On Hamiltonians Generating Optimal-Speed Evolutions
arXiv:0804.4755 · doi:10.1103/PhysRevA.79.014101
Abstract
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.
Published version
References in corpus (4)
- Faster than Hermitian Quantum Mechanics
- Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
- The quantum brachistochrone problem for non-Hermitian Hamiltonians
- Physical Meaning of Hermiticity and Shortcomings of the Composite (Hermitian + non-Hermitian) Quantum Theory of Gunther and Samsonov