| Abstract: | Metastable states and resonance phenomena are compactly described by effective Hamiltonians which are Non-Hermitian (NH). We study issues related to evolution speed of such Hamiltonians. The evolution speed is the rate at which a state evolves to other states (e.g. angular speed on the Bloch sphere). In Hermitian physics this speed is bounded by the energy difference of the instantaneous Hamiltonian. In NH physics, it is easy to find examples where the energy difference completely fails as a bound. We use a generalized Anandan-Aharonov “uncertainty” to derive a simple bound that works for both Hermitian and NH Hamiltonians. Using this new bound we define the notion of speed efficiency and show that for any quantum evolution it is always possible to construct Hamiltonians which are 100% efficient. |
