the upper bound on the speed of unitary evolutions.