General conditions for a quantum adiabatic evolution
量子物理
2007-05-23 v1
摘要
The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively valid for scaled timed hamiltonian and resonance processes as well as off resonance possible constructive St\"{u}ckelberg interference effects violate this usual condition for general hamiltionian. More general adiabatic condition and exact bounds for adiabatic quantum evolution are derived and studied in the framework of a two-level system. The usual criterion is restored for real two level hamiltonian with small number of monotonicity changes of the hamiltonian matrix elements and its derivative.
引用
@article{arxiv.quant-ph/0607118,
title = {General conditions for a quantum adiabatic evolution},
author = {Daniel Comparat},
journal= {arXiv preprint arXiv:quant-ph/0607118},
year = {2007}
}
备注
4 pages